#Logarithm tricks

[diz-eaze]

having albedo and scaramouche as both your roommates—ohh…damn. double whammy…

like yeah, if you think scaramouche’s picture taking habits are bad, take a look at this guy *thumb pointing at albedo* this guy is NUTS!!! i know he’s probably broken a camera or two because of that. and on a freak-off scale between the two, i’d wager money on albedo breaking that scale in full. sure, both are weird and creepy, but it’s always the calm and stoic ones that got the craziest unimaginable tricks up their sleeves. and tbf scaramouche isn’t completely overt about his interests and motives, but he’s a little more pathetic about it bc he’s prone to accidentally exposing himself if he ever fucks up. not albedo though. he’s too perfect. too pristine. and he has that same cleanliness and smile as to idk hannibal. albedo is perfect premeditated. scaramouche is just a hot mess with a wetter dick.

also kabukimono scaramouche 💆‍♀️💆‍♀️ i like to imagine that it’s some kind of childhood friends/crushes (possibility one sided), who got separated because one or the other moves somewhere, then reunited only to figure out that little boy you used to hang out with is now all grown up and completely different than what you remember. but he still likes you. but he reallllyyy likes you this time around. and might have been following you around all these years oh well

or kabukimono > scaramouche pipeline might have had happened after an intense breakup and he crashed out and did an entire personality 180. scaramouche has phoenixed into a bitter ex-boyfriend. his mom thinks it’s a phase like most kids this days, but oh boy this little guy truly means it this time

running laps around this ask because you get me so bad,,, you get me !!

yandere albedo is so delicious because it's impossible for him to get outed as a freak !! his countermeasures against being found out are too high; too elaborate. and also... it's speculated by the traveler in the paralogism quest that albedo would never be put on trial for murder because if he did commit the crime, he'd never be found out because he's just too good, thus never being suspected in the first place LMFAOOOO. his reputation and personality in general causes people to think of him being a freak to be like,,,, an impossible concept. fanfiction levels of OOC for them, if you will. but if they had mind-reading powers, then they'd see the degeneracy that plagues albedo's thoughts 24/7 :(((

random npc: wow, mister albedo looks so serious! :0 i wonder what he's thinking about! albedo, thinking about (y/n): no lube, no protection, all night, all day, from the kitchen floor to the toilet seat, from the dining table to the bedroom, from the bathroom sink to the shower, from the front porch to the balcony, vertically, horizontally, quadratic, exponent al, logarithmic, while i gasp for air, scream and see the light, missionary, cowgirl, reverse cow girl, doggy, backwards, forwards, sideways, upside down, on the floor, in the bed, on the couch, on a chair, being carried against the wall, outsid-

whereas scara, specifically modern au roomie, is the ultimate boyfailure who's just too unhinged and much of a gooner to keep all his freakyness to himself. it's quite impossible for him to function as a normal human being whenever your in the vicinity, in fact, just a simple whiff of your scent is enough to have his pants tightening :(( what more if you willingly speak to him, or accidentally... touch him !? he's so obvious to the point where even you get the hint a month or two in him being your roommate. though you mistake his infatuation as a simple crush instead of what it actually is: a maddening obsession.

and childhood friend scara is such a cute concept,,, he's literally been in love with you since the age where you could only waddle around, and he's never stopped being in love with you even after all this time... despite the distance and unfamiliarity. and while his version of love is a tad bit too intense for normal human comprehension, it's very much real and genuine :((((

[dialalagirl]

I can't decide if logarithms are reiji or shu

easy. reiji

is this a trick question?

[oliviabutsmart]

Physics Friday #14: Sound (Part 2/2)

Preamble: Let's get straight into it

Education Level: Primary School (Y5/6)

Topic: Sonic Physics (Mechanics)

The previous part 1 of my sound post is here.

Pitch and Frequency

Pitch and frequency are related to eachother, the only difference being that frequency is a physical interpretation of sound and pitch is our own mental interpretation of it.

But what exactly is frequency?

Go back to last time's example of a tick sound occurring at regular intervals ... because this sound is repeating, we can describe it's behaviour by measuring mathematical properites:

How much time passes in-between each tick (Period)

How many ticks occur every second (Frequency)

These two ideas are related to eachother, in fact Frequency is 1/Period. If you have a tick every half-second, then you can say the tick occurs twice every second.

We measure sound in Hertz, which is effectively a measure of ticks per second.

Most sounds, however, don't work this way, with repeated ticks. They act as proper waves. With zones of high pressure (peaks), and low pressure (troughs). This is where we have to introduce another variable into our equation:

The physical difference separating each peak (Wavelength)

Since these waves travel forward in the air, a detector (like our ears) will pick up the peaks and troughs as they reach our ear. We can measure frequency or period by recording the speed at which our peaks reach our ear.

But we also can relate frequency to wavelength. After all, the further apart the waves are separated, the more time it'll take for a peak to reach us after the previous one.

We quantify this relationship using c = fλ. Where c is the speed of the wave, f is the frequency, and λ is the wavelength.

Notice that we can also say cT = λ, where T is the period. This demonstrates that the physical wavelength is proportional to the amount of time between each peak.

So where does pitch come in?

As mentioned in part 1, if we continue to decrease the time between each tick, or increase the frequency, at some point we'll begin to hear a sound.

This is our brain playing a trick on us. It's like frames-per-second but for our ears. Below some fps threshold, we can see the individual pictures of a video, but above the threshold, it looks like a continuous film. Notice that fps is also another form of frequency.

When we reach this level, our brain can't distinguish between each tick and sees it as one sound. We begin to hear our first sound.

At this point, frequency becomes tied to pitch. The more rapid the ticking becomes, the higher of a pitch we hear. This is a choice that our brain makes - it's purely psychological.

Mixing different pitches

Combining different pitches allows us to create a foundation for music. In western music, our source of harmonics comes from Pythagoras, who kinda fucked it up by not using irrational numbers.

An octave is defined as a higher sound that has twice the frequency of the lower sound i.e. a ratio of 2:1. One octave above middle C (at about 262 Hz) gives us C5 (at about 524 Hz).

We can create further subdivisions like a perfect fifth, where frequencies form a 3:2 ratio. Or a perfect fourth, which has a ratio of 4:3.

Volume, Intensity, and the Inverse Square Law

Volume is directly related to the amplitude of a sound wave. Effectively, how strongly is the air being compressed at each peak?

Again, volume is just another psychological interpretation of a physical phenomena. Similar to how our eyes see brightness.

Amplitude isn't just interpreted as volume, it is also the power that the sound waves carry. Smaller amplitudes correspond to less energy contained within the moving particles.

We measure intensity logarithmically, because that's what our ears here. Effectively a wave sounds twice as loud only if the wave is 100 times as amplified. It's a similar effect to pitch, where we multiply frequencies instead of adding them.

That's where the decibel scale comes in. 1 dB = a 10x increase in the sound's power output. The decibel scale is used generally for a lot of measurements of wave/power intensity. However it just so happens that our ears behave in very similar ways.

Image credit: soundear.com

Notice that louder sounds are more likely to damage our ear. That's because when loud sounds reach our ear, it causes the inner components to vibrate. This vibration amplitude generally is proportional to the amplitude of the waves.

Too loud of a sound means that our eardrums are vibrating with too great of a physical movement. This can create tears in tissue that damage our ears' sensitivity to sound.

Sound looses power over distance

If you stand far away enough from a sound source, it sounds fainter, eventually becoming unhearable.

This is because of the inverse square law. As sound spreads out over distance, it has to emanate in the form of a sphere, going outward in every direction, in order to maintain consistency of direction.

The same amount of power gets spread thinner and thinner over the bubble that it creates. The surface area of a sphere increases to the square of it's radius.

Image Credit: Wikipedia

Thus we get a decrease in volume over time.

What the Actual Fuck is Timbre, and how do you pronounce it? (also Texture too)

Unfortunately I still don't know how to pronounce it.

Timbre is defined as the quality and the colour of the sound we hear. It also includes the texture of the sound. It's sort of the catch-all for every other phenomena of sound.

Timbre is a bit more complex of a phenomena. In that, it combines basically everything else we know about how we hear sound. So I'll go one by one and explain each component of what makes Timbre Timbre.

Interference

Wave interference is an important property that needs to be understood before we actually talk about timbre. Sound waves often can overlap eachother in physical space, normally caused by multiple sound sources being produced at different locations.

These sound sources often will create new shapes in their waveform, via interference.

Constructive interference is when the high-pressure zones of two sound waves combine to produce an even-higher-pressure zone of wave. Effectively pressure gradient add onto eachother.

Destructive interference is when a high-pressure zone overlaps with a low-pressure zone, causing the pressure to average out to baseline, or something close to the baseline.

Image Credit: Arbor Scientific (Youtube)

We can look at multiple waves acting continuously over a medium to see how their amplitudes will add up together using interference. This is the origin of more unique wave patterns.

The shape of a wave

Sound waves can come in different varieties. While the most basic shape is the sine wave. We can add different intensities, frequencies and phases of sine waves to produce more complex patterns.

I won't go into how this combination works because that's better left for a Fourier series topic. Just know that pretty much any sound can be broken down into a series of sine waves.

These patterns have a different texture, as they combine multiple different monotone sounds. Take a listen to a sawtooth wave vs a sine wave:

Warning: the sawtooth wave will sound a lot louder than the sine wave.

This gives us a different sound texture.

Resonance

When you play a musical instrument at a particular frequency, the instrument is often resonating.

Say you produce sound within an enclosed box. Producing it at one end. Eventually the sound will reach the end of the box and bounce back from reflection (as we'll see later).

The sound will bounce back and forth, combining itself with the previous waves to produce more and more complex waveforms.

But there is a particular frequency, at which, the waves will perfectly interfere with eachother to produce what's known as a standing wave.

A standing wave will oscillate, but it will appear as if it's not moving forward. Of course, power is still moving throughout the wave, as we'll still be able to hear something.

This standing wave can only occur at a particular frequency, one in which the wave perfectly interferes with it's reflection within the box.

A standing wave (black) that is produced by two sine waves (blue and red) moving in opposite directions Image source: Wikipedia

This frequency is called the resonant frequency of the box. This frequency depends on several factors like the speed of the wave, the material inside the box, the shape of the box, and the length of the box.

The resonant frequency can be activated by our voices, as our voices or just blowing air is already a combination of different sound frequencies. The non-resonant frequencies will eventually loose all of their power as they destructively interfere, leaving only the resonant frequency, which gets amplified by what we put in

For example, you can fill a glass bottle halfway with some water, blow in it, and it will produce a particular sound. Fill it with more water, and the pitch increases - i.e. by adding the water we increase the resonant frequency.

All instruments have one or more resonant frequencies based on their material and shape (I say multiple because some instruments can me modelled as multiple boxes. Like a violin will have the inside of the wood, the wood itself, the strings, etc.).

Instruments also allow us to alter the resonant frequency by playing it differently (like putting a finger over your recorder's hole (phrasing)).

These differences in how we obtain resonance can also affect the quality of the sound.

Overtones

Resonance is not just generated with a single resonant frequency, we can create resonance with higher multiples of the the same fundamental frequency.

This is because in our box model, multiplying the fundamental frequency will allow us to create a standing wave, just with a shorter wavelength:

The A's stand for antinodes, which vibrate in the standing wave with the maximum amplitude. The N's stand for nodes, which do not move at all.

Image Credit: Macquarie University

Direct multiples of the fundamental frequency are called harmonics. Instruments can also produce other frequencies not directly harmonic depending on the structure of the 'box' they utilise.

These additional frequencies, ones which come often in fractional multiples of the fundamental are called partials. Both partials and harmonics represent the overtones of an instrument.

Overtones are what give sound additional character, as they allow instruments to not just resonate at the note they play, but at other combined frequencies. In some instruments, the overtones dominate over the fundamental - creating instruments that can play at much higher pitches.

Envelopes and Beats

Say we add two sine waves together (red and blue), each with slightly different frequencies, what we get is this:

Image Credit: HyperPhysics Concepts

We can see that the brown wave has a singular oscillation frequency, but also it's amplitude continuously scales with reference to this hidden envelope frequency, called the beat frequency (dotted line).

This difference between the actual wave's real frequency and the wave's overall frequency envelope. Is another source of timbre.

Notes, and the way we play them will often generate unique and different envelopes depending on how they are played. For example a staccato quarter-note will have a different envelope to a softly played quarter-note.

Other properties of Sound

Reflection

Different mediums mean different speeds of sounds e.g. molecules in wood (solid) are harder to move than molecules in air (gas).

These different speeds create several effects. Including the reflection of waves. Often waves require a bit of power in order to physically overcome the resistances to vibration of a particular medium.

Often this leads to sound waves bouncing back off harder-to-traverse surfaces.

Say that a sound wave travels through the air and reaches a wooden wall. The atoms vibrating in the air will hit against the wooden wall, transferring only some of their energy to the resistant wood.

The wood atoms on the border of the wall will bounce back, as expected. But this time they will transfer energy back into the air at a much greater magnitude due to newton's third law.

Thus while some of the sound wave ends up going deeper into the wood, the wood will push back and cause the air to vibrate in the opposite direction, creating a reflected wave.

Image credit: Penn State

We characterise the amount of power being reflected versus transmitted versus absorbed using portions:

A + R + T = 1

A = Power absorbed into the material (e.g. warms up the material)

R = Power reflected back

T = Power transmitted into the new medium

This is both an explainer as to why rooms are both very good, and very bad at keeping sound inside them. It really depends on the rigidity and shape of the material they are bordered by.

Refraction

Just like light, sound waves can also refract. Refraction is actually a lot simpler to understand once you already realise that waves will both reflect and transmit across medium changes.

Refraction is just combining the results of incomplete reflection (i.e. transmission) with some angle.

I won't go into refraction in too much detail, as it's worth a different topic. But effectively we experience snell's law but modified for sound.

Diffraction

Sound waves, like all waves propagate spherically (or circularly in 2D).

When travelling around corners, sound can often appear louder than if you were further away, looking at the source more directly.

This is because spherical waves will often 'curve' around corners. This is better described by light diffraction. Which is something for another time.

Conclusion

In conclusion, that's how sound works, mostly. This is a topic that is a little less closer to my expertise. Mainly because it delves into more musically-inclined phenomena that I am less familiar with. But I'm sure I did a good job.

Unfortunately, it seems like the plague of the long post is not yet over. Perhaps I need to get into a lot more specific topics to make things better for me and you (the reader).

Anyways, my exams are done. I am done. I do not have to do school anymore. Until I remember to have to get ready for my honours year (a.k.a. a mini-masters degree tacked on after your bachelor's degree).

Until next time, feel free to gib feedback. It's always appreciated. Follow if you wanna see this stuff weekly.

Cya next week where I will probably try another astronomy topic, or something like that.

[geniustut]

Are you preparing for the CAT exam but running out of time? If so, don’t worry! With the right rapid revision techniques, you can boost your CAT score even in the last few weeks. In this article, we will discuss effective strategies to help you revise efficiently, improve accuracy, and maximize your score.

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Why is Rapid Revision Important for CAT?

The Common Admission Test (CAT) is one of the toughest MBA entrance exams. It tests your Quantitative Aptitude (QA), Verbal Ability & Reading Comprehension (VARC), and Data Interpretation & Logical Reasoning (DILR). Given the vast syllabus, smart revision is essential to retain concepts and improve problem-solving speed.

A well-planned revision strategy can help you:

Strengthen weak areas Improve speed and accuracy Boost confidence before the exam Reduce last-minute stress

With limited time left, focusing on effective techniques will make a significant difference.

Top CAT Rapid Revision Techniques

1. Focus on High-Weightage Topics

Not all topics carry the same weight in CAT. Therefore, prioritizing important topics will maximize your score.

Quantitative Aptitude (QA): Arithmetic, Algebra, Geometry, Number System DILR: Logical Puzzles, Tables & Graphs, Seating Arrangement VARC: Reading Comprehension, Para Jumbles, Critical Reasoning

By concentrating on these areas, you can improve accuracy and solve more questions within a shorter time.

2. Revise Shortcut Tricks & Formulae

Rather than solving new questions, focus on shortcut tricks and formulas for quick problem-solving.

Keep a formula sheet for:

Time & Work Percentages & Profit-Loss Permutation & Combination Logarithms & Surds

Tip: Solve at least 10–15 questions from each topic to reinforce concepts.

3. Take Timed Mock Tests

Mock tests are an excellent way to simulate real exam conditions. Practicing full-length and sectional mocks will: Improve time management Identify weak areas Enhance exam confidence

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4. Analyze Previous Mock Tests

Instead of only taking new mocks, reviewing past tests is equally important. It helps you: Recognize patterns in mistakes Identify topics that need improvement Learn from errors and avoid repeating them

Pro Tip: Maintain a mistake logbook to track and revise tricky questions efficiently.

5. Practice Question Selection Strategy

Managing time effectively in CAT is crucial. A structured three-round approach can help you decide which questions to attempt first.

1 Easy Questions (Solve first) — Secure quick marks 2 Moderate Questions (Attempt next) — Solve if time allows 3 Difficult Questions (Skip if needed) — Avoid time-consuming problems

This strategy will maximize accuracy and overall score.

6. Improve Reading Speed for VARC

The VARC section consists of RC passages that require fast reading and comprehension skills.

Practice speed reading techniquesSummarize articles in one sentenceSolve 3–4 RC passages daily

By improving reading speed, you can attempt more questions with accuracy and boost your verbal score.

7. Stay Calm & Avoid Last-Minute Cramming

Last-minute preparation should focus on light revision rather than cramming new concepts.

Avoid learning new topics Revise important formulas and strategies Get proper sleep before the exam

A fresh mind is your biggest asset on exam day!

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Originally published at https://www.geniustut.com on March 11, 2025.

[selkiette]

29.09.24

forgot to update my blog

barely studied because i was feeling so shit

today i made progress through unit 2 of my compsci module - binary conversion, boolean values, logarithmic scale, bytes, moore's law

i am comfortable enough with the process of converting binary into decimal numbers however i dont think it will be something i generally will be using like... ever, so i guess i can use it as a cool party trick to seem super mega smart :D

i need to finish unit 2 before october 4th so i can immediately work on my assignment once it becomes available. once thats finished i can put my focus into completing the statistics paper.

i want a mimo pro subscription so i can continue working on my cooooooooding, ive found that its the easiest way for me to understand python but its actually unbearable with the free version lol. but very mindful and demure of me to learn the difference between wanting something and needing something, so it isnt urgent and can wait (i also cant afford it rn so theres that lmao)

tomorrow im aiming to study for 6 hours. i also have to fit a 20 min pilates workout into there at some point..

[math-journal]

Algebra 1 — here — Next

Intermediate Algebra

Cheat Sheet

Rational Expression Properties, Exponential Properties, Radical and Fractional Properties, Complex Numbers, Quadratic Equations, Function Operations, Exponential and Logarithmic Functions, Parental Functions

UNIT 1

Functions

Introduction

Vertical Line Test

Translating Function aka shifting

Domain / Range

Interval Notation

Radicals

Basic

Simplify / Multiply

Addition/Subtraction

Foil/Factor Solving

F*ck off

Imaginary

Imaginary/Complex Numbers

Solving with Imaginary Numbers

Problem #1

Problem #2

Note: sometimes I write side-to-side rather than up-and-down while solving certain questions for ease. By math conventions, this is frowned upon. Stick to vertical orientation

Unit 1 REVIEW

.

Unit 2

Factoring Trinomial (R)

Sum of Square - Difference of Square (R)

2nd Degree Trinomial

3rd Degree Trinomial

Completing the Square

Quadratic Formula

Quadratic Function (parabola)

Flipping shortcut

Graphing Quadratic Functions

Standard to Vertex Form

Overview

Unit 2 Review

.

Unit 3

Decay and Growth Functions

Intro to Log + Properties

Common & Natural Log

Application Problems

More examples

3 Ways Solve Logs

Say Shit Outloud

Complicated Log / In

Log Property Cheat Sheet

Log Application Prob

Log Tricks

Domain/Range Fraction F(x)

Restrictions

Fractions + Restrictions

More Application

Canceling Review

Unit 3 Review

.

Unit 4

Review

Function Operations

.

[yashkhanna2042-blog]

How Optimizing Individual Pages Helps Rank Your Website

How Optimizing Individual Pages Helps Rank Your Website

                Digital Marketing is at its all-time boom right now. There are so many different aspects of digital marketing like SEO (Search Engine Optimization), SEM (Search Engine Marketing), SMM (Social Media Marketing), Digital Advertising, Online PR, Content Writing, and so many more. In the midst of all of these different emerging concepts, we often forget that the base of a website or online business is the webpage. And if we are starting small, at the beginning, it isn’t that difficult to come up at the top.

                So here is a guide on how to optimize individual pages in order to improve the rank of your website.

What Do You Mean By Page Optimization?

                Page Optimization also known as On-Page SEO, refers to all the efforts taken on the website itself, to help rank the website. To optimize a page there are several things that need to be taken into consideration. This includes the content, the keywords, the title tags and description, the accessibility and speed of the server, the different media that is put on the page, etc.

Why Do I Need To Optimize Individual Pages On My Website?

                If every single page of your website is optimized, it increases your page authority. A higher page authority generally leads to a greater Domain Authority and a high domain authority means better rank on the SERP (Search Engine Result Page).

                Why do you need to rank high you ask? Well because there are so many websites out there. For a single question, google shows you hundreds of results, and people don’t scroll through so many results, they simply click on the first few, and that’s it.

                Having a higher rank means that when a query is searched on Google, your website appears in the top results, increasing your CTR (Click Through Rate), and generating greater traffic on your website.

What Is PA (Page Authority)?

                The Page Authority or PA in SEO is the value that is assigned to the page. This value shows how good and trustworthy the page is. The higher the PA the easier it is to rank the page in the SERP. The value of the page is assigned out of 100 points. There is no absolute “Good” P. Your goal should just be to have a higher PA than that of your competitors.

How Does PA Help Increase Website Rank?

                Having a higher PA indicates that your web page is trusted by Google itself. It is proof that the information you provide is true and trustworthy.

                Page authority is scored on a logarithmic scale which makes it difficult to improve your score. All new pages start at a score of 1 and then move forward towards 100. The PA score relies heavily on backlinking and internal linking., while the DA (Domain Authority) Score depends on keywords, as well as backlinking. There are several websites out there which help you calculate and check your DA PA score for free.

How To Improve Website Rank Using PA?

                As discussed earlier, to improve the overall rank of your website, you need to start by optimizing individual pages. Although it may be a lengthy process to sit and optimize every single page, it is highly recommended and helpful in the long run. So here are a few tricks to help you learn how to optimize your website pages.

1.      How To Improve Your Site Ranking By Improving The Relevance Of Your Content

The content you put on your page matters. If you have relevant and reliable content, users will want to refer to your page for their queries. This builds trust in the user. If a user likes your content, they will want to refer to your content again and again, hence increasing your traffic.

2.      How To Improve Your Site Ranking By Improving Backlinks

The higher the backlinks the greater your PA score. And the greater your PA score, the higher your rank on the SERP. But just having 10,000 backlinks isn’t enough. These backlinks need to be created across different platforms and servers for better results.

3.      How To Improve Your Site Ranking By Improving The Quality Of Your Links

Just having a higher number of backlinks is not enough. The quality of these links also matters. The quality of your links depends on the DA PA score of the website that the backlink is on. The higher the DA PA Score of that website, the better the quality of your backlink. This means that you can’t just create a dummy website and then create thousands of backlinks through that.

4.      How To Improve Your Site Ranking By Improving and Optimizing Keywords

Your keywords are what will lead the traffic to your website through the SERP. If those aren’t optimized you will not be able to generate organic traffic through the SERP. Along with the keywords, your heading tags, the meta title and the meta description also influence how many people click on your website.

5.      How To Improve Your Site Ranking By Improving Loading Speed

If a user gets annoyed because of how long it takes to load your website, you risk losing a new customer. Having increased loading time also means that your bounce rate is higher. And this will harm your PA instead of improving it. So, you need to decrease your loading time. If the problem persists, try changing your server.

Conclusion

                In conclusion, everyone has to start somewhere, right? Taking small steps is what will make you good and even great at something. You can’t just become amazing at something without putting in any effort. Similarly, your website needs to start small and take small steps to improve to be able to come to the top.

[iambloop]

Math Doodle #1: Logs, Intuition and Approximations

Shortly after sharing Math Doodle #0, I played around a bit more with the expansion of ln(1+x). In particular, I wanted to see if I could use it to find ln(3) or ln(5) [Spoiler: you can't, but you can]. That lead me to think more generally about logarithms and why my intuition for them is so poor. I consider myself math-savvy, and within the little math I know, I know it fairly well, so I set out to see if I can improve my intuition for calculating logarithms.

I spent considerable time thinking first about those transformations over which I am able to reason intuitively (linear equations, quadratics, squares). My first hunch was that, a prerequisite for this instinct might be convenience: these tend to be continuous monotonic transformations (well, not entirely - but squaring is almost a monotonic transformation, or at least, the change in rate of change is conveniently placed at x = 0).

Logarithms, despite being continuous and monotonic, offer very little in the way of similar intuition. I attempted to tighten the bounds - so if log_2 maps [128, 256) -> [7, 8), can we partition these and come up with maps of finer resolution, without doing a lot of involved calculations? A little bit. {Hint: log_2 maps [128, 128*(2^0.5)) -> [7, 7.5) approximately}, but not too useful.

All of this made me go back to the transformations I considered initially. It made me realize that I am able to claim intuition for those only under very specific conditions - I know how the squaring transformation behaves, but intuition about its behavior does not help me compute large squares, or invert them. So there is, in a way, a difference to note - intuition about the behavior of a transformation, and intuition about the cold hard calculation of a transformation.

Trivia: Interestingly, the history of logarithms shows that the initial motivation for them came from their ability to simplify other arithmetic calculations: multiplying numbers with many digits is quite tedious, and logarithms offered a way out. They did rely on logarithm tables for this, though.

Circling back to the opening of this post, I tried to see if I could use the Taylor expansion of ln(1 + x) derived in Math Doodle #0 to get some bigger logarithms. By direct substitution, that's not possible, and that's quite expected: the series diverges for all |x| > 1 (this condition can be derived from the convergence test for alternating series).

However, I found a neat trick that allows one to use this expansion for an arbitrary positive integer k. Of course, this gets tedious quickly for large values of k, but that it can be expressed so succinctly is still beautiful.

[market-insight-solutions]

Tips and Tricks for Efficient Data Management in SPSS for PhD Students

Data management is a crucial aspect of any research project, especially for PhD students dealing with large datasets. Effective data management ensures that the data is organized, clean, and ready for analysis. SPSS (Statistical Package for the Social Sciences) offers a range of features that can aid PhD students in efficiently managing their data. In this article, we will provide practical tips and tricks for data management in SPSS, covering topics such as data cleaning, transformation, recoding variables, handling missing data, merging datasets, and creating derived variables.

Data Cleaning: Start by thoroughly checking your data for errors, inconsistencies, or outliers. Use SPSS's data view to identify any problematic values or missing data. Remove duplicates, correct errors, and ensure data consistency before proceeding with analysis. SPSS provides tools for data cleaning, such as filtering cases, recoding variables, and identifying outliers, which can help streamline this process.

Data Transformation: Depending on your research requirements, you may need to transform variables to create new measures or scales. SPSS offers functions for mathematical transformations (e.g., logarithmic, square root) and categorical transformations (e.g., creating dummy variables). By transforming variables, you can ensure that your data is in the appropriate format for analysis and better meet the assumptions of statistical tests.

Recoding Variables: Sometimes, it may be necessary to recode variables to simplify data analysis or create meaningful categories. SPSS allows you to recode variables based on specific criteria. For example, you can recode a continuous variable into a categorical variable by grouping values into meaningful ranges. This feature facilitates data reduction and enhances the interpretability of results.

Handling Missing Data: Missing data can be a common issue in research. SPSS provides tools for handling missing data, such as deleting cases with missing values or imputing missing values based on various methods (e.g., mean imputation, regression imputation). It is important to carefully consider the implications of different strategies and choose the most appropriate method for your analysis.

Merging Datasets: In some cases, you may need to merge datasets to combine information from multiple sources. SPSS offers options for merging datasets based on common variables. Ensure that the merge is conducted accurately, maintaining the integrity of the data. Merging datasets can be particularly useful when working with longitudinal data or integrating data from different surveys or studies.

Creating Derived Variables: Derived variables are new variables that are calculated based on existing variables in your dataset. SPSS allows you to create derived variables using formulas and functions. This feature can be handy when computing complex indices, aggregating data, or creating composite scores. Derived variables help simplify analysis and provide more meaningful insights.

Remember, it is essential to document all data management procedures thoroughly. Keep track of any modifications made to the data, including recoding, transformations, and variable creation. This documentation ensures transparency, replicability, and facilitates the interpretation of results.

Efficient data management in SPSS is vital for PhD students dealing with large datasets. By following these tips and tricks, you can ensure that your data is clean, organized, and ready for analysis. SPSS's powerful features for data cleaning, transformation, recoding variables, handling missing data, merging datasets, and creating derived variables simplify the data management process. By effectively managing your data, you can focus on conducting rigorous analysis and deriving meaningful insights to advance your PhD research.

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[sock-to-the-third]

This has taken me soooooo freaking long but it’s so worth it. I’ve been having trouble retaining math more complicated than logarithms so hopefully this will be the trick. Plus, once you have a deep understanding of math it’s like learning a language. Lot of the early hard stuff you forget how to do. So inevitably when you try to teach it makes it more difficult to understand why students don’t understand it.

I’m student myself but I often times end up being the one often explaining it to classmates (Then they remind me about basic arithmetic lol) so I already feel a bit like a teacher.

I think all this prep work will help when I go into tutoring math.

Once I finish making the first version of teachable notes, I plan on organizing it into an abbreviated version for memory retention.

After that, I plan on acquiring more practice problems, then solving them so I have answer sheets and blank sheets. I don’t like not knowing if the answers are right or not with online sources so that will hopefully make it accessible.

Plus math is super relaxing but finnicky. Most of the time I prefer stuff heavy with algebra but sometimes I like the occasional application problem. Ap problems will take longer to put together but it should be fun.

Have to remind myself to make a word doc version of all this so I don’t lose it if tumblr goes kaput.

Formal Review

Precalc 1 — here — Precalc 2

Algebra

Page 1 / Unit 1

[skipped PEMDAS]

Page 2 / Inequalities

Page 5 / Exponents

—-

Page 6

Page 7

Page 8 / Linear

Page 9

Page 10 / Systems of Equation

Page 11

Page 12

Algebra 2

Page 13 / Functions

Page 14

Page 15 / Radicals

Page 16

Page 17

Page 18

Page 19

Page 20 / Imaginary Numbers

Page 21 **

Page 22

Page 23 / Trinomials

[fraction rules]

Page 24

Page 25

Page 26

Page 27 / Logs

Page 28

Page 29

Page 30

Page 31 / [ 1/x ] *here

Page 32

Page 33

Precalc

aapc1u13 - pg34

[allmathtricks]

In this video we know about the following types of examples in logarithms tutorial

·         Logarithm Examples and Answers

·         Find the value of logarithmic expression  

·         Find the value of  log (2a + 3b)

·         Find the value of log 10 15 + log 10 2

·         log x = log 9.6 - log 2.4, then find the value of x

·         Find the value of  Log 625 √125

·         log (x2 - 6x + 6) = 0 , then find the value of  x

[geometropolis]

grt3D episode 12: the logarithm labyrinth

square and droplet were lying on their beds late at night, wide awake. 

“okay, so…” droplet started. “what’s your favorite number?”

“27,” square replied.

“favorite color?”

“gray.”

“favorite song?”

“fallen angle by poison. how about you?”

“well, um… 3, rainbow, and somebody to love by quintuple.”

“i love quintuple!” square exclaimed. “oh, have you listened to their song with data bowie?”

“under pressure? of course!” 

“not to mention other classic bands like fleetwood math, blue öval cult, guns and rulers…”

“i love those! wow, we have a lot in common!” droplet smiled.

“in terms of our music taste, anyway… hey, y’know what else we have in common?

“what?” 

“we’re both pretty darn awesome. we were so on top of today’s challenge.”

“you’re right. i wonder what we’ll do today…”

“nothing a pair of wings can’t help!” droplet’s wings were sitting on one of the empty beds.

“you don’t know that.”

“yeah, no, i don’t.” square sat up. “y’know, if origin already knows every challenge we’re gonna do, i wonder if i can trick him into telling us. so we can prepare ahead of time.”

“i mean we could, in theory. but that wouldn’t be very nice, would it?”

“i guess not…” a pause. “hey, i just realized i’m the only group twoer left. i mean, i knew already that my friends had been eliminated, but darn, they were my whole team then.”

“star and i are the only cool kids. i wonder how he’s doing?”

“you wanna find out?”

“can i?”

square smiled at her. 

the two left the cabin and started walking towards the homeslices’. droplet approached the window and looked through, to see star staring right at her! or… through her?

“aah!” she yelped, falling backwards. 

“golly!” he cried, shaking himself. he left his cabin and joined her outside. “droplet, what in math are you doing here?”

“i wanted to see how you’re doing, that’s all.”

“well i’m doing fine, buddy! bit nervous about tomorrow morning’s elimination, but otherwise, smooth sailing for me.”

“think you might get eliminated?”

“maybe.”

“well, if you do, you’ll get to see heart again!”

star chuckled sadly. “that’s the thing…”

“what?” droplet blinked at him.

“i want to prove to heart that i’ve really changed for the better. i only want to see him once i’m worthy to be his friend again.”

“but you’ve already grown so much, star!”

star smiled. “i know i have. but i want to be even better!”

square was leaning on the side of the cabin. “i think that’s a noble goal,” he said. “good luck with that.”

“hey, you haven’t wanted to win for a while, have you?” star asked.

“nope. i’m glad you two want to, though. hope you don’t get eliminated tomorrow.”

“thanks.” star looked slightly uneasy.

“hey, star,” droplet piped up. “...what’s your favorite song?”

“what makes you beautiful by one dimension. why?”

“noooo!” square cried over-dramatically. “he’s not one of us!”

“next thing we know he’s gonna say he listens to odd sheeran!” droplet chimed in, laughing. “unironically!”

star shook his head affectionately. “good night to neither of you.” and he went back into his cabin.

“i bet everyone else here also has garbage taste in music,” square retorted.

“all the more reason why we’re on the same team…!” droplet giggled.

…

“so, oval… how was your first day of co-hosting?”

“not bad, not bad… well, i guess it was a little rough.”

origin sighed. “yup. that’s just how it is around here… the contestants are always mad about something. and i don’t blame them.”

“neither do i. hey, what’ll we do if möbius never comes back?” oval had a worried expression. “then the winner won’t be able to go to the 3rd dimension… this’ll all be for nothing…”

“there’s nothing i can really do to get in contact with möbius strip, unfortunately.”

“hey, how did you end up working for him anyway? what’s your connection to him?”

“well, hm… möbius strip heard about me from my older sister a while back, and she has basically the same abilities i do. then he used his powers to come here, and he found me, and he told me about this idea he had for a game show. he told me that hey, he could travel between the 2nd and 3rd dimensions, and that it’d be fun if he could have a little competition where a shape could win the ability to go to the 3rd dimension. he just wanted my help with some stuff, and i obliged, as i had nothing better to do.”

“but why you in particular?”

“well, because of my sister he knew about my ability to access the paradox. maybe that’s why?”

“do you not know?”

“no, not really.”

oval was still curious. “how long have you known möbius strip?”

origin paused to think. “well, i–”

“hey guys!” hexagon greeted, hand in hand with octagon. “we’re back to our early morning walks.”

“oh!” oval exclaimed. “good morning, you two!”

“how are you?”

“i’m doing well. hey, glad to see you two cheering up a bit since yesterday morning.”

octagon smiled slightly. “yeah. we’ve had time to process.”

“good thing we did that during the challenge rather than instead of it!” hexagon chuckled.

“yup. we talked afterward too, though.”

hexagon nudged octagon with her elbow. “late into the night…! just like we’re on a sleepover…!”

octagon rolled her eyes but couldn’t stop herself from smiling. “shut up.”

“hey, you think it’s time to wake everyone up?” oval asked origin.

“yeah, um, probably. you wanna do it?”

“sure! i’ll be back in a jiff.” 

as oval left to rouse the other contestants, origin translated over to hexagon and octagon. “so?” he asked eagerly. “what’s up with you two?”

“nothing,” octagon muttered, biting her pacifier. “we’re just…really good friends now. we talk a lot.”

“for hours and hours~!” hexagon said in a dreamy sort of voice. she chuckled. “sorry, it’s just cute when you get flustered.”

“aaugh!! shut up!!!!”

as oval was walking over to the cabins, he spotted something strange behind a bush; he picked it up and tucked it away.

soon enough, he returned to the main field with the other contestants.

“so?” parallelogram asked origin drily. “who’s next on your list?”

origin edged back uncomfortably. “we’ll get to the elimination in a moment. how’s everyone doing?”

“pretty good,” square said. droplet nodded.

“yeah, i’m okay,” star agreed.

“okay, well, yes,” origin continued, “it is time for the elimination.” 

“and the homeslices lost yesterday’s challenge,” oval said. “so one of you will be sent to the paradox.”

“you may take this time to talk.”

parallelogram looked at his teammates. both looked antsy.

“to talk about what?” he asked. “enough with the theatrics, origin. you know who’s being eliminated. just spit it out already…”

origin sighed. “okay… the eliminated contestant is, um… parallelogram.”

“i knew it!” parallelogram cried. “i swear to the primes!”

“i’m really sorry, parallelogram.” origin began to buzz.

heptagon stared up at him with wide, glistening eyes. “parry…”

“take it easy, heptagon,” parallelogram said in a grave voice as he floated towards origin. “and star… figure out what you wanna do, and do it. just make my elimination worth it…”

star nodded silently as origin vanished, parallelogram gone with him.

“okay,” oval went on, “origin told me what today’s challenge is going to be, so i might as well explain it to you all.”

“yeah, go ahead,” square said.

“okay. so just northwest of where we are right now is the logarithm labyrinth.”

“oh, i’ve heard of that place!” hexagon piped up. “it’s this complicated cave system, right?”

“you got it! it’s this system of really intricate caves, like a maze. the challenge will be to get from one end of the tunnels to the other. but what’s important to note is that only one member of your team needs to reach the other side for you to be safe. the last team to have someone get across will be up for elimination.”

“that doesn’t sound too bad,” droplet said. “right?”

origin soon reappeared. “oval, you explained everything?”

“indeed i did!” 

“okay! so i’ll take you all over there. now hold still everyone~!” origin began to buzz again.

“hey, can you not take me?” oval asked. “i just want to walk.”

“oh, okey doke!” the remaining shapes lost their limbs and stuck to origin; together they translated over to the logarithm labyrinth, oval right behind them. 

origin released the contestants, still missing their arms and legs. but before he could use his powers to fix that, a beam of light hit them all. 

“the grapher!” origin gasped, seeing oval holding it proudly. “that’s where that thing went!” 

“i found it by a bush,” oval explained. 

“how about you hold onto it for now? so i don’t lose it again?”

“sounds like a plan!” oval gave him a thumbs up.

“okay, so are we starting?” octagon asked, crowded around the labyrinth entrance with the other contestants who now had their limbs.

“oh, yes! 3… 2… 1… go!”

everyone squeezed through the opening to find a large cavern with many tunnels branching off of it.

“i think we should split up,” square said. “only one of us needs to get to the end, after all.”

“okey doke!” droplet replied. “i’ll see you on the other side!” she popped into one of the tunnels, while square popped into another.

“we should probably do the same,” hexagon told octagon. 

“oh…” octagon frowned. “i thought we’d do it together…”

hexagon paused, then shook herself. “y’know what? yeah. c’mon, octagon!” she grabbed her hand and led her into a tunnel.

star began to go one way, with a sulking heptagon trailing behind him.

“y’know, heptagon,” star piped up, stopping, “we don’t both need to get to the other side. you can just relax if you want.”

“but that’ll lessen your chances of–”

“shshh, i don’t care, dude! i’m still figuring out if i even want to win! just go back and take a nap. that’s the most helpful thing you could do right now.”

star smiled. heptagon’s harshly lined face softened. “...okay. thank you.” with that, heptagon turned back.

“now it’s just you and me, star,” star said to himself. “just you and me…”

droplet was pretty small, so she found it relatively easy to navigate through the tunnels – there were little crevices and narrow shortcuts that few others would likely be able to fit through.

it’s weird going this alone, she thought. it’s for the best of course, but i dunno… it’s weird. hey, what’s that?

she had spotted a crystal poking out of the tunnel’s rocky wall, and marveled at it for a moment.

meanwhile, origin and oval had made their way to the other side of the labyrinth to wait for the contestants as they exited; origin had his camera lens.

suddenly, oval groaned.

“what is it?” origin asked.

“i forgot to tell them all to be careful. sometimes the walls break up and rocks go flying around – i hope none of them get hurt…”

“i’m sure they’ll be fine, don’t worry.”

“you’re probably right…” but oval remained uneasy.

“also, i’m just now realizing that the eliminated contestants won’t be seeing much. it’s not like i can broadcast inside the labyrinth itself…”

hexagon bumped into a wall. “oy vey, a dead end.”

“i guess we should’ve gone right at the fork, not left,” octagon said. “we’ll just retrace our steps.”

“okey doke! you lead the way, octy!” 

the two began to walk in the other direction.

“y’know, octagon…” hexagon said, “sorry for making so many jokes about, um, us being good friends now, and us talking and stuff… you just have such a funny reaction to it!”

“hm.” octagon stopped as they reached the fork in the tunnel, and took the path they previously hadn’t taken. “well, for the record, i’m not actually that bothered by it. i just have to wonder… how is my reaction funny???”

“i dunno, it just is! it’s adorable!” hexagon giggled. “you look away and your face gets all red whenever i so much as mention the fact that we talk…”

“well it’s because you make it sound like it’s a big deal!!! when it isn’t!!!!!” octagon stopped herself and took a breath. “...i just did it again, didn’t i?”

meanwhile, square was traversing the caverns by himself. 

it’s just like the time i was going it alone through the forest for the turf war challenge, he thought grimly. the other three are in the paradox without me… i wonder if they miss me…

he soon found himself at a dead end and shook his head. “how many dead ends has this been? 5? screw this.” he kicked the rocky tunnel wall in frustration.

a distant rumble could be heard…

heptagon had just exited the cave. suddenly, the tunnel walls that had just enclosed him broke up into rocky pieces, blocking the passageway. 

“geez,” he muttered to himself. “i got out just in time.”

hm, he thought. where would it be easiest for me to relax? should i stay here? or go back to the cabins? or go around to where origin and oval are? …i’m overthinking this, aren’t i?

so heptagon simply sat down right by the labyrinth and closed his eyes. 

hexagon and octagon were still chatting as they made their way through.

“guess what!” hexagon exclaimed. 

“what?” octagon responded.

“i heard that droplet won the citywide storytelling contest this past year.”

“oh really? wow.”

“yeah. and kite got first prize in a creative writing competition.”

“have you gotten any awards?”

“well…” hexagon chuckled sheepishly, “maybe a few…”

“wait – you’re the one who won the citywide spelling bee five years in a row! that’s you!”

“the one and only!”

“that’s crazy!” octagon nudged her affectionately. “you’re like a celebrity!”

“hey!”

“when we get back i have to get your autograph.”

“knock it off!” hexagon nudged her back. “i bet you’ve gotten your fair share of achievements yourself.”

“you don’t know that!”

“oh c’mon octagon, you’re a smart cookie!”

“so you’re gonna steal me? you cookie thief?”

the two burst into laughter.

“but really,” hexagon continued. “i bet you got straight As in grade school. gold honor roll. ms. valedictorian herself.”

“yeah, you got me…”

“what was your score on the SAT?”

“1520. why?”

“oh my primes!” hexagon laughed. “you’re insane!”

“no, you’re insane!”

at the same time, star was walking through the tunnels at a casual pace, talking to himself.

“it’s been, like, a week since heart was eliminated. that’s crazy, man! hey, this place looks familiar…”

he found himself in a large cavern.

“i’m right back at the beginning, aren’t i!” he exclaimed. “lol, oh well…”

star began to pace back and forth in the empty space before him, thinking to himself.

i only really signed up for this whole thing so i could hang out with him, he pondered, so i could hang out with this IDEA of him. i had just attached myself so strongly to the idea of a perfectly happy, carefree heart… when that isn’t real. there’s no perfectly happy, carefree star either. 

“what am i doing with myself now?” he said aloud. “i don’t know if heart and i will be friends after this… but that shouldn’t be all i’m thinking of. i need to do something with myself.”

he looked toward one of the tunnels.

“i need to win.”

droplet had found a multitude of crystals in the labyrinth walls. and they were colorful! everything in geometropolis was gray, minus its inhabitants – so droplet’s eyes were wide in awe at the sight of these marvelous gems.

the crystals made a path through the caverns which she followed eagerly. much to her surprise, droplet saw the light creeping in at the end of the tunnel! she had found the exit!

“AAAAAAAAAAAH!” 

droplet jolted at the sound of the cry. it was square!

she ran back through the tunnels and finally reached her teammate, surrounded by broken cavern walls.

“what’s wrong?” droplet asked. “i heard you yell!”

“one of these rocks crushed my foot,” he groaned. “but i’m fine. sorry to worry you.”

“just glad you’re okay.”

“how far along were you?”

“i just found the exit…”

“oh…”

meanwhile, hexagon and octagon were continuing along at a steady pace.

“it’s hard to say who’s the toughest competition,” octagon said. “most of the others still in the game don’t really want to be.”

“i suppose you’re right,” hexagon responded. “square? no. heptagon? definitely not. star? not sure, but i don’t think so. as far as i know the only one who really wants to win is droplet.”

“hm.”

“i guess my toughest competition is you!” hexagon elbowed octagon playfully. 

“...hey, i think that’s the exit!” octagon pointed ahead towards the light.

the two made it out of the labyrinth to greet origin and oval.

“and nothing without pentagon is the first team safe!” oval announced. “congratulations! now it’s down to go the DSTance and the homeslices!”

square sighed. “i’ll make my way. but go without me, droplet. i don’t want to slow you down.”

droplet hesitated. “okay.”

she ran off to find the crystals again, and noticed a flash of pink ahead of her.

“star!” she exclaimed.

he barely caught a glimpse of her as he sped past. “droplet!”

“it looks like a race between the last of us cool kids!”

“indeed it does!”

droplet was on star’s tail, but she couldn’t catch up to him. she spotted a little crevice in the wall and jumped through the shortcut, emerging a little ways in front of her old teammate.

“you’ve always been the inventive type!” star exclaimed, “but i won’t let that stop me!” he jumped ahead of her and kept running.

the two were coming up on the exit, lined with crystals sparkling in the light. 

“i never knew you were so fast!” droplet huffed.

“i’ve never had a reason to run!”

“and there we go!” oval exclaimed. “the homeslices are safe! that means go the DSTance is up for elimination.”

droplet emerged from the labyrinth mere seconds after star and collapsed in exhaustion. 

“that was epic,” star said, helping her up to her feet.

“hey,” origin started, “where’s heptagon and square?”

“square’s still inside,” droplet replied, an edge of concern to her voice. “his foot got smooshed by a rock… he’s coming out, but he’s probably going pretty slowly.”

“and heptagon’s somewhere,” star answered, “just not in the labyrinth. i told him to go take a nap.”

“where did he go?” origin asked.

“dunno. i thought he would’ve gone to you, but maybe he just plopped down by the entrance.”

“okay. hm, i have an idea…”

origin started buzzing; star, droplet, hexagon, and octagon all lost their limbs and stuck to him at once – and soon enough, square and heptagon were dragged over to him as well, like metal to a magnet.

“oh!” square gasped. “my foot can’t hurt if it’s gone.”

and so origin took the contestants back to the main field while oval followed behind him, using the grapher to return the arms and legs to his fellow shapes.

“does your foot still hurt?” droplet asked square.

“nope. it’s good as new. hey, sorry we lost.”

“it’s fine. anyway, it wasn’t your fault.”

square shrugged. “i dunno, it feels like it is.”

“well möbius strip is wrong. no need to feel bad.”

droplet smiled. square smiled back. “if you say so.”

octagon and hexagon had been chatting ever since they had emerged from the logarithm labyrinth, and continued to do so as they went to their cabin.

“so what about that autograph?” octagon asked cheekily.

“what do you want me to sign?” hexagon replied, grinning.

octagon lifted up her pacifier. “this!”

…

“AAAAH I HATE MӦBIUS STRIP I HATE THIS SHOW I HATE EVERYTHING!!!!”

“...hello to you too, parry.”

parallelogram suddenly rushed over to kite. “primes, how i’ve missed you! geez!”

kite chuckled. “i’ve missed you so much… hey, crazy to think heptagon is the last one of us still standing, huh?”

“yeah… he’s a good guy. he doesn’t deserve this.”

“you don’t deserve this either.”

“yeah, i don’t. screw möbius strip!! that pathetic jerkwad!!!”

“kinda hope he never comes back. origin is a much better host.”

“you got that right! but then the bar is incredibly low.”

“true.”

soon enough all of the inhabitants of the paradox gathered round to watch the contest – only to be treated with a static view of the mouth of a cave.

“this isn’t very exciting,” triangle said. “y’know what? how about we go over the standings again?”

“sounds like a plan,” trapezoid replied. “so who’s left?”

“we have hexagon and octagon on nothing without pentagon, square and droplet on go the DSTance, and heptagon and star on the homeslices,” rhombus said. “pretty interesting variety.”

“three who really want to win and three who really don’t…” heart murmured. “and yet all of them are d-doing pretty well for themselves.”

“we can all agree that heptagon does not want to be there,” rectangle said, “like at all. i’m on the fence about square – he came to the competition with the intention of winning, so i’m not ruling out the possibility of that coming back.”

“and he is a pretty darn good teammate,” trapezoid noted. “we should definitely watch out for him.”

“how about star?” pentagon asked. “i’ve never known what’s going on with him.”

“yeah, he’s a bit of a mystery,” circle said, “surprisingly enough. why is he here?”

“well, um…” heart started, “he j-just came here to have fun with me. of course, heh, at this p-point it’s clear that that didn’t really pan out…”

“so what’s he doing now?” parallelogram asked. “do you think he might want to actually win now?”

“maybe. he’s never cared about that kind of stuff before… but i d-dunno, things have changed.”

“hm.”

“well, okay, so we can put heptagon at the bottom,” kite concluded, “but from there it’s hard to tell. maybe we should go from the top down?”

“i’d say hexagon and octagon are at the top of their game,” triangle said. “those two are probably the ones to beat at the moment.”

“who would you say is stronger?” rectangle asked.

“i’d think hexagon, only by slightly,” rhombus interjected. “both are very strong, and work incredibly well together, but octagon seems to be a bit more volatile emotion-wise. hexagon has a better handle on things like that, at least generally speaking.”

“you’re not wrong,” trapezoid conceded.

“not to mention how hexagon is good at being sociable with anyone, while octagon’s only just getting used to this type of thing. once teams dissipate, which i’m assuming they will soon, hexagon will have more flexibility in terms of making alliances.”

everyone seemed to agree with this.

“so on top is hexagon and octagon,” circle restated. “then who?”

“rectangle’s right in that square might rediscover his desire to win,” parallelogram noted, “but as of right now? he still doesn’t really want to. he has potential, but at least in the current moment, square would place pretty low.”

“and i’d place star right next to him for the same reason,” kite said. “things have changed and he’s changed, but nobody has any clue what he’s really been up to lately or what he wants. at least up until now he has yet to definitively say he wants to win, but i could see him pushing through if it did come to that.”

“then droplet would g-go right below hexagon and octagon,” heart continued. “she isn’t the most skilled or experienced, sure, but she’s incredibly creative and great in teams – and she really does w-want to win!”

the group continued to discuss the state of the competition despite having little to no idea what the current challenge was. eventually, however, go the DSTance ended up losing.

“so…” triangle started. “how have things changed in the past 5 minutes…?”

“star is up,” rhombus said. “way, way up.”

[kaleiidoskope]

oooooh god let’s see… i’ve got a couple

“aren’t pools just domesticated water?”

“could you make a game where you skate around and whenever you do a cool trick it says stuff like logarithmic! as a compliment?”

“if every f was replaced with a ph, would “off” be spelt “ophph” or “opphh”?”

I'm gonna start a reblog game with this question: what's the most random thought you've had recently

for me it's this random idea of one (or more) of my AO OCs interacting with Sebastian (which I now would love to see someone draw) that suddenly came up for absolutely no reason

no-pressure @'s: @simply-windy, @discothemechanic, @2coffeeday, @crowrave, @placardd

[brandstifter-sys]

Under Pressure

Chapter 11: Tennis            (Ao3)

Word Count: 1408

Relationships: Royality, implied Royaliceit

Characters: Roman, Patton

Rating: T

Warnings: Villain!Logan, mood swings, emotional confrontation, fire, mild angst

----

It was strange passing through the door, like he was pulled on a different path from the others, like splitting apart from his brother all those years ago. Roman couldn't be sure why he felt that tug in his navel but he knew it meant trouble.

"What the hell is this?" Patton questioned as the two of them entered the room. It was odd. The ceiling was higher than expected, about twenty feet up, and the left wall was a giant mirror. There were six outcoves on the back wall, close to the tile ceiling, all blocked by glass.

"It's a puzzle, Padre, obviously," Roman scoffed and scanned the ground, "Why don't you pretend to have the answers while I figure this out."

"What?" Patton questioned in disbelief. Roman shrugged and carefully paced along the tiles, searching for switches and traps.

"I'm not blind to your tactics," Roman shrugged, "and you played me for a fool for long enough, I ought to know by now." Patton's jaw dropped, too flabbergasted to even squeak indignantly. He glared at the king, fighting back the bile of harsh words brewing in the back of his throat. Roman paid him no mind, more focused on the floor. There were two tiles that were sightly raised and off-color.

“My tactics,” Patton hissed after a beat of silence, “were never meant to influence you that much. I was confused and trapped in a corner. Wasn’t it obvious I was pushing and pushing for my own sake?”

“If it were obvious, then mark me as oblivious,” Roman quipped and stood on one of the raised tiles. It sank under his weight and merged with the rest of the floor.

“If you’re so unsure about what you should be doing, make yourself useful and come here and stand on this switch,” Roman commanded with a regal air that made Patton see red.

“How about you ask nicely instead, since I’m a person, not a dog,” the emo huffed and crossed his arms. Roman stared at him tiredly and rolled his eyes. He was going to be trapped here with Patton for a very long time.

“Would you please make yourself useful and stand on this switch?” he asked as if the words burned his mouth, caramelizing the sickeningly sweet tone he opted for. Patton huffed and marched over to him, gracelessly shoving him aside and standing where he was told. Roman stuck his nose in the air and marched two feet to the other switch.

A satisfying click sounded when Roman's weight caused the switch to slide in place. Then a loud noise overhead caught both of their attention. The glass blocking the outcoves lowered, exposing the candles to the air.

"We need to light them. I could throw you, and that fiery temper of yours would do the trick," Roman mused.

"You're the one who was literally on fire, I should be throwing you!" Patton argued and crossed his arms, "But we shouldn't have to throw anyone."

"Is this another one of your moral lectures?"

"No! Think about it! It's a puzzle! Would Logarithms really want to make any of us use brute force to get back to the main mindscape?!" Patton fumed. There had to be a trick to it all. He couldn't jump high enough to light those tiny candles, and he couldn't throw Roman. Besides, the wind would blow out any matches.

"I suppose you have a point," Roman sighed dramatically and flicked his wrist, conjuring a ball of fire, "It's too far to aim a blast of fire, even if you had the strength to throw me." He lazily bounced the ball on the ground and caught it, using the motions to help him think.

Patton would have corrected him, he was strong enough, but his attention was on the fireball. He couldn't look away from the swirl of flames moving up and down.

"I suppose we'll be here for a while," Roman mused, "you could use it to apologize to me."

"It wouldn't matter, I can only apologize so many times, you don't want to forgive me. I don't want to forgive me, but I know demanding another apology won't change my mind," Patton said and slumped his shoulders, still hypnotized by the fire.

"Patton I trusted you, I believed that you could never steer me wrong. I loved you and you turned my world upside down. Now I have to depend on my own judgement, and I don't know how I can forgive you without becoming dependent on you."

"Then don't. But stop asking me to apologize if you don't want to accept it. I can tear myself apart fine on my own. I hurt everyone and now the only one who actually wants to talk to me is Janus."

"Say one foul word about him and I'll—"

"I hurt him as bad as I hurt you, but he's still willing to hear me out and help me do better," Patton cut him off, blushing brightly, "He really cares deep down and he gives me the honey glows something fierce."

"You dare try to steal my queen?!"

"He's not your property, and last time I checked you decided you hate him and you insulted him repeatedly," Patton snarled and glared at him, "Or is that just how you show people that you love them?" Roman paused and stared at him, never halting with his toy. Patton sniffed and shook his head.

"No, that would mean you love me and I can't handle that kind of revelation," he sighed and blinked back tears. Roman was silent, studying him. The only sound was the impact of the fireball on the floor, echoing in the empty room.

That crackling and echoing bouncing was maddening, like the silence was deafening. Patton's eye twitched as the slow rhythm got louder and louder. He wanted to hear Roman denounce his claims, that he didn't love him. He would have been okay with him changing the subject, or even confirming his statement—anything but the looming doubt and wordless passage of time.

"Roman, stop bouncing the ball," Patton demanded as he shoved his hands in his pockets, clenching his fists to quell the rage bubbling up from his core.

"I need it to think. You don't want to be trapped here forever," Roman answered stiffly, not stopping, "Unless you have an idea, stand down."

Patton snarled and reached into his inventory. He had just the thing to break up that rhythm.

"By Zeus!" Roman yelped as Patton slapped his ball from under his hand, narrowly missing the royal fingers with the rim of a tennis racket.

The fireball hit the wall and hurdled back toward Patton. With a growl, he smacked it away, sending it upward toward the candles.

Roman's jaw dropped as his creation uncurled and vanished, lighting one of the candles. A grin spread across his face as he conjured another.

"How's your aim?" the king asked almost smugly, "You might have found our escape, Sunny Dad Real Estate."

"Better than yours," Patton jeered, already feeling the rush of adrenaline and endorphins filling him. Roman scoffed and tossed the fireball at him. He spiked it up and got another candle.

Roman kept throwing more balls, amused by the change in Patton's expression with each one. His bright smile was returning as well as his bubbliness. Roman's heart swelled when a giggle escaped Patton's lips as the final candle was lit.

"Perhaps you are right," Roman said finally, "Maybe I shower my beloved with ire and ill-tempered words. Perhaps it's my turn to—to apologize to you, Patton." The fire behind his eyes was reduced to embers, and Patton swore he saw the prince in that gaze.

"I'm—I'm sorry for treating you so poorly and demanding so much emotional labor. I would have followed you to the ends of the earth without question, you were my hero. Now I can see that I don't want a hero. I want a partner, perhaps not in a romantic sense, but a companion to support and be supported by."

Patton's jaw dropped at the same time as a door opened on the back wall. Without thinking he tackled Roman into a hug, far too elated to care about the exit appearing.

On the other side of the mirror, Remus watched the pair and groaned. He would need them to get to the next room, his current room, to keep going.

----

(Master Post)

[nautiscarader]

More math time! Here are some unusual (fore mortals at least) numbers from last episodes. We see square root of 2, an irrational number , and arguably the first irrational number discovered by Pythagoreans, who, erroneously believed that every single number can be expressed as a fraction, or proportions (or ration), until thy tried to calculate the length of the hypotenuse of a right isosceles triangle... and they couldn’t find a rational number that does the trick. hence the term, ir-rational. 

Pi is a much more well-known member of this club, a number that is a ratio of circle’s perimeter to its diameter, and if you see anything remotely circle-related, you can bet you will find Pi somewhere there. And even if it has nothing to do with circles at all. Since Pi can be expressed as tons of infinite sums, products, and integrals, it tends to appear in many places. 

Then we have φ, also known as the golden ratio, another irrational number that’s gotten somewhat popular in the last two decades. It pops up in many places, though most people know it as a limit of a ratio of two consecutive Fibonacci numbers.

e is next, and it is a tremendously important number in mathematics, as it is a base of natural logarithm, and just like Pi, it likes to pop up unexpectedly in many calculus-related calculations. 

And finally, the big one, i. The imaginary unit, a counterpart to 1 in the complex plane, that quite literally opens up a whole new dimension of numbers.  

[aftermathdb]

DEATH BATTLE Review: Venom vs. Crona

Two on two that are within one! Who will win, who will lose?

Venom′s Preview.

We open on a history lesson, about the Klyntar. And how they were a peaceful race that kicked out a loser named Venom. Who went through a multitude of different hosts. From heroes, to villains, to… Deadpool.

And then the Symbiote met Spider-Man.

And, after a lot of adventures, Peter got rid of the thing because it was a creepy goop monster. After this, the Symbiote bonded with one Eddie Brock.

Whose life was screwed from the start.

Between an abusive dad that blamed him for his mother’s death, and having terminal cancer, the guy had nothing to lose and everything to gain by joining with the Symbiote.

Aside from the powerset he got from Spidey, the hosts go over his other abilities, like camouflage, shapeshifting, and 360° vision, and all that other stuff. We get into our first animated segment.

Now, to be fair, Wiz is kinda right.

After going over their feats, they go over his past a bit more.

After accidentally killing a kid after stealing his dad’s car, he was told to plead innocent, and rig the jury. So, he’s been carrying around that guilt ever since.

And on the road to redemption, Venom and his host have fought and gone through a lot of crazy things. From fighting off most of Spidey’s rogues gallery to tanking a sonic blast that shattered glass miles away.

And… Some really weird convoluted comic book bullshit.

After fighting the Symbiote God that tried to turn them all into living weapons, Venom has proven himself a hero in his own right. Even teaming up with Spider-Man on occasion.

Sure, he’s always hungry for brains, but with Eddie’s influence, he’d rather bite the head off of a criminal than an innocent.

Crona′s Preview.

The hosts open up on the history of the world of Soul Eater, which, for those of you unfamiliar, is very… weird. Death is a goofy-looking dude who opened a school where warriors trained to stop evil.

Of the many characters, Crona Gorgon… Was not one of them.

Crona basically had your typical power-hungry abusive mother, who basically tried turning the poor kid into a living weapon… And by living weapon, I don’t mean the ones that actually turn into weapons, I mean the… uncomfortable kind.

Crona’s weapon is Ragnarok (Which I have now recently realized I misspelled numerous times in the captions, so… Apologies).

With all that power at their finngertips, Crona and Ragnarok became a formidable team. And that leads into the animated segment.

And after going over some bonuses of how the powerset works, what with the whole “eating souls” thing, we go into even more powers. Specifically, of the Black Blood.

From being able to project Madness onto others, to shapeshifting, to all sorts of sonic attacks, Crona has some major firepower under their metaphorical belt.

In addition, they go over how Crona has gone up against plenty of Death Academy students like Death the Kid, Maka, and Black☆Star (And for those of you wondering, yes, the star in his name is the official spelling.

Now, Death the Kid could reach supersonic speeds, and Black☆Star is eveen faster.

Since Crona can keep up, this means that they’re in the same ballpark of speed.

And all that Black Blood is also really damn powerful and plentiful.

It could cover this entire city, given similar comparisons to other similar cities in the area, that’s nearly 10,000,000,000,000 tons of Mad Blood.

Thankfully, through the power of friendship and good feelings, Crona ended up saving the world. And made a new kind of Madness that… made everyone obsessed with boobs.

The Battle Itself.

Luis is lead on this fight. Venom will be reprised by Adam Wennick, Crona will be voiced by Sarah Anne Williams, and Ragnarok will be voiced by John Van Doren. “Madness Envenom” by Brandon, and audio led by Chris Kokkinos.

We open on a church, where there’s a single person praying before Crona comes in.

Now, I gotta say: Mad props to the animator who is working on Ragnarok, that is some quality movement. You can’t tell because this is a screenshot, but the animation on Ragnarok is pretty fluid.

Anyways, it turns out the person who was there first was Eddie. And, in true Season Seven fashion, the fight starts because of food. Because why not?

After a very brief back and forth, Venom manages to trap Crona.

But, they’re a tough cookie, and they manage to blast away and make some distance.

Now, this being a sound attack, it deals some significant damage to Venom.

I am so glad I managed to pause it here. This is an epic shot.

And I guess Luis was watching some Jojo, because we get a punch clash.

Venom manages to get by, and camouflages to get the drop on them.

Five Nights at Venom’s.

Venom manages to get in a hit, but the Black Blood is a bit too tough for Venom to beat.

Fitting for a Halloween episode, there’s blood everywhere.

Anyways, the fight takes to the skies, where neither seems to have a specific advantage… Aside from Crona managing to get in a few more licks in and block more hits than Venom.

Crona manages to take the fight back into the church.

Five Nights at Crona’s.

Venom decides to boast one more time before, uh, well…

Yeah, finishing blow in

5…

4…

3…

2…

1…

Verdict + Explanation.

Anyways, Boomstick makes our second Lucy vs. Carnage callback.

Now, Wiz notes that the only advantage Venom had was shapeshifting, camouflage, and weapon versatility. That’s literally it. Venom was screwed everywhere else.

Crona could match Black☆Star, who could get to Mach 9000.

Compared to Venom matching Spidey 2099, who only has Mach 2000, that’s a pretty clear speed difference.

Strength was another. Venom hasn’t displayed anything comparable to Crona opening the Moon’s mouth.

And really, with the Black Blood, Venom couldn’t pull any puppeteering tricks.

Now, the big one: Could Venom survive Crona’s sonic attacks?

Now, the sonic attack that nearly killed him that shattered glass miles away is a good high point to gauge. That clocks in at about 244 dB. Crona’s feat of covering the moon clocks in at 275dB.

And if you remember anything from Black Canary vs. Sindel, sound changes on the logarithmic scale. So Crona’s attack was over a thousand times more powerful than the blast Venom barely survived.

Overall impression.

Magento vs. Robot Man anyone?- I mean… That’s the impression this episode gave me. Like… I know that Ben was largely unfamiliar with Soul Eater going in, and I can assume that the same can be applied to a few of the other team members, but… really? Why not pit Robotboy against EMP Man? How about seeing who wins between Sandman and Juvia? The only way this can feel like it wasn’t “My Weakness is Sound man” vs. “Has Sound as an Explicit Weapon Person” is if the big question was “Could Venom survive Crona’s sonic attack?” They don’t put much emphasis on it, so it feels like they knew going in that Crona would utterly destroy Venom. And while I’m not inherently against fights that are basically stomps (Hell, I still enjoy Flash vs. Quicksilver), they really should have put more emphasis on that question if they didn’t want it to feel like it was one-sided.

I’m happy that Soul Eater is getting some rep before the inevitable Ruby vs. Maka fight (Uh, more money on Maka please), but I was honestly expecting Black☆Star to make it in before Crona. And even then, I would have thought that they would do something more creative than “Black Goopy buddies that bonded with a human host”

I tend to rag more on matchups than I do on animation, and I’ll be real: The animation is still good. Ragnarok is well-done, and they definitely landed the creepy factor quite well.

My own first viewing was a bit tainted because my own mother demanded that I not spend time for myself and instead sit at a table listening to her and my dad talk about  whatever, so my own feelings are a bit skewed because I had to watch this in a rush. Just a little disclaimer.

8.7/10

Next Time…

Speaking of ragging on matchups…

Can anyone vouch for having wanted this? Or, failing that, can anyone vouch for having seen this as a suggestion in the comments section?

Is there a fight that you want me to review? - Send an ask/request, and I’ll look into it!

Do you want to read my fanfic based around DEATH BATTLE itself? click here!

Thank you for reading, and I hope to see you next time for…

Red vs. Red… Blue vs. Blue… It’s I against I, and me against you…