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hose270 · 2 years ago

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I remember the exact moment math clicked for me, not in a “I understand it” sense, but in an “I understand why this is meaningful” sense.

I was in calculus, and we were using integrals to calculate the area under a curve. The teacher showed us how to use that process to derive the formula for the volume of a cone—a formula I’d had to memorize five years before in geometry class. My mind was blown, not only because there was logic behind that seemingly arbitrary formula, but because I understood that logic.

It wasn’t the first time I’d understood something, but never before had something so incomprehensible been so quickly transformed into something so rational, and that moment of understanding still stands out in my memory six years later. It taught me that, with enough study and research, almost anything can be understood. Now, I haven’t used the formula for the volume of a cube in years, let alone to calculus necessary for deriving it, but I have used that principle of study and research, and that’s something that math taught me.

Are you willing to make a long personal post about how Math should be presented in an educational environment or in general conversation trying to convince the other participants about its daily usage. How it can advance a person’s problem-solving skills and approach in life.

I’m really good in Mathematics. I’ve given help for my classmates and friends about Math when they are having trouble or ask for it. But I have never been convinced of its importance outside of the classroom, outside of the test papers that gives me the variables to substitute in the given equation of that test of the day.

How can Math and it’s many properties relate back to everyday life in a casual manner?

Hm. Well, as someone who hasn't had to solve an antiderivative in years, my perspective on this is that the most important and widely-applicable skill math can teach you is the stuff behind the math - mostly the muscle-memory you get from proofs.

Math is, at its core, puzzles and logic and pattern-recognition. You learn a set of tools, you practice those tools on a set of simple problems until you get a feel for them, you are presented with a bigger problem, you recall which tools best applied to problems that are shaped like this, you break the problem down using your tools and eventually reduce it to something you know how to solve.

The fact of the matter is, the tools that are specific to branches of math don't really have much widespread use outside pure mathematics, and unless you go out of your way to keep using them you're likely to lose track of them. Studying math is not going to turn you into a super-calculator-wizard who can bounce stuff off the walls at perfect angles and do six-figure arithmetic in seconds, and I think some people feel overwhelmed at the assumption that that's what's expected of them if they learn math, and some other people feel cheated when they learn that that's absolutely not going to happen, because most writers don't know math and when they tell stories with math in them their best guess is it makes you a wizard.

I think the most advanced math I've used lately was trigonometry, and that was just because I was curious about how fast my plane was traveling relative to the sun's apparent movement at my latitude. We were flying back to the US from Iceland and we'd taken off at sunset, and we had been in that sunset for at least an hour by the time I got curious how the math worked out and started estimating our latitude, the circumference of the slice of the earth at that latitude, and correspondingly how fast we were flying vs how fast it was spinning to complete a full rotation in 24 hours. But even if the math involved didn't tap into any of the higher-level stuff I'd learned post-trig, those years doing proofs and figuring out which tools applied to which geometry meant that I could use the tools and my training applying those tools to calculate what I wanted to know, and confirm that our plane was actually outflying the sun when we were at iceland latitude, but as we curved south the sun's apparent relative movement (aka the rotational speed of that latitude of the earth) slowly accelerated until we were falling behind, landing right as the sun finally set. The math involved was high school level, but if I'd been given that problem in high school it would've taken more work and more stress to figure out how the tools I had needed to be applied to the problem I was facing. The years of practice I had tackling much more complicated proofs made the diagnostic process much faster.

I saw someone once analogize studying math to lifting weights. Where am I going to use this in real life? How often will I really be faced with two dumbbells that need to be lifted in three sets of twenty? Where am I going to apply the skill of holding a heavy thing straight out to one side of my body?

You don't lift weights because lifting weights is such a valuable and widely-applicable skillset, you do it because lifting weights makes you better at lifting everything.

You don't study math because math is going to fill your daily life with concepts that you need to prove true for 1 and for n+1 given true for n, or complex solids that you need to sum an approximate volume for, or a surplus of sunset plane flights that demand you calculate a bunch of cosines. You study math because it is the skillset of making things make sense. It trains you to break a huge, incomprehensible problem down into a series of small problems you already know how to solve. It lets you reach true and correct conclusions by starting from facts and transforming them through operations that preserve truth, and correspondingly that if you reach a false conclusion from these methods, then either the methods are flawed or the initial assumption is not as true as you believed. It teaches you to put two and two together and be confident, once you've double-checked your work, that you can say four.

This is stuff I use all the time in both my video research and my freeform writing. Building out a slow picture of how a story was told or changed over time involves finding the context it was created in, and reverse-engineering what parts of that context could have produced what standout portions of the story - what authorial or cultural bias results in this standout story element. Worldbuilding where I take two wildly disparate parts of the world, put them together and see what web of implications springs out of combining them, following the threads to new and interesting concepts that follow from what I've already established. Building a character arc by breaking down exactly what events are happening to them and what transformation each component will apply to the underlying character. If I want the story to go in a certain direction, what transformations do I need to apply to make that happen while still preserving truth? If I'm faced with a seemingly insurmountable problem, what methods can I use to break it down into bite-sized pieces?

This isn't something I think about most of the time. It's just how my brain works at this point, and I can't promise it'd work for anyone else. But thanks to all my years of hard work and training, my brain has been buff enough to solve every problem I've tangled with since graduation, and that feels pretty good.

#also #trigonometry is probably the only complex math I still use #and it’s almost never necessary #I spent hours building an intergalactic atlas for my worldbuilding #and I used sohcahtoa to figure out pre-existing distances #and the pythagorean theorem for calculating new distances #all for a spreadsheet no one else will likely never use lol #trig was the hardest unit for me to learn in math #so I had to work really hard to understand it #and now it’s the only math I remember how to do fairly well #so there’s probably a principle there too

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bubbloquacious · 2 years ago

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Not a mathy math ask, but you didn't specify what kind you want so here goes nothing. I was reading a paper titled 'the unreasonable effectiveness of mathematics in natural sciences' by Eugene Wigner who was a physicist. He was (if I understood it correctly) expressing a kind of surprise that mathematicians can arrive to a theory, or to an area of mathematics, without thinking of anything about the physical world, that later turns out to be the perfect theory behind a phenomenon in physics. Do you think that's surprising or could it be expected? what is your opinion about this situation, if you have any?

Well any answer to this I'd have to preface with the fact that I am not a scientist. I know the basics of physics, chemistry, biology, etc. but I am not at all trained in their history. That being said, the whole phrase 'unreasonable effectiveness' never struck me as all that apt. One way to characterize mathematics is as the study of consistent rules. If A, then B, that sort of thing. Science is the study of the world, and the way we get science to answer our questions is to think of rules that the world might consistently follow and then test whether they do in practice. It's not very surprising that mathematical models factor into this!

This doesn't answer the question, of course. Why is it that sometimes a strand of mathematical inquiry is pursued purely for the sake of itself, as intellectual curiosity, and then later on the developed theory was a perfect fit to formalize some new paradigm in physics? I'd be hard pressed to say anything new on the matter, I think. Sometimes though it's definitely because some mathematical theory (that of complex number, for example) is such a neat bundle of various fundamental mathematical ideas that it's almost inevitable that later models of various phenomena rely on it.

I really enjoy questions that ask 'why' certain things are modelled the way they are. Why is distance in the real world 'two-ish'? The Pythagorean theorem gives us that a distance between coordinate points can be calculated as the square root of the sum of the squares of the coordinate differences, but where do the squares come from? You kick the question once more down the road. The squareishness is because geometry may be defined in terms of a bilinear form: the dot product. But why does this (approximately) capture our notions of angle and distance in the real world? It's questions like this I think that get you to the heart of why certain mathematical theories find such nice homes in physical models. In a certain sense mathematicians and scientists are doing the same thing: we're all just exploring phenomena and seeing how they tick.

#math

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maryellencarter · 4 years ago

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jesus fuck. i went and explored some while waiting for my baby cows to breed, looking for a village, and i did not find any, so i finally looked at the map on chunkbase, and the closest four villages are all about a thousand blocks away from spawn. jesus murphy

just. how. i mean it's very nice that i got a trident from my very first drowned kill in this world, but without a villager i can't fucking put mending on it in order to heal it up and use it! i can't make an iron farm or basically anything. i could try to make a fucking *nether tunnel* to the nearest goddamn village, and bring back villagers and make a villager breeder, or i could go... hm.

there's a village at about 550 by 650 positive, and the closest jungle chunk to it is about 450 by 700 positive. of course we want to build in or near the jungle because that's the point of this spawn. so... hypothetically. if one was to pack up house and move all the way over to that jungle chunk sort of near a village. it'd still be about... *makes pythagorean theorem noises* something like eleventy-one blocks as the crow flies, according to my phone's square root calculator function, but even on foot i can do something like 4+ blocks a second, so that's like half a minute's quick trot on foot, way faster if one has a minecart or a good horse. my iron farm in the abandoned village seed was something like 127 blocks from my base camp so none of my tools sould interfere with it. i could probably just convert the village itself into my iron farm, or leave the village as the place for trading (it's a taiga village which are pretty visually nifty so it depends on what exactly the layout is and whether it is full of horrible ravines i would have to patch up) and build the iron farm 100 blocks away in a different direction.

i've never built any distance from spawn before. it's a little nerve-wracking, because if you don't have your spawn set on a bed -- say you're traveling to a woodland mansion and you have to pick up your bed each morning and then you die -- then you get sent back to your original spawn, not to where your base is built, whoch could be annoying.

maybe... hm. let's see. maybe before i leave, i should build a compass, find my original spawn, put a spare bed there and probably a chest with some food and handy tools, and make a note where it is relative to both the little base i've been building and my new near-village base.

i think it would be smart to finish getting all the bookshelves i need before i move. i'd want to pack, at minimum... the enchanting table, the lapis, the food, some stuff to replant my garden (so basically potatoes, wheat seeds, and sugarcane; we'll find cocoa beans along the way since we'll still be in a jungle), the diamond pickaxe, the iron pickaxe, the iron sword, a stack of cobblestone for tools, all the remaining torches (it's kind of a shame i used up so many on the cave systems around here but i wasn't expecting a thousand blocks overland to the nearest village!), all the remaining wood... might as well leave the animals in their pens, i can make more fencing later. bring a furnace, a crafting table, all the valuables like gold and redstone and diamonds.

gonna have to dig a new strip mine. nothing to be done about that. is the entire minecraft world just made of gravel under the surface? i guess we'll find out.

it'll be interesting to see what i can actually fit into my inventory and how many trips i have to make. (i did peep the woodland mansion coordinates and it's around -15,000 by 6870, so it's very much closer than the one in the abandoned village world, only like 16k blocks as the crow flies if my math is right. a lot of that is ocean too, which means fast traveling unless a drowned decides to throw a trident at my boat and dump me in the water, which reportedly can happen. i am so deeply uncertain that i want to tackle a woodland mansion in unpeaceful, though! they're very full of strong dangerous enemies who can kick your ass.)

#jt plays minecraft

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calebmatthew1 · 2 years ago

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[Infographic]Achieve Math Excellence: Unleash the Pythagorean Theorem Calculator

What is the Pythagorean Theorem?

The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

It can be expressed using the formula: a² + b² = c², where 'c' represents the length of the hypotenuse, and 'a' and 'b' represent the lengths of the other two sides.

Benefits of Using a Pythagorean Theorem Calculator:

Time-saving: By automating the calculation process, a Pythagorean Theorem calculator saves valuable time, especially when dealing with complex triangles or multiple calculations.

Accuracy: Manual calculations can introduce errors, but calculators provide precise results, reducing the risk of mistakes.

How to Use a Pythagorean Theorem Calculator:

Time-saving: By automating the calculation process, a Pythagorean Theorem calculator saves valuable time, especially when dealing with complex triangles or multiple calculations.

Accuracy: Manual calculations can introduce errors, but calculators provide precise results, reducing the risk of mistakes.

How to Use a Pythagorean Theorem Calculator:

Enter values: Input the lengths of the two sides (a and b) into the calculator.

Calculate: Click the calculate button to obtain the length of the hypotenuse (c).

Interpret results: The calculator will provide the precise length of the hypotenuse, allowing for accurate measurements and calculations.

Real-World Applications:

Architecture: Architects use the Pythagorean Theorem to ensure precise measurements for building foundations, angles, and diagonals.

Engineering: Engineers rely on the theorem for structural designs, determining distances, and creating accurate blueprints.

Conclusion

Allcalculator.net provides a user-friendly Pythagorean Theorem calculator that simplifies complex calculations and enhances understanding of right triangles. Some calculators are a powerful tool for students, professionals, or anyone curious about math, unlocking new possibilities and achieving math excellence.

#Pythagorean Theorem Calculator #Allcalculator #Financial Calculators #Math calculators #Fitness and Health Calculators

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finishinglinepress · 2 years ago

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NEW FROM FINISHING LINE PRESS: The Poet Who Loves Pythagoras by Fran Abrams

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The Poet Who Loves Pythagoras is a collection of light-hearted poems on such topics as algebra, fractions, Newton’s Third Law, inertia, Pi, and other math and science subjects you probably studied in school. Read deeper and it’s a commentary on life and love. Fran Abrams loves Pythagoras because his theorem always works, whereas life does not offer much that is certain. In her poem “Ice Cubes,” you’ll understand about relative density as the cubes float in your glass of scotch. Algebra helps you decide whether to buy that candy bar. Percentages are simply fractions with fancy symbols. With titles like “Poetry is a Word Problem,” “Define Infinity,” and “Solve My Life,” these poems will have you appreciating poetry, math, and science from a refreshingly different perspective. Poet Sandra Beasley says of this book, “Readers who prize the consideration of big questions, balanced against agile specificity of phrase, will delight in this quirky collection.”

Fran Abrams lives in Rockville, MD. She has had poems published online and in print in Cathexis-Northwest Press, The American Journal of Poetry, MacQueen’s Quinterly Literary Magazine, The Raven’s Perch, Gargoyle 74, and many others. Her poems appear in more than a dozen anthologies. In 2019, she was a juried poet at Houston (TX) Poetry Fest and a featured reader at DiVerse Gaithersburg (MD) Poetry Reading. In December 2021, she won the WWPH Winter Poetry Prize for her poem titled “Waiting for Snow.” In July 2022, her poem “Arranging Words” was a finalist in the 2022 Prime Number Magazine Award for Poetry. Her autobiographical book of poems titled I Rode the Second Wave: A Feminist Memoir was published in 2022 by Atmosphere Press. Please visit www.franabramspoetry.com.

PRAISE FOR The Poet Who Loves Pythagoras by Fran Abrams

The Poet who Loves Pythagoras is very funny at times, profound at others, and exceedingly well-done. Anyone who loves math or poetry or both will also love this book!

–Raima Larter, Author, Spiritual Insights from the New Science

In the aptly titled collection, The Poet Who Loves Pythagoras, Fran Abrams gives us a surprising perspective: the poet and the mathematician. In the first poem “Pythagorean Theorem,” she writes, “Few things in life are certain,” but we are certain of her talent and craft. At this convergence of math and poetry, Abrams strives for precision and economy, which is often the case in mathematics. She questions what we know as true and pure and opens its relationship to equations and proof. Whether she is discussing trying to find “true love” or the shortest distance between A to B, Abrams wants us to consider life’s puzzles—remembering what can stabilize the chaos of the everyday. She asks us to consider Pythagoras and his theorems and trust them with our hearts.

–Jona Colson, Author, Said Through Glass and Co-president, Washington Writers’ Publishing House

Equal parts clever and vulnerable, The Poet Who Loves Pythagoras wields the vocabulary of mathematics and science like a blade. Fran Abrams reveals a wry humor in poems such as “Solve My Life,” which makes available a series of calculations: “The number of siblings I have is equal to / the number ounces in a quarter pound…The number of children I have brought into the world / is the same as half the number of siblings I have…The number of pounds I have gained and lost and gained during my life / is higher than the highest speed recorded at a NASCAR race.” Parallel lines engage loneliness; a road trip becomes a matter of counting the miles, literally. Readers who prize the consideration of big questions, balanced against agile specificity of phrase, will delight in this quirky collection. To quote an Abrams title that playfully promises a commercial device to harvest extra minutes: “Save Time! Order Today!”

–Sandra Beasley, Author of Made to Explode

Please share/repost #flpauthor #preorder #AwesomeCoverArt #read #poems #literature #poetry #math

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precastersblog · 3 years ago

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Why we opt for precaster for industrial laser distance measuring module?

The rate and level of complexity that new hand-held technologies are now coming available, is nothing short of amazing. So after recently trying out a new precaster for industrial laser distance measuring module, I have but one comment to make, and that is "what will they come up with next"?

How Does the Device Work?

The first thing I had to see was how the thing functioned, so I set about doing the explore to find out. It turns out that as multifaceted as the expertise is, the way the thing functions is quite simple. It mostly measures the time it takes for the light from the ray to leave the device and bounce back.

The Precaster Laser Measure Does All the Work for You

This eradicates measuring tape imprecisionsas there's no tape bending, loose tip or untrustworthy set of hands holding the tape at the other end. Just fact and shoot, and the measurement is exhibited in precaster or standard terms, and also automatically logged, so there's no more requirement for a pencil and paper.

It Performs Several Calculations

It gets way well than that yet. For instance, the precaster for industrial laser distance measuring module similarly performs numerous calculation tasks, like coming up with rectangular or cubic volumes. In fact, it can even fix length of the slope of a right triangle. It's called the Pythagoras function.

If Pythagoras Individual Knew What It All Would Main to

Pythagoras was a mathematician who existed a few centuries back, who came up anactual clever mathematic formula for defining the length of the hypotenuse of any right triangle. It's termed the Pythagorean theorem. A formed, plus B squared, equals C squared.

The Length of the Hypotenuse of a Right Triangle

If it all sounds too perplexing, just think of it this way. If a carpenter requirement to control the length of a roof rafter, without ascending up a ladder and sagging off the ridge while holding a tape, he now has alternativechoice. He can use the precaster for industrial laser distance measuring module to regulate the distances to the internal of the building, and to the crest.

Tons of Uses on Today's Construction Site

That's all he requirements because with those two lengths, this maneuver can spit out the length of his rafter as that is the length of the hypotenuse of the right triangle. Also, that same carpenter can use the device to speedily and easily take any number of other measurements athwart large open spaces that used to need a ladder and extra set of hands.

It Cuts Time and Materials Waste Too

Then again there are limitless uses for a laser measuring device on today's job site, commencement with the surveying of the stuff, and all the way through to manipulative how much paint is required for the building. The precaster for industrial laser distance measuring module not solitary cuts time, but it also cuts waste too, by empowering far tighter and dependable measurements.

#precaster for industrial laser distance measuring module

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calcurator · 5 years ago

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Jobs That Use the Pythagorean Theorem

As a math student, the Pythagorean Theorem shouldn’t be new to you. After all, this is one of the most popular and easiest theorems that serves a wide range of uses.

Simply put, and according to the Pythagorean Theorem, the sum of the squares of the lengths of the two legs of a right triangle is equal to the square of the length of the hypotenuse.

Discover the best online calculators.

The reality is that while some students love math, others simply hate it. That’s a fact. And if you belong to the latter group, then you may be wondering why you should learn this Pythagorean Theorem and how it may be useful for you in the future.

One of the things that you need to know about the Pythagorean Theorem is that a lot of jobs actually use the Pythagorean Theorem. Unlike other topics that you need to learn at school, the Pythagorean Theorem is one that can serve you on your future depending on the carer that you choose.

Jobs That Use the Pythagorean Theorem

#1: Jobs In Management:

In case you are considering a career in management, then you want to ensure that you understand the Jobs That Use the Pythagorean Theorem well.

The reality is that the Jobs That Use the Pythagorean Theorem is very used by a wide range of managers including engineering managers, construction managers, information systems managers, and even natural science managers.

Check out our Pythagorean Theorem calculator.

#2: Jobs In Agriculture:

While you may think that if you want a career in agriculture that you don’t need math at all, then you are wrong. The reality is that from farmers to environmentalists and even gardeners use maths a lot on a daily basis.

Just think of the times when they need to draw precise lines to determine growing spaces, for example. And the truth is that no matter if you intend to work directly with trees, plants, animals or food crops, you need math and you need a good understanding of the Pythagorean Theorem.

Looking for the best Pythagorean Theorem calculator.

#3: Cartographers And Surveyors Jobs:

These jobs are usually regarded as tasks that use a lot of mathematical tools. After all, you need to know how to determine distance and length.

In case you don’t know, cartographers and surveyors are the ones that measure and map properties, they set official water, land, and air boundaries for the government, businesses, and homeowners. So, they want to make sure that they can do their work fast and this is why the Pythagorean Theorem and other math theorems and tools are needed.

#4: Production Workers:

While this is a very wide field of jobs, the truth is that most production workers need to have a good grasp of math especially of the Pythagorean Theorem. For instance, when creating specialized items for a company that produces tractor parts, the ability to measure across both long and short distances makes the process that much easier.

Looking for the easiest Pythagorean Theorem calculator?

#5: Architects:

As you probably already know, this is the type of job that uses a lot of math. After all, architects can’t deal with the risk of measuring things wrong and have a building collapse.

The post Jobs That Use the Pythagorean Theorem appeared first on CalCurator.org.

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mathematicianadda · 6 years ago

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Thanksgiving, football, Black Friday, and giving (11 activities)

Macy's new balloons - Students measure Macys's new balloons in handler-height, taxicab widths, stories tall, and bicycles long. 5.MD, 6.RP.A, 6.SP, 7.RP, 7.G.A, 7.G.B, 8.G

Not enough mashed potatoes - Use Brian's famous mashed potatoes recipe to practice changing decimals to fractions; calculating ingredient measure for various-sized Thanksgiving gatherings; have students explain their reasoning; and to have students figure out how many servings 7½ pounds of potatoes would make. 5.NF.6 , 5.NF.6 , 6.RP.1 , 6.RP.2 , 6. RP.3 , 7.RP.1

Macy's Thanksgiving Day parade - Students study a map of the Macy's Thanksgiving Day parade, describe, measure and hypothesize why this route was chosen. Then they calculate how long each band will be marching and at what time they will arrive at the finish. Students even approximate the volume of two parade balloons including the Pikachu balloon, and from five year's ago, the Wizard of Oz balloon. 4.NBT.4, 4.MD.1, 4.MD.2, 5.NBT.6, 5.MD.1, 5.MD.5b, 6.NS.3, 7.NS.3, 7.G.1, HSG.MG.1

How should I cook my turkey? - Students judge timing, cost, tastiness, and quantity necessary as they plan for the feast. 4.MD.1, 5.NBT.7, 4.MD2, 6.RP.3, 6.NS.3, 7.NS.3 Great video on a deep frying fire with William Shatner.

4th down - Should you punt kick or go for a field goal? This is two activities. One is on graph reading. This is perhaps suitable for younger students. The other activity is on data analysis and the creation of the chart shown to the right. 7.NS, 7.SP.C.7, HSS.MD.A.2, HSS.MD.B.5, HSS.MD.B.6, HSS.MD.B.7

Watson Saves - Watch the video with your class and use our activity to motivate students to figure out who ran a greater distance by using the Pythagorean Theorem. In the video Teddy Bruschi says that Watson must have ran about 120 yards, maybe even more. Use the video and/or our activity to see if Teddy’s estimate is about right. 8.G.7, G-SRT.8

NFL Home field advantage Students use an infographic to compare NFL team home and away wins. Students consider the best home team, the best away team and consider if NFL teams really do seem to have a home field advantage. 6.RP.1, 6.RP.2, 6.RP.3, 7.SP.4

Canstruction This is a 3-act activity about an annual display of creativity, engineering, and design as artists contribute cans of food for the shelters and food banks of their city. Students analyze, look for patterns, discuss solutions, and finally quantify the number of cans. 4.MD.3, 6.EE.1, 5.MD.5, 7.G.6, HSF.LE.2, MP2, MP3, MP7

Black Friday - Students calculate savings in dollars and percents as they analyze this year's sales. 6.RP.3 , 7.EE.2, 7.EE3

Delicious pumpkin pie - Students estimate, multiply fractions and use proportional reasoning as they calculate the ingredients necessary for my wonderful pie. 4.MD.1, 4.NF.4, 5.MD.1, 5.NF.4, 5.NF.6, 6.RP.2, 6.RP.3

Consumer Spending - Students look for patterns in an historical view of the times of year that we spend money. They look for spikes and drops in spending and hypothesize which trends will repeat and which movements are a one-time event. 6.SP.5, 8.F.5, HSS.IC.6, HSS.ID.3

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calebmatthew1 · 2 years ago

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From Theory to Reality: Dynamic Pythagorean Theorem Calculator

Allcalculator.net, where theory meets reality with the dynamic Pythagorean Theorem Calculator In the realm of geometry, the Pythagorean theorem is a fundamental concept that forms the backbone of countless calculations. Understanding this theorem is essential for solving a wide range of geometric problems, but what if there was a tool that could simplify the process and provide interactive solutions

Exploring the Dynamic Pythagorean Theorem Calculator

Allcalculator.net has developed a remarkable online calculator that takes the Pythagorean theorem to new heights. Gone are the days of manual calculations and lengthy problem-solving. This dynamic calculator allows you to input the lengths of two sides of a right triangle and instantly computes the length of the third side, also known as the hypotenuse.

Interactive Features

One of the most impressive aspects of the dynamic Pythagorean Theorem Calculator on Allcalculator.net is its interactive nature. As you enter the values of the two sides, the calculator updates in real-time, displaying the result as soon as you provide the inputs. This interactive feature enables you to experiment with different values and instantly see the impact on the triangle's dimensions.

Step-by-Step Solutions

While obtaining the final result is undoubtedly convenient, the dynamic Pythagorean theorem calculator on Allcalculator.net goes beyond that. It also provides step-by-step solutions, guiding you through the calculation process. This feature is particularly helpful for learners who want to understand the theorem's application and the methodology involved in solving the problem.

Also Read: Discover The Power Of Pythagorean Theorem Calculator: Simplify Your Math

User-Friendly Interface

Allcalculator.net ensures that their dynamic Pythagorean theorem calculator is user-friendly and accessible to individuals of all skill levels. The interface is intuitive and straightforward, allowing you to input the side lengths effortlessly and retrieve accurate results promptly. Whether you are a student, a professional, or an enthusiast, this calculator caters to your needs effectively.

Practical Applications

The Pythagorean theorem finds applications in various fields, such as architecture, engineering, and physics. With the dynamic Pythagorean theorem calculator from Allcalculator.net, you can quickly solve problems related to distance, right angles, and triangle measurements. Its versatility and simplicity make it an indispensable tool for professionals and students alike.

Also Read: Pythagoras's Theorem - Discovering the Amazing Power of Math

Conclusion

Allcalculator.net has brought the Pythagorean theorem to life with its dynamic calculator, making complex geometric calculations a breeze. From its interactive features and step-by-step solutions to its user-friendly interface, this tool empowers users to explore and understand the theorem in a practical way. Visit Allcalculator.net today and experience the revolution of solving geometric problems with ease.

Allcalculator.net offers a wide range of other calculators to simplify complex mathematical concepts and provide instant solutions for various disciplines.

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felord · 6 years ago

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SOLVED: Functions and Loops

1 Part I: Function Writing Drills In this section you will write a number of functions that do not need turtle graphics. For each function you will write code in main to test the function and convince yourself it works properly (like we did in the fruit example in lecture). There are no speciﬁc requirements on what you should put in main to test each function. It is ��ne to comment out the test code you have in main for functions you’ve already ﬁnished. Create a new ﬁle called “functions.py”. In the ﬁle write the following functions (10 points each): 1.) Write a function called print word that takes two parameters. The ﬁrst is for an integer (assume it will always be non-negative). The second is for a string. The function will print the given string the given number of times each time preceded by a count. See the examples below for the format of the output (i.e. if you call your function with the same arguments as in the examples your output should look like the output in the examples). • Here are some examples of calling the function with diﬀerent arguments (The code executed is in blue, the output produced is in green): print word(3, 'banana') 1 -- banana 2 -- banana 3 -- banana print word(4, 'mississippi') 1 -- mississippi 2 -- mississippi 3 -- mississippi 4 -- mississippi • Note: look carefully at the output in the examples above. The function is printing more than just the string. • Write code in main to test this function. Don’t just test it on the arguments given in the examples. Test it on enough diﬀerent values to convince yourself that it works properly. 2.) Write a function called bacteria that will print out information showing the number of bacteria in a Petri dish at equal time intervals. The function takes two parameters. The ﬁrst is an integer giving the number of minutes it takes for a bacterium to split into two new bacteria. The second is an integer giving the number of bacterial generations to include in the output. Assume you always begin with a single bacterium in the dish and every bacterium always splits into exactly two bacteria at the end of each time period. 2 • Here are some examples of calling the function with diﬀerent arguments (The code executed is in blue, the output produced is in green): bacteria(10, 5) after 10 minutes: 2 bacteria after 20 minutes: 4 bacteria after 30 minutes: 8 bacteria after 40 minutes: 16 bacteria after 50 minutes: 32 bacteria bacteria(21, 3) after 21 minutes: 2 bacteria after 42 minutes: 4 bacteria after 63 minutes: 8 bacteria • Write code in main to test this function. Don’t just test it on the arguments given in the examples. Test it on enough diﬀerent values to convince yourself that it works properly. 3.) Write a function called convert to copper that takes three integer parameters. The ﬁrst represents a number of gold coins. The second represents a number of silver coins. The third represents a number of copper coins. The function will print the numbers of each type of coin followed by the total value of all of the coins when converted to copper. The exchange rate for coins1 is given in the following table: 10 copper pieces (cp) = 1 silver piece (sp) 20 silver pieces (sp) = 1 gold piece (gp) • Here are some examples of calling the function with diﬀerent arguments (The code executed is in blue, the output produced is in green): convert to copper(5, 10, 7) 5 gp, 10 sp, 7 cp converted to copper is: 1107 cp convert to copper(15, 23, 12) 15 gp, 23 sp, 12 cp converted to copper is: 3242 cp • Write code in main to test this function. Don’t just test it on the arguments given in the examples. Test it on enough diﬀerent values to convince yourself that it works properly. 4.) Write a function called convert from copper that takes a single integer parameter representing a number of copper pieces. The function prints out 1Gygax, G. Players Handbook (1978) 3 the number of gold pieces (gp), silver pieces (sp), and copper pieces (cp) you would end up with if you ﬁrst converted as many of the initial copper pieces to gold as possible and then converted as many of the remaining copper pieces as possible to silver pieces. • Examples of calling the function with diﬀerent arguments (The code executed is in blue, the output produced is in green): convert from copper(200) 200 copper pieces is: 1 gp, 0 sp, 0 cp convert from copper(1107) 1107 copper pieces is: 5 gp, 10 sp, 7 cp convert from copper(3242) 3242 copper pieces is: 16 gp, 4 sp, 2 cp • Write code in main to test this function. Don’t just test it on the arguments given in the examples. Test it on enough diﬀerent values to convince yourself that it works properly. 5.) This function requires a bit of preparation ﬁrst: Try entering each of the following in a Python shell: print('Hobbit' * 10) print('Hobbit' * 2) print('Hobbit' * 1) print('Hobbit' * 0) Using what you just learned, write a function called repeat word that has three parameters. The ﬁrst is for a word (a string). The second is for an integer representing a number of rows. The third is for an integer representing a number of columns. The function prints the word in a number of rows equal to the value of the rows parameter and each row contains the word repeated a number of times equal to the columns parameter, as shown in the examples below: • Examples of calling the function with diﬀerent arguments (The code executed is in blue, the output produced is in green): repeat word('Goblin', 3, 5) GoblinGoblinGoblinGoblinGoblin GoblinGoblinGoblinGoblinGoblin GoblinGoblinGoblinGoblinGoblin 4 repeat word('Kobold', 5, 3) KoboldKoboldKobold KoboldKoboldKobold KoboldKoboldKobold KoboldKoboldKobold KoboldKoboldKobold • Write code in main to test this function. Don’t just test it on the arguments given in the examples. Test it on enough diﬀerent values to convince yourself that it works properly. 6.) Using what you learned in the previous question, write a function called text triangle that takes an integer parameter and prints X’s in a triangle shape as seen in the following examples: • Examples of calling the function with diﬀerent arguments (The code executed is in blue, the output produced is in green): text triangle(3) X XX XXX text triangle(10) X XX XXX XXXX XXXXX XXXXXX XXXXXXX XXXXXXXX XXXXXXXXX XXXXXXXXXX • Hint: think about how many spaces you will need in front of each X. • Be careful, make sure you end up with the correct number of X’s! • Write code in main to test this function. Don’t just test it on the arguments given in the examples. Test it on enough diﬀerent values to convince yourself that it works properly. 7.) This function requires a bit of preparation ﬁrst: In other programs we’ve used the turtle module (import turtle) to give us access to turtle graphics functions. The math module gives us access 5 to a number of useful math functions and constants. Add the following import statement to the top of your ﬁle (before your ﬁrst function deﬁnition): import math The math module has a variable called pi that contains the value of π (3.14...) carried out to many decimal places. Anywhere you need that value use: math.pi Write a function called surface area of cylinder that takes two parameters. The ﬁrst is a ﬂoat representing the radius of a cylinder. The second is a ﬂoat representing the height of a cylinder. The function calculates and prints the surface area of a cylinder with the given radius and height. Recall from math: The area of a circle = πr2 (where r is the radius of the circle) The circumference of a circle = 2πr If you’re having trouble, imagine cutting the top and bottom oﬀ of a soup can. Then slice up the side of the can and lay it out ﬂat. • Examples of calling the function with diﬀerent arguments (The code executed is in blue, the output produced is in green): surface area of cylinder(10.0, 10.0) The surface area of a cylinder with radius 10 and height 10 is 1256.6370614359173 surface area of cylinder(3.0, 1.0) The surface area of a cylinder with radius 3 and height 1 is 75.39822368615503 surface area of cylinder(0.0, 10.0) The surface area of a cylinder with radius 0 and height 10 is 0.0 • Write code in main to test this function. Don’t just test it on the arguments given in the examples. Test it on enough diﬀerent values to convince yourself that it works properly. 8.) The math module has a function called sqrt that returns the square root of its parameter. It is used like this: math.sqrt(100). 6 Imagine you are ﬂying a kite and the kite gets caught in the top of a perfectly straight palm tree. The string pulls free from the kite leaving you with the full length of string and your kite stuck in the tree. You measure the distance from you to the base of the tree. Given the length of the kite string and the distance from you to the base of the tree you can calculate the height of the tree using the Pythagorean Theorem: a2 + b2 = c2 In this case a is the distance from you to the tree, b is the unknown height of the tree, and c is the length of the kite string. Write a function called tree height that takes two parameters. The ﬁrst is a ﬂoat representing the distance from you to the base of the tree. The second is a ﬂoat representing the length of the kite string. The function will calculate and print the height of the tree as shown in the examples below. • Examples of calling the function with diﬀerent arguments (The code executed is in blue, the output produced is in green): tree height(300, 500) Kite string: 500 Distance: 300 Height: 400.0 tree height(100, 141.421356) Kite string: 141.421356 7 Distance: 100 Height: 99.99999966439368 • Write code in main to test this function. Don’t just test it on the arguments given in the examples. Test it on enough diﬀerent values to convince yourself that it works properly. 9.) Note: since we are not using turtle graphics in this program your main function does not need: input('Enter to end') but you do still need the last two lines: if name == ' main ': main() 10.) Verify that your documentation makes sense and that you’ve added documentation to each of your functions. 11.) Verify that your program works 12.) Upload your ﬁle to the Program 3 dropbox folder on D2L 2 Part II: Shape Chooser (20 points) Create a new ﬁle called “shapechooser.py”. In the ﬁle write a program that does the following: 1.) Ask the user how many polygons to draw. 2.) For each of the polygons perform the following steps: i.) Ask the user how many sides the polygon should have. ii.) Ask the user what color to use. iii.) Ask the user for the length of a side of the polygon. iv.) Using the values you collected from the user’s input, set up the turtle and draw the desired polygon • Copy your polygon function from your last homework into this ﬁle 3.) Note: remember that user input will be a string, when you need a diﬀerent type you’ll need to convert 4.) Here’s an example run of the program (see below for screenshots taken after each shape is drawn) (Output is in green, user input is in turquoise): 8 Enter the number of polygons you’d like to see: 3 Enter the number of sides: 4 Enter the color: red Enter the side length for your polygon: 50 Enter the number of sides: 3 Enter the color: green Enter the side length for your polygon: 100 Enter the number of sides: 5 Enter the color: blue Enter the side length for your polygon: 200 Enter to end 5.) Here are screen shots taken during the example run: 9 10 11 6.) Verify that your documentation makes sense and that you’ve added documentation to each of your functions. 7.) Verify that your program works. 8.) Save your ﬁle (e.g. to your Locker) 9.) Upload your ﬁle to the Program 3 dropbox folder on D2L Read the full article

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jacewilliams1 · 6 years ago

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Two on the runway – what would you do?

It was a bright spring day in Central Ohio and my in-laws had come from New York to visit my wife and me for a few days. I had often spoken of flying with my father-in-law, but until now we had not had the chance to go up together. The time had come, and he was eager to see me do my thing. I reserved a Warrior at the Ohio State University Airport (KOSU), my home base, and set out a plan that would give us a couple of hours in the sky over the fields of central Ohio.

We would do a couple of touch-and-goes; I would demonstrate a short and soft field take-off for him; and, depending on how he felt, I might even do a few steep turns just to give him that sight picture as well. Nothing crazy – just a short introduction to the types of things that private pilots are required to demonstrate on check rides and flight reviews. He had his GoPro camera ready, so we set out for the airport. My plan for that day included non-towered airports: we would head southwest toward Madison County (KUYF), from there stop at the Grimes Airport in Urbana (I74), perform a couple more landings at Delaware (KDLZ), and then head back to KOSU.

Grimes Field (I74) is a great airport to visit – but only if you can land first.

Madison County was devoid of traffic, which is not unusual for this small strip. A few instructors take their students to KUYF for pattern practice sometimes, but in general it is a pretty quiet little airport. As I overflew the field, circled over a pasture, and entered the downwind, making my calls on the CTAF when appropriate, I began to explain to Peter everything that I was doing. Our approach to landing was smooth, I put our little bird down with no problem, and we exited the runway. As we taxied back for departure, I told Peter that we would now do a short-field takeoff and head toward Grimes, where we would make a pit stop and grab something to drink from the airport diner.

The short flight from KUYF to I74 was uneventful. I climbed to 3000 MSL (around 2000 AGL) and began to make my calls on the CTAF within just a few minutes. At five miles southeast I made my second call, and then again at two miles to let everyone know that we were approaching the left downwind for runway 20. Once established on the downwind, I called again, and then on my base turn, and yet again when I turned final – the standard procedure. Using the landmarks that my former instructor and I had used to mark off the pattern at I74 on one of the numerous flights he and I had made there, I knew when I turned that we were somewhere between a half-mile and three-quarter mile final.

Within a few seconds of my announcement, as I was making my corrections for the light crosswind blowing across the field, a scenario that my former instructor and I had talked through several times became real right before my eyes – a pilot on the ground announced that he was departing runway 20. I saw him move from the hold short line onto the runway, and I announced that I was about to execute a go-around – by this point I was well within half a mile of the end of the runway. He immediately responded, “Don’t go around! You’ve got plenty of room to land!”

And that’s exactly what happened – I did not go around; the other pilot did not stop moving from the moment he crossed the hold-short line; he rolled down the runway and lifted off just before I reached the “piano keys” at the end of runway 20. I made a smooth, yet nervous, landing, taxied off, and said a few choice words under my breath as Peter and I walked into the airport terminal.

FAR 91.113(g) states that, “Aircraft, while on final approach to land or while landing, have the right-of-way over other aircraft in flight or operating on the surface […]” The text continues by stating that an aircraft on final cannot force another aircraft off the runway if it “has already landed and is attempting to make way for an aircraft on final approach.” The second part of this regulation seems to apply to two aircraft landing on the same runway, one ahead of the other that is then expected to exit the runway before the other touches down.

The first part of the regulation, however, indicates to me that I, less than half a mile from the end of the runway at the moment the other pilot made his announcement, had right-of-way and that the other pilot should not have entered the runway for departure. If I had called a two-mile final or even a one-mile final, I would not have become so upset over the situation. After all, in those circumstances there is plenty of time and space for the pilot in the air to make a reasonable decision regarding the actions of a pilot on the ground.

Nor would I have become as nervous about the situation if I74 were a towered airport. We know, for example, that at towered airports ATC permits a Category I aircraft such as a Warrior to land on the same runway from which another Category I aircraft (a C-172 in this case) is departing, as long as 3000 feet of separation are maintained.

What would you do?

However, at a non-towered airport, where pilots alone – without the help of ATC – are making the decisions, it seems unwise for an aircraft to take the runway when another is on a final leg of less than a mile. Is there any way to ensure that at least 3000 feet separate the two aircraft? An aircraft half a mile has a horizontal distance of approximately 2640 feet from another aircraft sitting at the end of the runway. If we really want to be technical, using the Pythagorean Theorem we find that an aircraft entering the final leg at 500 feet AGL, one-half mile away, is around 2687 feet from the end of the runway. Whichever way we want to calculate it, there are fewer than 3000 feet separating the two aircraft.

I know that daring pilots will always exist, and many will do dangerous things that have no lasting negative results. The situation I have just described does not present the level of danger that certain high-risk maneuvers might present. However, in this case both the pilot who decided to take the runway and the pilot on final (me) crossed the limits of what should be considered safe. The pilot on the ground made a decision quite possibly guided by the “get-there-itis” that we are told over and over by instructors to avoid. He assumed that he would have no mechanical issues before taking off and that he would, in fact, get off the ground before I touched down.

I made the same assumption. Reacting to the other pilot’s advice not to go around, I decided to continue with a landing that, in retrospect, I should not have performed. What if that C-172 had experienced engine failure or had blown a tire and veered off the side of the runway? Would I have had enough time and distance to get back off the ground without crashing into his backend, clipping his wing, or catching my landing gear on his rudder? Would I have been able to slow down quickly enough to taxi off the runway without flipping my own plane over in the process? These are, of course, hypotheticals that cannot be answered but that, nonetheless, should be considered.

My father-in-law and I made it back to KOSU that day with no problem, and he bragged to everyone about my professional “pilot’s voice” on the radio. In the end I felt good about the flight, in general, and his comments boosted my ego temporarily. But I have thought through that one part of our flight many times since then, and all of those times I have told myself that I should have gone around, that I should not have attempted that landing.

Speaking of non-towered airport operations, Swayne Martin says, “Plan to land and takeoff with the runway environment fully clear.” Maybe I’m a little too paranoid or maybe I’m a little too cautious, but I prefer that runway environment to include not just the pavement but also the imaginary centerline stretching out into the sky for a mile in both directions.

The post Two on the runway – what would you do? appeared first on Air Facts Journal.

from Engineering Blog https://airfactsjournal.com/2019/08/two-on-the-runway-what-would-you-do/

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things-i-need-to-know · 7 years ago

Video

youtube

Euclidean distance is the straight line distance between two points in the Euclidean space.

This distance can be calculated using Pythagorean theorem by connecting the two points as the hypotenuse of a right angle triangle – getting the length of the two other sides (catheti) – then adding the two sides squared.

New word: In a right angle triangle, the sides opposite of the hypotenuse is known as the catheti.

https://www.khanacademy.org/math/basic-geo/basic-geometry-pythagorean-theorem/pythagorean-theorem-distance/v/example-finding-distance-with-pythagorean-theorem

Code - Work In Progress

def ecludian_distance(c1, c2): hypothenuse = c1**2 + c2**2 distance = math.sqrt(hypothenuse) print distance

# Todo c1 and c2 are the lengths of the catheti - learn the formula to get the lengths given the xy coordinates of two points.

http://codepad.org/ttkNdqWI

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elizabethspeciale-blog · 8 years ago

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DBM 449 Laboratory Procedures Ilab 4 Answers

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Laboratory Procedures DeVry University College of Engineering and Information Sciences

I. OBJECTIVES

Understand and become familiar with current capabilities and limitations of the OpenGIS implementation in MySQL.

Learn to create, update, and use spatial indices.

Explore practical approaches to calculating distances between points on the Earth’s surface.

Understand fundamentals of geotagging.

Create stored procedures to determine real-world distances, and to process spatial queries returning result sets of data points within a bounding rectangle.

Explore visualization of GIS data.

II. PARTS LIST

EDUPE-APP Omnymbus MySQL Environment (https://devry.edupe.net:8300/) and/or:

MySQL (dev.mysql.com/downloads)

III. PROCEDURE

The argument could be made that Business Intelligence (BI) and Data Analytics revolutionized Online Analytical Processing (OLAP) by making it simple for users to traverse, examine, and visualize different aggregations of data over the dimension of time. Geographic Information Systems, once an arcane, rare, expensive, and highly specialized type of information system, have brought about a similar revolution using the spatial dimension. As these systems have become affordable and entered the mainstream—indeed, they are now ubiquitous—they have also become mainstream; or perhaps it would be more accurate to say that mainstream DBMS systems have come to commonly adopt and integrate the specialized data structures and algorithms required to implement spatially enabled, data-driven systems at will.

In this laboratory exercise, you will create a GIS-enabled database by implementing a spatially indexed table, populating it with spatially encoded data, and creating stored procedures to provide augmented functionality to determine distances between points, and to process queries returning results containing points within spatially defined boundaries. Finally, you will learn to express and explore spatial data in its most natural and intuitive form: visually displayed as maps and plots.

This lab may be completed using MySQL running on either your own computer, or the DeVry iLab. In either case, it is presumed that you will begin the initial lab step AFTER addressing any necessary routine housekeeping chores, such as creating an appropriate schema (e.g., DBM449LAB2), and creating any necessary user accounts, permissions, and so on.

Note: At the time this lab was written, the full OPENGIS standard was not implemented in the current production release of MySQL, but new features were being added with each point release of MySQL. It is entirely possible—in fact, quite likely—that improved OPENGIS compliance, including functions for distance calculation for spherical projections (e.g., points on the Earth’s surface) and circular proximities (e.g., “within radius of”) will become built-in to the MySQL database. However, as the study of the underlying mathematical and topographical principles needed to implement non-planar distance calculations, and for determining envelope or bounding box point results are a very worthwhile study, you should implement your own stored procedures for these functions, rather than substituting any built-in capabilities that become available. You may, however, repeat steps using such features as available, in order to compare and study the similarities and differences between your calculation methods and those later implemented as part of the OPENGIS API.

Important Further Note: At the time of this writing, spatial indices are supported ONLY in the MyISAM storage engine, and not in the InnoDB or other storage engines. BE SURE TO CREATE YOUR DATABASE TABLE FOR THIS LAB USING THE MyISAM STORAGE ENGINE!

Designing a Spatially-enabled Table, and Creating a Spatial Index

Create the table indicated in the following ERD.

Figure 1

Be sure you have first addressed the assigned research for this week’s unit involving Spatial Indices, and then use the following DDL to create a spatial index on the table just created:

CREATE SPATIAL INDEX `location` ON `Points` (`location` ASC);

Paste the complete SQL Data Definition Language (DDL) you used to create this table and index into your lab report.

Choose a point of interest (e.g., your house, your local DeVry campus, etc.), and at least three additional points within 20 miles, and three additional points more than 40 miles from the first point. For example, I chose my house, and three favorite restaurants in town, and three favorite restaurants in a distant town where I used to live. Using Google Maps or other service capable of converting street addresses to geographical (longitude and latitude) coordinates with good precision, note the geolocation of each point. Record this data in your lab report.

From your research, you should anticipate that you cannot simply insert these values directly. Model your insert statements for the data to be inserted into your Points table on the following example.

INSERT INTO Points (name, location) VALUES ( ‘point1’ , GeomFromText( ‘ POINT(31.5 42.2) ‘ ) )

CHECKPOINT QUESTION: Explain what the GeomFromText() function does, and why it is necessary to use this? Paste your response into your lab report.

Run your insert statement(s) to add the data to the Points table. Paste a screen shot showing your SQL statement AND result into your lab report.

Displaying Spatial Data in Human-readable Form

Attempt to retrieve all of the table’s contents using a SELECT * statement. You should find that this does not produce readable results. Your results may resemble the following.

Figure 2

CHECKPOINT QUESTION: Why does this query not produce the results you might typically expect from a SELECT * statement? How can the AsText() function be incorporated into a query returning every field in the table in a readable format? Paste your response into the lab report.

Execute the query you composed in the previous step, and paste a screenshot of the results into your lab report. The results should be similar to the following.

Figure 3

Calculating Distances on Earth’s Surface (Spherical, or Nonplanar Distance Calculation)

CHECKPOINT QUESTION: Your assigned research and graded threaded discussion questions this week should quickly lead you to discover that although the Pythagorean Theorem is marvelously useful for calculating the distance between points on a Cartesian planar surface, on a curved surface (such as the surface of the Earth), the further apart two points reside from one another, the greater is the error that results from misapplication of this formula to a curved (in this case, roughly spheroidal) surface. Better (less imprecise) results can be obtained by making use of the Great Circle Formula, haversine formulas, and cosine transforms. You will need to select and appropriate formula, and compose a stored procedure which can be used to calculate the geographic distances between points in your table. You will also need to use a coefficient or conversion factor so that the units of the results are expressed appropriately (e.g., kilometers, meters, miles, yards, feet, etc.), and with reasonable precision. Record your determination of the formula you will use, the reason you believe this is a good approach, and discuss both the degree of precision/error to be expected, and the units you elected to use for your measurement, and why. Record your answer in the lab report.

Compose and install your stored procedure or function for calculating geographic distance, into the database. Take a screen shot showing your SQL statement, and the result showing that the procedure was successfully created. Paste this into the lab report.

Spatial Queries: Retrieving Data Points Within a Bounding Polygon

CHECKPOINT QUESTION: Your assigned research and graded discussion questions this week will inform your understanding of the use of a bounding box or bounding polygon used to return all spatially indexed points stored in the database which reside within the area defined by the boundary. Parameters for a bounding rectangle can minimally be specified using the vertex points of either diagonal. For example, the upper-left corner, and the lower-right corner. In such case, all points with a horizontal value equal to or between the x-axis elements of the bounding points, that also have vertical value equal to or between the y-axis elements of the bounding points, reside within the qualifying region. You will want to easily be able to center this bounding rectangle on a point which you choose. How will you accomplish this? Design and document the stored procedure or function you will use to implement a bounding rectangle function, and paste your analysis and design into the lab report.

Install the stored procedure or function you designed in the previous step into the database. Create a screen shot showing the SQL used to create the procedure, and the result of its successful creation.

Write SQL to use your bounding box function, centered on your original point of interest, and all of the surrounding points of interests within 20 miles (horizontal and vertical distance) from that point. The results should show that points outside the region are not returned by this spatial query result. Paste a screen shot showing your query and the result, into your lab report.

CHECKPOINT QUESTION: It is possible for a point residing within 20 miles of your original point to correctly be omitted by the bounding box query. Explain why this is the case, and what improvements/refinements might be undertaken in order to improve upon this.

Visualization: Mapping and Displaying Spatial Data Graphically

CHECKPOINT QUESTION: Having created a stored procedure that can easily calculate the distance between any two points in your table, it will occur to you that you could easily create queries that would find “the point B, nearest a given point, A, meeting some additional criteria”. However, consider carefully that you would do this by using a calculated field (Distance). For how many points in your database would the query need to calculate Distance? What are the implications of this to performance and efficiency, if your table is quite large (millions of rows)? What approach could you take that would result in greater efficiency, perhaps allowing Distance to be calculated for a relatively small subset? (Hint: Think about your bounding box function. It returns a small set of points within a given proximity of a specified point, and does so pretty efficiently if the proper indexes are available, because it filters for latitude and longitude values within a bounded numerical range. What if you calculated Distance for only this subset, and further filtered for the minimum Distance?) Record your answers to these questions in your lab report.

With your answers to the previous questions in mind, formulate an EFFICIENT query that returns only the latitudes and longitudes for two points: the original point, and its nearest neighbor, in a single row (Hints: 1. A JOIN statement might be useful here; 2. It may be convenient to use the X() function and Y() function on your point data type columns, for example: “SELECT X(Points.location) as longitude1, Y(Points.location) as latitude1 FROM Points;”).

Test your query, and when you are satisfied that it is working correctly, paste a screen shot showing your query and its results into your lab report.

Modify your query using concatenation and string manipulation functions as needed so that the output of the results resembles:

https://www.google.com/maps/dir/34.297106,+-119.164864/34.279759,+-119.191578

Notice that the highlighted elements in this output should be string literals. Only the X() and Y() values from the first and second points are values obtained from the database.

https://www.google.com/maps/dir/34.297106,+-119.164864/34.279759,+-119.191578

Take a screenshot of your query, showing both the SQL and the result, and paste it into your lab report.

Test the URL you have generated in the previous query, by pasting it into the address bar of your internet browser. A route map should be generated with characteristics similar to the figure below (your map will, of course, reflect the unique points/locations you selected for your database).

Figure 4

In your lab report, provide a description explaining the route image, for example, “Closest Pizza Parlor to my home.”

CHECKPOINT QUESTION: What are the benefits of displaying spatial data visually? What are some examples of this sort of spatial visualization of GIS data OTHER than driving directions for consumers? Record your response in your lab report.

Laboratory Report DeVry University College of Engineering and Information Sciences

Course Number: DBM449

Laboratory Number: 4

Laboratory Title: Spatial Indices

Note: There is no limit on how much information you will enter under the three topics below. It is important to be clear and complete with your comments. Like a scientist you are documenting your progress in this week’s lab experiment.

Objectives: (In your own words what was this lab designed to accomplish? What was its purpose?)

Results: (Discuss the steps you used to complete your lab. Were you successful? What did you learn? What were the results? Explain what you did to accomplish each step. You can include screen shots, code listings, and so on. to clearly explain what you did. Be sure to record all results specifically directed by the lab procedure. Number all results to reflect the procedure number to which they correspond.)

Conclusions: (After completing this lab, in your own words, what conclusions can you draw from this experience?)

#DBM 449 Laboratory Procedures Ilab 4 Answers

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our-stevencook-blog · 8 years ago

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DBM 449 Laboratory Procedures Ilab 4 Answers

Follow Below Link to Download Tutorial

https://homeworklance.com/downloads/dbm-449-laboratory-procedures-ilab-4-answers/

For More Information Visit Our Website ( https://homeworklance.com/ )

Email us At: [email protected] or [email protected]

Laboratory Procedures DeVry University College of Engineering and Information Sciences

I. OBJECTIVES

Understand and become familiar with current capabilities and limitations of the OpenGIS implementation in MySQL.

Learn to create, update, and use spatial indices.

Explore practical approaches to calculating distances between points on the Earth’s surface.

Understand fundamentals of geotagging.

Create stored procedures to determine real-world distances, and to process spatial queries returning result sets of data points within a bounding rectangle.

Explore visualization of GIS data.

II. PARTS LIST

EDUPE-APP Omnymbus MySQL Environment (https://devry.edupe.net:8300/) and/or:

MySQL (dev.mysql.com/downloads)

III. PROCEDURE

Designing a Spatially-enabled Table, and Creating a Spatial Index

Create the table indicated in the following ERD.

Figure 1

Be sure you have first addressed the assigned research for this week’s unit involving Spatial Indices, and then use the following DDL to create a spatial index on the table just created:

CREATE SPATIAL INDEX `location` ON `Points` (`location` ASC);

Paste the complete SQL Data Definition Language (DDL) you used to create this table and index into your lab report.

INSERT INTO Points (name, location) VALUES ( ‘point1’ , GeomFromText( ‘ POINT(31.5 42.2) ‘ ) )

CHECKPOINT QUESTION: Explain what the GeomFromText() function does, and why it is necessary to use this? Paste your response into your lab report.

Run your insert statement(s) to add the data to the Points table. Paste a screen shot showing your SQL statement AND result into your lab report.

Displaying Spatial Data in Human-readable Form

Attempt to retrieve all of the table’s contents using a SELECT * statement. You should find that this does not produce readable results. Your results may resemble the following.

Figure 2

Execute the query you composed in the previous step, and paste a screenshot of the results into your lab report. The results should be similar to the following.

Figure 3

Calculating Distances on Earth’s Surface (Spherical, or Nonplanar Distance Calculation)

CHECKPOINT QUESTION: �� Your assigned research and graded threaded discussion questions this week should quickly lead you to discover that although the Pythagorean Theorem is marvelously useful for calculating the distance between points on a Cartesian planar surface, on a curved surface (such as the surface of the Earth), the further apart two points reside from one another, the greater is the error that results from misapplication of this formula to a curved (in this case, roughly spheroidal) surface. Better (less imprecise) results can be obtained by making use of the Great Circle Formula, haversine formulas, and cosine transforms. You will need to select and appropriate formula, and compose a stored procedure which can be used to calculate the geographic distances between points in your table. You will also need to use a coefficient or conversion factor so that the units of the results are expressed appropriately (e.g., kilometers, meters, miles, yards, feet, etc.), and with reasonable precision. Record your determination of the formula you will use, the reason you believe this is a good approach, and discuss both the degree of precision/error to be expected, and the units you elected to use for your measurement, and why. Record your answer in the lab report.