#trigonometry example

[er-cryptid]

Vectors with i and j [Ex. 3]

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[maxvchamp]

i believe that you should not remember stuff but be able to do stuff even if you forget the formula or whatever

[nanzyn]

underrated writing emotion: when your math actually (accidentally) works out and your characters are walking long distances at the correct pace

[lara4eclipze]

Santa Baby » 05 - under the mistletoe

masterlist || next || back

the day came , your hands were sweaty from how nervous you were yet your heart pounded with thrill, i mean the way you two would have to "hang out" is unconventional

and maybe your friends have teased you about it enough for you to think of cancelling it , yet something about the way lara texted you and how it felt like she was nervous when texting sparked something inside you

it made you think that she also felt the same for you, maybe she saw you as more than a friend yet you didn't want to jump into speculations, maybe you're just delusional

the doorbell rings and you shoot up from where you sat, you walk to the door giving yourself a pep talk—to possibly not mess up or stumble over your words

"hey come in" you smile as you saw lara , she looked unbelievably pretty , it was like she was a painting of life - and gosh her smile it made you all giddy about seeing her more often

"thanks, by the way i got carbonara buldak - yoonchae said you liked this the most" lara delivers , you unknowingly blush at the thought of her going to lengths like so to satisfy you

"really? thank you! - ill get this cooking, and uhm, you can sit there, " you reply, pointing at the couch in the middle of the apartment , "sorry for the mess i just got busy this week" You sigh

"its alright" she responds

you take the bag from her hands making your touch hers for a split second

"uh- ill get to cooking this now" you say before walking to the kitchen and getting started

lara looked around the place spotting some pictures of you and freinds , family or even just by yourself - she smiles taking in your soft nature

you peek from the kitchen and saw lara smiling at some of the pictures

"im actually gonna fall in love," you mutter to yourself, as you finish cooking the food, you go back to the living room handing lara one of the two plates

"if you want it more spicy i have some sauce there" you say

"thanks, so what topic do you struggle with?" lara mumbles as she takes a bite out of the noodles , some of her hair was out of place so you helped her hold it, securing it with an hair tie

"well i struggle with loads but i struggle most with trigonometry and calculus" you replied casually as if you didnt feel like jumping with the smallest interaction

"ooh a lot of my friends also struggle with that, manon and megan for example" she responds taking another bite of her food

"oh manon the one with giselle right? , and yeah megan has always had a hard time with math" you relpied finishing up your food

"oh your freinds with megan?" lara asks curiosity tinging her voice

"mhm, for a few years now" you respond

she just nods and finishes her food, putting it a side lara picks up her books from her bag , it looked somehow intimidating due to how thick some of the books were

the tutoring went surprisingly well , lara was patient with your stupid ass and she honestly was so kind as well

that made you dread that she had to go though

"sure?? you can stay for longer you know" you pout at lara as she stood up and packed her things

"maybe next time y/nnie you have my number anyways" lara responds

"fine lets sleep call then" you mumble

"why not"

taglist (open) : @artrizzler19 @sixflame438 @c-yerim @lmaoursickbro @meganskiendielsbtc @hwonnrinji @ohmyhaely @d1spact @yeetaberry127 @vrtualstar @goofymickeyr

[uncharismatic-fauna]

Uncharismatic Fact of the Day

Squirrels are often portrayed as brainless, but they can actually be quite clever. For example, northern flying squirrels are great a trigonometry! Before they leap from a tree branch, adults will lean out and sway side to side; it's believed that this helps them calculate the distance to their target and the angle at which they need to glide in order to make it to the other tree.

(Image: A northern flying squirrel (Glaucomys sabrinus) by Phil Myers)

[ultimateswag]

𝚂𝚝𝚎𝚟𝚎𝚗 𝙼𝚎𝚎𝚔𝚜- Study Sesh

Paring : Steven Meeks x fem reader

TW : (brief) mentions of biblical studies and Pythagorean Identities.

[this is my first imagines by the way, so please excuse any mistake or poor writing (I tried to not mention any racial aspects, but lmk what I can improve)]

Latin was always a subject you mastered. It got much easier once you began to assimilate Latin with French, which, by the way, you were also pretty good at. One was a dead language, not spoken nowadays, but really useful when doing biblical studies, and then the other was the language of romance, the one people thought of when asked to say the most romantic and sexy language there is.

Though, besides languages and the occasional English, you weren’t really exceptional in any other subject, especially Trigonometry. It's not like you were failing, not at all actually, but you simply couldn't excel it like, by example, literature. That's why you’re pushing yourself to the edge, so you can get better at the calculus assimilated subjects, and that's why you asked Steven Meeks for help.

The two of you have always been friends, talking to each other in the corridors, of course being together in study groups, and also being a part of the same secret society. But apart from those friendly interactions, you didn't stand out as actually being friends, so much so, that few people actually believed that you even knew who Steven was. Being the only girl at Welton preparatory school due to your high intellectual level ( and family history) made you quite popular, so why would you, willingly, hang out with Steven Meeks? That's what they all thought, though, no one dared to say it out loud.

"I still don't understand this." You said, a loud sigh leaving your mouth quickly after as you stared at the problem filled paper in front of you.

Steven let out a small low chuckle, though it was clear he didn't mean it in an offensive way. "This is actually simpler than it looks" he begins, moving the paper a bit closer to him, and scooting lightly closer to you. "Once you understand the concept, it'll all make sense." And to that, you nods, gaze switching from the paper to his face, admiring his soft freckles, beautiful eyes and- and how he begins to explain Pythagorean Identities.

"Alright. So. Pythagorean identities. The most important one is kind of like the golden rule of trig: sin?0 + cos 0 = 1. That's the foundation, everything else branches from this." He explains.

You leaned in, the scent of your sweet raspberry perfume just barely brushing the air between them. "But why does that even work?"

Steven looked at you not just any glance, but the kind of look that says I see you struggling, and I want to help you out of it. "Because it comes from the Pythagorean Theorem." He says, but swing the confusion linger on your face, he grabs a piece of blank paper and a pencil and begins to draw." Picture this: a right triangle inside the unit circle. The hypotenuse is 1. The x-value is cose, the y-value is sine. So when you square both and add them up... it just always equals 1."

You blinked, eyes narrowing slightly in concentration as they switch from the homework, to Steven's drawing. "So it's not just a random formula-they actually mean something."

He nodded, a little too pleased you were catching on. "Exactly. And the other two identities are built off this one. Like, if you divide everything by cos?0, you get: 1 + tan?0 = sec?0. And if you divide by sin'® instead, it becomes: cot?0 + 1 = cscª0. It's like a family of truths that are all connected."

You bit your lip, scribbling it down, then looked sideways at him. "Do you always talk about math like it's poetry?" You ask with a small smile. Steven, just like you, has always taken a special liking to poetry, and just like everyone else, after just a few classes with Mr. Keating, it became a bigger, more important part of his life, so of course it was no surprise to see him romanticizing trigonometry.

Steven smiled, a faint flush rising in his cheeks. "It makes it easier to understand, does it not?" he tilts his head lightly at you, seeing as you wrote the problem's answer down on the paper, with your perfect calligraphy, while your beautiful, hair fell next to you. Your eyes seemed to shine as you understood each problem, they looked beautiful, you looked so beautiful. At least that's what he thought.

"I suppose it does" A soft laughter is heard leaving your mouth. There was a beat of silence-just the hush of pages turning in the distance and the soft tapping of your pen again. "You know," you said, not looking at him this time, "I usually hate asking for help."

"I know," he replied, glancing at her-noticing the tension in your jaw softening a little. "But I kind of like that you asked me.

Their eyes met. Just for a second. A heartbeat.

“I do too.” She said softly, turning to look at her notes once again. Her cheeks were feeling hotter, she didn’t want to look up.

“Do you need help with anything els-“ Before he could finish his frase, Aurora began speaking once again, mustering up enough courage to glance at him.

“Would you like to hang out? Outside of school?” She asks, cheeks getting hotter and hotter .

“That’d be pretty nice, actually.” Steven’s now held held a crimson tint, although he tried to act like he wasn’t about to jump out of happiness.

“Cool” she says, attempting to act nonchalant, but giving him a shy smile.

“Cool.” He answers back, returning her smile.

[study-diaries]

Math Tips

(Pictures are not mine)

Well, let me tell you, we all have this love-hate relationship with this subject, right? The worst part is that when you don't know what the heck is going on, so, as a girl who studied maths (2 Volumes/textbooks) on her own during the year she was homeschooled, here are some tips and tricks that I did to get an A+ in my math finals!

Get your syllabus together

In the beginning I had no damn idea what was going on and it was just confusing. I had to do the first thing I did was taken my index/table of contents and mark the chapters which i knew very well and the ones I had no clue about. And then i arranged them with the marking scheme, like which one carries the most marks etc etc and study accordingly.

Complete lessons/chapters that you already know

When you finish off the things you already know then that's gonna give you the confidence you need even if you know only 1-2 chapters, learn it throughout and make sure that you'll get the answer no matter how twisted the sum is. If you're doubtful about the whole textbook like any normal person.... Start with the easy ones. (I know there are literally really no "easy" chapters, spare me)

Harder chapters need hard work

Most chapters like Trigonometry proofs, Geometry proofs, Algebra, Graphs, Mensuration and Calculus etc need more than minimum effort but here's a trick, what is the common thing in this? Yes, they're all formulae and theorem based which goes to my next point. These chapters are completely based on how much you've understood your basics.

Formulae and theorem cheatsheets

Make a list of all formulae and the theorem used in the book, write them chapter wise and no printouts or digital notes. Take a paper and write it down, no excuses. It helps you while you're practicing, revising and in the last minute review, it helped me damn much. Remember, maths is a sport. The basic formulae must come to you like reflexes.

YouTube is your best friend.

For every single chapter, go and watch the basics and how a sum is done step by step. A recommendation for this is Organic Chemistry Tutor who literally is one of the reasons i passed. He has videos from basic geometry, trigonometry, statistics to calculus. Search for your own YouTubers and be clear with concepts.

Math is fully memorization

Memorize formulae and theorems with the back of your hand, you should be able to recall them within seconds. Be thorough.

Memorize basic math values (if calculator isn't allowed)

Do this if you have a majority of chapters like Statistics, Mensuration, Profit/loss calculation etc, where large numbers are concerned. Memorize the first 10 square, cube, decimal and multiplication values. It may be dry but there are literally songs available for these things, I'm serious, i learnt the first 10 cube roots by listening to Senorita xD Search for rhymes and they'll definitely be many!!

Work it out!!!!!!

Can't stress this enough, atleast 30-40 mins is the minimum for maths. I'm serious, work out each sum, don't ever think it's a waste, you'll see the results. Practice makes perfect. Work out every single sum, from examples to exercise ones cause let's be honest, our examiners love to take problems from every nook and cranny of the book.

Whiteboard method

So, I made this up and it actually works, if you have a whiteboard or anything else, once you completed a chapter, take a random page and whatever sums you have on those two pages, you need to complete within a given time limit. It helps you to identify your weak points and where the hell you're losing both time and effort and not to mention that it gives you confidence boost up.

Hope this helps :))

[snickerdoodlles]

another example card for @mailed-it, this time branching out into my school president :D

drew this one first on notebook paper before gluing it to cardstock because I wanted it to look like something Tinn might doodle in his maths notebook next to his heart based trigonometry. because he's a sweetheart shaped nerd❤️

exchange sign-ups here !!

[keegsruss89]

too bad,

math lesson for you! (Based on what I learned last minute for a final! I think it's correct-) To understand (basic) trigonometry, you must know SOH (Sine=opposite/hypotenuse), CAH (Cosine=adjacent/hypotenuse) and TOA (Tangent=opposite/adjacent). Now let's take a triangle ABC rectangle in B. If we look at the angle C, the BC side is adjacent to it, AC is obviously the hypotenuse, and AB is opposite of C. To calculate an angle using trigonometry, all you have to do is now which sides are what to the angle, and then you’ll always get the lengths of two. For example, for our ABC triangle, let’s say CB = 3 and AC = 7. We know CB is adjacent, and AC is hypotenuse; so we use cosine: 

Cos C = BC/AC Cos C = 3/7 C = Arccos OR cos^-1(3/7) = 64,62306647 ~ 65º

Of course this is on a calculator, these aren’t the Elias’ old times where he had to know those cosine, sine, tangent formulas.

….

My brain just broke

[timesacircle]

Rhind Mathematical Papyrus - the oldest (1650 BC) manuscript written in Algebra and Irigonometry.

"Rhind Mathematical Papyrus": It is named after Alexander Henry Rhind, a Scottish antiquarian. He bought the papyrus in 1858 in Luxor, Egypt. It was found during illegal excavations in or near the Ramesseum. The Rhind papyrus dates to the Second Intermediate Period of Egypt. It was copied by the scribe Ahmose from a now-lost text from the reign of Amenemhat III (12th dynasty).

The Papyrus is probably a mathematics textbook, used by scribes to learn to solve particular mathematical problems by writing down appropriate examples. The papyrus has work and writing on arithmetic, algebra, geometry, trigonometry, and fractions. Eighty-four problems are included in text covering tables of divisions, multiplication and handling of fractions; and geometry, including volumes and areas.

The scribe dated papyrus in year 33 of Apophis, the penultimate king of the Hyksos 15th Dynasty. The other side of the papyrus mentions 'year 11' without a king's name, but with a reference to the capture of the city of Heliopolis. In the opening paragraphs of the papyrus, Ahmose presents the papyrus as giving "Accurate reckoning for inquiring into things, and the knowledge of all things, mysteries... all secrets". He continues with: This book was copied in regnal year 33, month 4 of Akhet, under the majesty of the King of Upper and Lower Egypt, Awserre, given life, from an ancient copy made in the time of the King of Upper and Lower Egypt Nimaatre (?). The scribe Ahmose writes this copy.

[er-cryptid]

Find Ratios [Ex. 3]

Patreon

[yuri-is-online]

How do you think Yuu’s otherworldly education compares in common subjects between Twisted Wonderland and Yuu’s world? Would a Yuu being 16 influence if the prefect is ahead in any classes? I’m sure this would be dependent on the standard age for levels in a school system and what kind of school system we are looking at.

I’m going to use math as an example for my rambling. Math isn’t a skill that requires any magical knowledge as a background, so Yuu could theoretically be ahead in that subject. (I have no clue what math skills are required by grade in a Japanese school which NRC is partially based on.)

Using my high school as an example. Our math courses followed the track: Algebra 1, Trigonometry, Algebra 2, Pre Calculus, and then AP Calculus or AP Statistics depending on the year. A freshman could easily make it into a higher math like Calculus before graduating if that person started farther along in the track.

So a Yuu (from the 4 year system of schools) could have been approaching a higher level of a subject at 16. And if Yuu’s math skills were better than the level of a first year, I’m not sure a placement test would have been offered to Yuu since that would require effort from Crowley Grim’s level would have to be accommodated on top of fitting Yuu’s schedule with normal first year classes. Which would be such a disservice to Yuu, even if the class being easy gives more time for the subjects that need to be learned from the ground up.

I have thought way too hard about this. I am sorry for the rabbit hole and the asks being so close together.

- 🦐

No need to apologize for sending asks shrimpy friend, you always have the nicest theories. You can spam me if you please.

We know from a few tidbits here and there that grade skipping is allowed, but it depends on where you are in Twisted Wonderland. Given that the original intent for Idia was to have him be a child prodigy who had speed ran his way into NRC, I would assume grade skipping is allowed by the school board, but well. You have already hit on the tiiiiny wittle issue with Yuu.

Grim and Yuu's grades are averaged, if I understand what Crowely says at the start of the game and Crewel's vignette correctly. The idea was that since Yuu would automatically fail any magic based classes, Grim would pick up the slack there and Yuu would be able to help him learn practical life skills. Yuu being smart probably would help them, but their other half would still need to be brought up to speed about things like basic math before Crowley would consent to let them jump ahead a year.

You are correct that this would be a disservice to Yuu. Deuce's dorm uniform vignette has him struggling to solve simultaneous equations. Ace and Cater both list this as a basic math skill they learned in middle school, meaning they are excepted to know this, so a Yuu who was in something like Calc or AP Stats would be in a very advantageous position... but they still would need to teach basic math to Grim and keep on him so he did his homework for his other classes.

So the TL;DR:

No Yuu being more advanced than the other freshmen probably wouldn't help them graduate faster. It might help them educate Grim faster, but this assumes he wants to work which he does not.

Yes this is almost entirely down to Crowley not wanting to put in effort and his decision to count Yuu and Grim as one student.

If we are being honest it probably is more convenient for Crowley to have Yuu be a first year given the work he wants them to do for him. He gets to keep them around longer that way lol.

[the-sonic-crew]

Tails, do you know how the quadratic formula works? I have a math exam tomorrow and my parents said they’ll get me a parrot if I get a 90% and above. This and how the cosine law works (trigonometry) I’m struggling… PLEASE HELP 😭🙏

Of course! It's all under the undercut! ;D

Quadratic Formula:

The quadratic formula is a way to solve equations that look like this: ax2+bx+c=0ax^2 + bx + c = 0

Where a is the number in front of x2x^2, b is the number in front of xx, and c is the number by itself.

The formula is:

Here's an example!

x2+3x−4=0x^2 + 3x - 4 = 0.

a = 1, b = 3, c = -4

Simplify it step by step:

Do the two versions:

Final Answer:

x = 1 or x = −4

That’s it! The quadratic formula always works if there's a solution! :D

The Cosine Law

The cosine law is a formula used to find the missing side or angle in a triangle that is not a right triangle!

Formula:

Where a and b are the lengths of two sides, c is the length of the side opposite the angle C, and C is the angle you're working with.

When do you use it?

When you know two sides and the included angle and need to find the third side.

When you know all three sides and need to find an angle.

Another example!!:

A triangle has sides of 7 cm and 10 cm, and the angle between them is 60°. Find the third side.

And another!:

If the sides of a triangle are 5 cm, 6 cm, and 7 cm, find the angle opposite the 7 cm side.

That's it! The Cosine Law works when the triangle isn't a right triangle, making it super helpful when the Pythagorean theorem can't be used!

I hope you get your parrot! <333

[narcoticwriter]

Can These Guys Do Basic Math?

I blame Sin for this.

Brief and buckshot (let me emphasize this again, brief and buckshot) explanations under the cut, I did not THINK and I'm doing this for the funny, watch for some spoilers to the story and characters here or there though:

Dr. Faust: At this point in what I know about the canon, I do not believe he genuinely cares any more.

I-No: As a manifestation of humanity's hatred for the Gears turned into a literal god, I think that she is beyond math.

Happy Chaos: The kind of fucker who'd instigate something about the numerical value of three actually being fifty-five.

Ramlethal Valentine: "I was made with the capability to compute and solve a multitude of problems concerning algebra, trigonometry, statistics-"

Testament: They would scoff at whoever asked, then make an offhanded comment about how stupid that question was or an insult at the one who asked.

Bedman(?): Both Bedman and Delilah would openly call them twenty words that mean some variation of 'absolute imbecile'.

Asuka R♯: Math is a hobby to this guy, he would be more confused than insulted if you knew him even casually.

Slayer: The man has not been alive for this long and amassed this much power by being a chump. Please.

Sol Badguy: If the man of science didn't know how to do basic math, I'd wonder how he did it all in the first place.

May: Well now, someone has to keep track of how much money Johnny blows at the casino.

Millia Rage: A job requirement, if I'm being completely honest.

Zato-1: Debated putting him in the 'math is fake' tier, but decided that he has to use too much of it to be there.

Anji Mito: A man like that has to keep his ducks in a row and his math is an example of this because he's taken how many risks now?

Jack-O Valentine: I believe that she has to know some math and fairly well at that given her situation and by exposure.

Ky Kiske: I choose to divorce his knowledge from his application of it. This man is doing just fine on the fundamentals. So sue me.

Potemkin: With all due respect, I think the fact that he's here is monumental of the work Gabriel put in. The man is quite competent.

Leo Whitefang: How else would he be able to keep count of the dead and his sins accordingly?

Nagoriyuki: I think he gets by, but I don't see him in many situations where he would have to go beyond some basic algebra.

Elphelt Valentine: Can keep count of potential suitors, the tickets sold, and other things of that priority. Also a Valentine.

Queen Dizzy: Testament saw what Sol did to Sin and gave themselves a pat on the back.

Axl Low: Clearing up the streets and making them safe was a bit higher on the list of things to do while he was growing up, you know.

Giovanna: Would rather not, to be honest, but she can.

Goldlewis Dickinson: I DON'T HAVE TO THINK ABOUT IT-

Bridget: Off of sheer vibes alone, I don't think she thinks all that much outside of bounty hunting.

Chipp Zanuff: His intuition has done him many favors, but doing the mental math isn't one of them. I also blame the drugs. He can try.

Baiken: Controversial in the sense that at a certain point, I think she just stopped learning normal things for her age and hit the road. Could pick it up, but mostly for like, money and managing her stuff.

Johnny: Extremely selective, will ensure that his girls are taught right, but what there's no way I gambled away that much!

A.B.A.: If she's calm, sure, but God forbid someone looks at Paracelsus for a bit too long.

Sin Kiske: Sol may have kept him alive, but he failed him in every other way that matters. What do you mean he's still learning his time tables?!?

[tthatsonme]

Intellect, by molly.

— People often underestimate the seriousness of your sudden shift of motivation, in this day and age; it’s uncommon to see anyone (especially younger people) read a book or have any interest in having goals whatsoever, but you’re different, you’ve set the curve, you’re the centre of attention and everyone should be like you especially when it comes to academics, parents are constantly asking you to teach their kids your way because of how effortless your work ethic and dedication to school seems.

— Whenever the teacher needs an example on how to do a math equation or what a well written and worded essay SHOULD look like they always hold up your assignments as an example, you are 100% the best example of what a student should be like an any generation but especially this one, all of the parents and guardians with the “brain rotted iPad babies” or “wasting their lives away because of technology addiction teenagers” beg you to tell them what your “secret is” but maybe you’re not even fully aware of your greatness or level of discipline and success.

— You have a very distinct and important morning routine that you do every day, whether your routine has 4-steps or 40-steps it’s almost like it’s been burned into your DNA to follow it daily, your routine is not optional, you have the most perfect sleep schedule it’s almost as perfect as you, but in case you need a late study night you wake up everyday well rested regardless of whether you slept a full 8-hours or not, your memory to do things is amazing, you have a better memory than most people in your classes, you remember everything that you hear, read, and write in terms of school, you remember how to spell everything, your handwriting is always neat and legible, you could basically rewrite the dictionary at this point, fun fact: most people in this generation aren’t fluent in English because of the lack of spelling and vocabulary (my teacher said this so it’s probably true), while the other people in your class are crying over the phone ban if you have you you’re perfectly fine without your phone for 6-8 hours a day, you’ve never had any issues writing stories or having original thoughts, you have an extremely expanded vocabulary and are an amazing writer, “You don’t use brain rot?? Nerd alert!” It’s surprising to hear someone only use quote “brain rot terms” ironically, whilst the rest of the world is having unintelligent conversations about skibidi toilet and whatnot you’re the complete opposite.

— You have no issues in and are the best at all forms of mathematics, geometry, algebra, calculus, arithmetic, trigonometry, number theory, statistics, set theory, topology, discrete mathematics, probability, combinatorics, numbers, mathematics analysis, analytical geometry, differential equations, applied mathematics, game theory, pure mathematics, linear algebra, numerical analysis, and matrix algebra, natural sciences, engineering, medicine, finance, computer science and social sciences, biology, chemistry, physics, astronomy, earth sciences, zoology, ecology, microbiology, astrophysics, neuroscience, logic, ethics, psychology, philosophy, mechanics, and social sciences, morphology, sociolinguistics, pragmatics, psycholinguistic, linguistics, phonetics, historical linguistics, stylistics, and computational linguistics plus whatever other courses and classes that you have. [If this last part seems random it’s because it is, it’s copy and pasted from a personal sub I made a year ago for 11th grade :p]

_Things to remember

You can and will only ever manifest what you desire from this subliminal

Make sure not to obsess over your results because they can lead to limiting beliefs

You don’t have to listen daily or 1-7 times or anything like that, one is always enough with any subliminal :)

[sihedwu]

How Timepulse Works

Hey everyone, so… this was supposed to be a reply to a question from the esteemed @wary-taru, but the topic turned out to be pretty broad, and in my humble opinion, it doesn’t really fit the “question-answer” format, so I decided to make a separate post. ¯\_(ツ)_/¯

In case anyone forgot, let me remind you: Timepulse on Atmos works as a local navigation system, kinda like Atmos’s version of Earth’s GPS, and, jumping ahead, I’ll say right away that it seems to work on a similar principle, but, as often happens, a little differently. How exactly? Let’s find out.

How GPS Determines Location

So, before talking about Timepulse, I need to briefly explain GPS, since they should work the same in their most basic principle. As we all know from school, distance = speed * time. For us, this means that if we have a radio signal source whose location is precisely known, then, knowing the speed of light (299,792 km/s - veeery fast! >:D) at which radio waves travel, and the send and receive times of the signal, we can determine the distance to the transmitter. Therefore, if we know the distances to just 3 GPS satellites, then through something called the scary word “trilateration,” we can accurately determine our location on Earth. Okay, we’ve covered GPS, now let’s move on to Timepulse.

How Timepulse Determines Location

So, as we learned, the basic principle of GPS is calculating the distance to a transmitter based on the send and receive times of the signal. And the tower on Terra Glockenchime should perform the exact same function - sending a signal with the send time throughout Atmos so that everyone else can receive it. Now it’s clear why all that clock equipment is on Glockenchime. :D

But, I believe the most attentive of you should have already noticed that GPS needs 3 satellites to determine location, but there’s only 1 tower on Atmos. And, as you’ve probably already guessed, that’s where the difference lies. Now let’s see how this system works.

As with GPS, we need to calculate the distance, only not to a satellite, but to Glockenchime. However, one landmark isn’t enough; we need at least one more. As one, we can use, for example, the direction to the North Pole. So, now that we have the distance to Glockenchime, we can measure the angle between the direction to it and the direction to the North Pole. That will be the second landmark. Thus, through some not-so-complex trigonometry, Atmosian ships can calculate their location. But, as you might have already guessed, there’s one thing in all of this that we just can’t fail to mention. Namely - the accuracy of the measurements.

Atomic Clocks

So, if we measure the distance from the transmitter to the receiver through the travel time of the signal, we need to measure time very accurately, because with such a huge speed as the speed of light, even the slightest inaccuracy will be critical. To accurately measure such quantities, atomic clocks with accuracy down to attoseconds (one billionth of a billionth(!) of a second) are used on Earth. And… I wouldn’t say that the gear-driven equipment on Terra Glockenchime has the same accuracy as atomic clocks, so that gives us the right to assume that the signal sent by Timepulse travels much slower than the speed of light, otherwise the measurement errors would be just huge. And also, it’s worth noting that because not everyone can afford an atomic clock, all civilian GPS receivers, like in phones, are forced to use 4 or more satellites to achieve sufficient accuracy - and, as you’ve probably already guessed, even then it remains not very high. ¯\_(ツ)_/¯

Limits of Operation

So, since the canon doesn’t talk about the limits of Timepulse’s operation, we can’t say for sure whether it would work or not work at some distance/in some area (except, of course, the Great Expanse). However, judging by the fact that it radiates in all directions, its signal should weaken according to the inverse-square law. That is, if you move 2 times further from the source, the signal will weaken 4 times. Timepulse’s power isn’t reported in the show, but I would say that it can hardly operate beyond a few thousand kilometers. In any case, the canon data allows us to talk about such distances, but this is all, of course, inaccurate. ¯\_(ツ)_/¯

So… I think I haven’t forgotten anything. Then that’s all for today. Thanks for your attention, bye!