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<!DOCTYPE html>
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<head>
<title>Where is the Parabola? - The Universal Parabolic Constant Mystery</title>
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<meta name="description" content="Explore the mysteries of the Universal Parabolic Constant with Manas Shetty, Prajwal DSouza, Sparsha Kumari and Vinton Adrian Rebello. Dive into a journey of understanding average distances, shrinking random walks, and the unexpected links between parabolas and squares. Discover the complexities of curve length division and the elegance of parabolic arcs. A perfect resource for those intrigued by the fascinating world of mathematical problem-solving.">
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<div style="background-image: linear-gradient(to bottom, var(--generalBackground), transparent); color: hsl(0,0%,20%); font-size: small; " class="text-ignus p-4 pl-5 pr-5 p-md-3 pl-md-4 pr-md-4 text-md-left text-center">
<b>Where is the Parabola? The Parabolic Constant Mystery</b><br/>
<p style="font-size:x-small">Manas Shetty, Prajwal DSouza, Sparsha Kumari, Vinton Adrian Rebello</p>
</div>
</header>
<main>
<div class="w-100 text-center text-ignus pt-5 mt-3 pb-4" style="font-family: Raleway;">
<div class="pl-3 pr-3">
<b style="font-size: x-large;">Where is the Parabola? </b><br/>
<b style="font-size: large; color: gray">The Parabolic Constant Mystery</b><br/>
<p style="font-size: medium; color: hsl(0,0%,30%)">Manas Shetty, Prajwal DSouza, Sparsha Kumari, Vinton Adrian Rebello</p>
</div>
</div>
<div class="w-100 pl-4 pr-4 pl-sm-5 pr-sm-5 d-flex justify-content-center">
<div class="our-text-block text-center" id="gph1-starting-block">
<p>Let us start with a innocent looking problem. Picture a <span class="p-lightYellow">unit square</span>, a perfect little 1x1 entity. Now, pick a point <span class="p-lightPurple">Q</span> at random along the square's boundary. What do you think is the <span class="p-lightPink">average distance</span> between this chosen <span class="p-lightPurple">point Q</span> and the very heart of our square, the <span class="p-lightBlue">center C</span>? </p>
</div>
</div>
<div class="w-100 pl-0 pr-0 pl-sm-5 pr-sm-5 d-flex justify-content-center">
<div class="our-text-block text-center" style="height: 400px; width: 100%; position: relative;">
<div id="upc-measurement-graphHolder" style="display: inline-block; position: relative; width: 100%; height: 100%;"></div>
</div>
</div>
<div class="w-100 pl-4 pr-4 pl-sm-5 pr-sm-5 d-flex justify-content-center">
<div class="our-text-block text-center" id="gph1-explaining-block">
<p>Surprisingly, the answer is approximately <span class="p-lightPink" id="parameter-measured-parabolic-constant-by-4">0.5738967</span>... a peculiar figure, isn't it? This number equals <span class="p-White" >P</span>/4 where <span class="p-White" >P</span> is known as <span class="p-White" >Universal Parabolic Constant</span>. The value is around <span class="p-White" >2.295587149...</span> Hold on a second - a Parabolic Constant? But our question was about squares, wasn't it? <span class="p-White" >Where does the parabola come in? </span></p>
</div>
</div>
<div class="w-100 pl-4 pr-4 pl-sm-5 pr-sm-5 d-flex justify-content-center">
<div class="our-text-block text-center">
<p>This might seem like a co-incidence. But, we look for a circle when <span class="p-White" >pi</span> pops up in various places right? Just check <a class="p-lightBlue" href="https://www.youtube.com/watch?v=HEfHFsfGXjs" target="_blank" >3B1B</a> :P So, why not dig a little deeper. And if we explore a little more, there are other seemingly unrelated math problems where you see this number show up. </p>
</div>
</div>
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<div class="w-100 pl-4 pr-4 pl-sm-5 pr-sm-5 d-flex justify-content-center">
<div class="our-text-block text-center">
<p>
So, What do you think is the average <span class="p-lightPink" >distance </span>between any two points inside a <span class="p-lightYellow" >unit square</span>? Take a guess. :D
</p>
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<label id="distance-between-any-two-points-SliderLabel" class="p-lightPink pl-sm-3 pl-0" for="distance-between-any-two-points-Slider" style="min-width: 100px;" >0.8</label>
<div>
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Points <span class="p-lightBlue">A</span> and <span class="p-lightPurple">B</span> above are draggable. :)
</p>
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<div class="our-text-block text-center">
<p class="mt-5">
It is about <span class="p-lightPink" >0.52140.</span> To be more precise, it is. <br/><br/>
<span class="p-lightPink" >8 (0.0416*<span class="p-White" >P</span> - 0.030473)</span><br/>
And exactly, it is
<div class="p-lightPink" style="font-size: 25px;">
\(8\left(\frac{P}{24}-\frac{\sqrt{2}}{30}+\frac{1}{60}\right)\)
</div>
<br/>
<p>
Yep. Yep. Strange combination of numbers. There's a <span class="p-White" >P</span> there. <br/>
There's many more instances where we see this. But, mostly involving a unit square.</p>
</p>
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<p>
<span class="commonButton p-2 pl-4 pr-4 mt-1 btn-ignus" onclick="upcApp.chooseSection(1, 1)" id="rotatingSectionButton-1-1"> Center-Point Distance</span>
<span class="commonButton p-2 pl-4 pr-4 mt-1 btn-ignus inActiveSectionButton" onclick="upcApp.chooseSection(1, 2)" id="rotatingSectionButton-1-2"> Corner-Perimeter Distance</span>
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<div class="w-100 pl-4 pr-4 pl-sm-5 pr-sm-5 d-flex justify-content-center">
<div class="our-text-block text-center pb-1">
<p>
Here is a slightly similar problem. <br/>
What do you think is the average <span class="p-lightPink" >distance </span>between the <span class="p-lightBlue" >center</span> and <span class="p-lightPurple" >any point</span> 'inside' the <span class="p-lightYellow" >unit square</span>?
</p>
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<div class="w-100 pl-4 pr-4 pl-sm-5 pr-sm-5 d-flex justify-content-center">
<div class="our-text-block text-center">
<p>
Take a guess. :D
</p>
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<label id="distance-between-center-and-point-inside-SliderLabel" class="p-lightPink pl-sm-3 pl-0" for="distance-between-center-and-point-inside-Slider" style="min-width: 100px;" >0.8</label>
<div>
<p id="distance-between-center-and-point-inside-SliderInfo" class="text-small-ignus" style="color:hsla(198, 0%, 47%, 1)">
Point<span class="p-lightPurple">B</span> above is draggable. :)
</p>
<div id="gph3-checkAnswerButton" class="commonButton p-2 pl-4 pr-4 mt-1 btn-ignus" style="border: 1px solid hsla(var(--lightPinkH), var(--lightPinkS), var(--lightPinkL), 0.2); color: hsla(var(--lightPinkH), var(--lightPinkS), var(--lightPinkL), 1);">Check</div>
<div id="reveal-sub-section-1-continueButton" class="commonButton p-2 pl-4 pr-4 mt-1 btn-ignus">Continue</div>
</div>
</div>
</div>
</div>
<div class="w-100 pl-4 pr-4 pb-5 pl-sm-5 pr-sm-5 d-flex justify-content-center reveal-sub-section-1 revealable">
<div class="mt-2 text-center">
<p>
It is about <span class="p-lightPink">0.38259785</span> ... To be exact, it is.
</p>
<div class="p-lightPink" style="font-size: 25px;">
\(\frac{P}{3}\)
</div>
<br />
<p>
Yep. There's a <span class="p-White">P</span> here too. <br />
</p>
</div>
</div>
</div>
<div id="rotatingSection-1-2" class="rotatingSection-1" style="display: none">
<div class="w-100 pl-4 pr-4 pl-sm-5 pr-sm-5 d-flex justify-content-center ">
<div class="our-text-block text-center pb-1">
<p>
Here is another problem. Try to guess this one.<br/>
What do you think is the average <span class="p-lightPink" >distance </span>between a <span class="p-lightBlue" >corner</span> and <span class="p-lightPurple" >a point</span> on the <span class="p-lightYellow" >unit square</span>?
</p>
</div>
</div>
<div class="w-100 pl-0 pr-0 pl-sm-5 pr-sm-5 d-flex justify-content-center rotatingSectionGraph-1-2" id="rotatingSectionGraph-1-2-1" style="position: absolute; left: 200vw;">
<div class="our-text-block text-center" style="height: 400px; width: 100%; position: relative;">
<div id="distance-between-corner-and-point-on-square-graphHolder" style="display: inline-block; position: relative; width: 100%; height: 100%;"></div>
</div>
</div>
<div class="w-100 pl-4 pr-4 pl-sm-5 pr-sm-5 d-flex justify-content-center">
<div class="our-text-block text-center">
<p>
Take a guess. :D
</p>
<div class="mt-1 pb-2">
<input type="range" min="0" max="2" value="0.2" step="0.001" class="commonSlider mb-3" id="distance-between-corner-and-point-Slider">
<div class="d-block d-sm-none"></div>
<label id="distance-between-corner-and-point-SliderLabel" class="p-lightPink pl-sm-3 pl-0" for="distance-between-corner-and-point-Slider" style="min-width: 100px;" >0.8</label>
<div>
<p id="distance-between-corner-and-point-SliderInfo" class="text-small-ignus" style="color:hsla(198, 0%, 47%, 1)">
Point<span class="p-lightPurple">B</span> above is draggable. :)
</p>
<div id="gph4-checkAnswerButton" class="commonButton p-2 pl-4 pr-4 mt-1 btn-ignus" style="border: 1px solid hsla(var(--lightPinkH), var(--lightPinkS), var(--lightPinkL), 0.2); color: hsla(var(--lightPinkH), var(--lightPinkS), var(--lightPinkL), 1);">Check</div>
<div id="reveal-sub-section-2-continueButton" class="commonButton p-2 pl-4 pr-4 mt-1 btn-ignus">Continue</div>
</div>
</div>
</div>
</div>
<div class="w-100 pl-4 pr-4 pb-5 pl-sm-5 pr-sm-5 d-flex justify-content-center reveal-sub-section-2 revealable">
<div class="mt-2 text-center">
<p>
It is about <span class="p-lightPink">0.76519571</span>... To be exact, it is.
</p>
<div class="p-lightPink" style="font-size: 25px;">
\(\frac{P}{3}\)
</div>
<br />
<p>
There's a <span class="p-White">P</span> here too. <br />
</p>
</div>
</div>
</div>
</div>
<div class="w-100 pl-4 pt-4 pr-4 pl-sm-5 pr-sm-5 d-flex justify-content-center hidden-element reveal-1 revealable">
<div class="our-text-block text-center">
<p>
Let's branch out a little and delve into a problem unrelated to the unit square. A problem related to <span class="p-lightPurple" >Shrinking Random Walk</span> appeared in Tom Yuster's April 2017 Math Horizons piece (pp. 32-33)
</p>
</div>
</div>
<div class="w-100 pl-4 pt-4 pr-4 pl-sm-5 pr-sm-5 d-flex justify-content-center hidden-element reveal-1 revealable">
<div class="our-text-block text-center">
<p>
Consider a drunkard walking in a plane that starts at the <span class="p-White" >origin</span> and moves only in the east and north directions. He randomly chooses a direction and takes a step. The walk is such that the length of the <span class="p-lightOrange" >first step must be √2</span>, the length of the <span class="p-brightYellow" >second step must be √2/2</span>, the length of the <span class="p-lightGreen" >third step must be √2/4</span>, and <span class="p-lightBlue" >so on</span>.
</p>
</div>
</div>
<div class="w-100 pl-0 pr-0 pl-sm-5 pr-sm-5 d-flex justify-content-center hidden-element reveal-1 revealable">
<div class="our-text-block text-center" style="height: 500px; width: 100%; position: relative;">
<div id="random-shrinking-walk-graphHolder" style="display: inline-block; position: relative; width: 100%; height: 100%;"></div>
</div>
</div>
<div class="w-100 pl-4 pt-0 pr-4 pl-sm-5 pr-sm-5 d-flex justify-content-center hidden-element reveal-1 revealable">
<div class="our-text-block text-center">
<div class="mt-1 pb-2">
<input type="range" min="0" max="30" value="1" step="1" class="commonSlider mb-3" id="random-shrinking-walk-Slider">
<div class="d-block d-sm-none"></div>
<label id="random-shrinking-walk-SliderLabel" class="p-lightBlue pl-sm-3 pl-0" for="random-shrinking-walk-Slider" style="min-width: 100px;" >0.8</label>
<div>
<p id="random-shrinking-walk-SliderInfo" class="text-small-ignus" style="color:hsla(198, 0%, 47%, 1)">
There are infinitely many steps. But, you can choose how many steps to show. :)
</p>
</div>
</div>
</div>
</div>
<div class="w-100 pl-4 pt-4 pr-4 pl-sm-5 pr-sm-5 d-flex justify-content-center hidden-element reveal-1 revealable">
<div class="our-text-block text-center pt-4">
<p>
Imagine the endless steps taken by the drunkard, how far would you expect to be from the starting point, <span class="p-White">the origin</span>? Let's denote this distance as <span class="p-lightPink">D</span>. But, what about the average value of <span class="p-lightPink">D</span>? How could we possibly calculate that?<br/>
This problem might seem to be a departure from our discussion about the unit square. Still, it maintains a common thread: the concept of averages.
(Note that the length of the path is <span class="p-brightYellow">√2</span> + <span class="p-lightOrange">√2/2</span> + ... , and we are not referring to that) <br/><br/>
So, how about we roll up our sleeves and crunch some numbers? Let's simulate the Drunkard's Walk, taking about 30 steps, and observe where we end up. From there, we can compute the distance, <span class="p-lightPink">D</span>, from the origin. To get an approximation of <span class="p-lightPink">D</span>'s average value, we'll repeat this process a few times.
</p>
</div>
</div>
<div class="w-100 pl-0 pr-0 pl-sm-5 pr-sm-5 d-flex justify-content-center hidden-element reveal-1 revealable">
<div class="our-text-block text-center" style="height: 500px; width: 100%; position: relative;">
<div id="random-shrinking-walk-trials-graphHolder" style="display: inline-block; position: relative; width: 100%; height: 100%;"></div>
</div>
</div>
<div class="w-100 pl-4 pt-4 pr-4 pl-sm-5 pr-sm-5 d-flex justify-content-center hidden-element reveal-1 revealable">
<div class="our-text-block text-center pt-4">
<p id="random-shrinking-walk-trials-info-for-trial">
</p>
<p id="random-shrinking-walk-trials-holder">
</p>
<p id="random-shrinking-walk-trials-average-statement">
</p>
<span class="commonButton p-2 pl-4 pr-4 mt-1 btn-ignus" onclick="gph6.addNewWalk()"> Add another trial</span>
</div>
</div>
<div class="w-100 pl-4 pt-2 pr-4 pl-sm-5 pr-sm-5 d-flex justify-content-center hidden-element reveal-1 revealable">
<div class="our-text-block text-center">
<p>
After looking at these values, what do you think is the average value?
</p><br/>
<div class="mt-1 pb-2">
<input type="range" min="0" max="4" value="0.2" step="0.001" class="commonSlider mb-3" id="random-shrinking-walk-distance-answer-Slider">
<label id="random-shrinking-walk-distance-answer-SliderLabel" class="p-lightPink pl-sm-3 pl-0" for="random-shrinking-walk-distance-answer-Slider" style="min-width: 100px;" >0.8</label>
<div>
<p id="random-shrinking-walk-distance-answer-SliderInfo" class="text-small-ignus" style="color:hsla(198, 0%, 47%, 1)">
</p>
<div id="gph6-checkAnswerButton" class="commonButton p-2 pl-4 pr-4 mt-1 btn-ignus" style="border: 1px solid hsla(var(--lightPinkH), var(--lightPinkS), var(--lightPinkL), 0.2); color: hsla(var(--lightPinkH), var(--lightPinkS), var(--lightPinkL), 1);">Check</div>
<div id="reveal-2-continueButton" class="commonButton p-2 pl-4 pr-4 mt-1 btn-ignus">Continue</div>
</div>
</div>
</div>
</div>
<div class="w-100 pl-4 pt-4 pr-4 pl-sm-5 pr-sm-5 d-flex justify-content-center hidden-element reveal-2 revealable">
<div class="our-text-block text-center pt-4">
<p>
The answer is <span class="p-White">2.295587149</span>...
Yes. It is <span class="p-White">P</span>. It's here too.
<br/>
This problem doesn't seem to have a square, but still deals with concept of averages.
<br/><br/>
But, why? What does this have to do with the parabola we've been discussing? Could it be linked to a concept you're already familiar with?
<br/>
Here's a hint. The drunkard destiny isn't that random after all. It's about the <span class="p-lightPurple">final point</span> after large iterations . (where the drunkard lands after infinitely many steps)
</p>
</div>
</div>
<div class="w-100 pl-0 pr-0 pl-sm-5 pr-sm-5 d-flex justify-content-center hidden-element reveal-2 revealable">
<div class="our-text-block text-center" style="height: 500px; width: 100%; position: relative;">
<div id="random-shrinking-walk-reveal-graphHolder" style="display: inline-block; position: relative; width: 100%; height: 100%; overflow: hidden;"></div>
</div>
</div>
<div class="w-100 pl-4 pt-0 pr-4 pl-sm-5 pr-sm-5 d-flex justify-content-center hidden-element reveal-2 revealable">
<div class="our-text-block text-center">
<div class="mt-1 pb-2">
<input type="range" min="1" max="200" value="2" step="1" class="commonSlider mb-3" id="random-shrinking-walk-reveal-Slider">
<div class="d-block d-sm-none"></div>
<label id="random-shrinking-walk-reveal-SliderLabel" class="p-lightBlue pl-sm-3 pl-0" for="random-shrinking-walk-reveal-Slider" style="min-width: 100px;" >2 trials</label>
<div>
<p id="random-shrinking-walk-reveal-SliderInfo" class="text-small-ignus" style="color:hsla(198, 0%, 47%, 1)">
Well. More trails? :)
</p>
</div>
</div>
</div>
</div>
<div class="w-100 pl-4 pt-4 pr-4 pl-sm-5 pr-sm-5 d-flex justify-content-center hidden-element reveal-2 revealable">
<div class="our-text-block text-center pt-4">
<p>
Does it look familiar now? i hope we got your attention and excited about the problem.
</p>
</div>
</div>
<div class="w-100 pt-5 pb-5"></div>
<div class="w-100 pt-5 pb-5"></div>
</main>
<div style="position: fixed; height: 100%; width: 100vw; pointer-events: none; bottom: 0px; left: 0px;" id="lottie-popper"></div>
</div>
</div>
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darkmode = true
if (darkmode) {
document.body.style.background = 'black'
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</script>
<script type="text/javascript">
upc = 2.2955871493926380
upcApp = {}
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upcApp.graphFontSizeSmall = 2.8;
upcApp.graphFontSizeLarge = 4;
upcApp.graphPointSize = 1.3;
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upcApp.handleLayoutStyles()
upcApp.anim = {}
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var animationData = {
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renderer: 'svg',
loop: false,
autoplay: false,
path: 'https://assets7.lottiefiles.com/packages/lf20_C51Bca6c0m.json'
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upcApp.chooseSection(1, 1);
gph5.setUpShrinkingRandomWalk();
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// gph5.setAtValue(6)
gph6.addNewWalk()
gph6.addNewWalk()
// gph6.addNewWalk()
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document.getElementById('rotatingSectionButton-' + rotatingSectionIndex + '-' + s).classList.add("inActiveSectionButton");
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viewX.removeGraph('distance-between-corner-and-point-on-square-graph');
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gph4.setUpDistanceBetweenCornerAnyPointOnSquare();
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// First graph : upc-measurement-graph
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unitAspectRatio: 'yes',
fixAxisStretchCentrally: 'yes',
scrollZoom: "no",
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// Code by GPT-4
function pickAPointOnSquare(givenPointOnPlane) {
A = givenPointOnPlane;
let center = [0.5, 0.5];
// Compute the vector from center to A
let vec = [A[0] - center[0], A[1] - center[1]];
// Normalize the vector
let dist = Math.sqrt(vec[0]*vec[0] + vec[1]*vec[1]);
let normVec = [vec[0]/dist, vec[1]/dist];
// The maximum length from the center to the edge of the square
let maxDist = Math.min(Math.abs(0.5 / normVec[0]), Math.abs(0.5 / normVec[1]));
// Compute the intersection point
let intersectionPoint = [center[0] + maxDist * normVec[0], center[1] + maxDist * normVec[1]];
return intersectionPoint;
}
function calculateAverageOfPoints(points) {
if (!Array.isArray(points)) {
throw new Error("Points must be an array.");
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throw new Error("Points array must not be empty.");
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distanceValue = []
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distanceValue.push(viewX.distF([0.5, 0.5], points[i]))
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const sum = distanceValue.reduce((total, point) => total + point, 0);
const average = sum / distanceValue.length;
return average;
}
function removeRandomPoint(points) {
if (!Array.isArray(points)) {
throw new Error("Points must be an array.");
}
if (points.length === 0) {
throw new Error("Points array must not be empty.");
}
const randomIndex = Math.floor(Math.random() * points.length);
const removedPoint = points.splice(randomIndex, 1)[0];
return removedPoint;
}
gph0 = {}
gph0.initialSetup = function() {
// var audio = document.getElementById("backgroundMusic");
// audio.play();
}
gph0.initialSetup();
// Code For 1st Graph : upc-measurement-graph
gph1 = {}
gph1.displayAverage = function(value) {
str1 = value.toString()
str2 = (upc/4).toString()
theHTML = ""
streak = 'unbroken'
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theHTML += str1[i]
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theHTML += "<span style='color: hsl(var(--lightPinkH), 20%, 47%);'>" + str1[i] + "</span>";
}
}
return theHTML
}
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document.getElementById('gph1-explaining-block').addEventListener('mousemove', function(e) {
document.getElementById('parameter-measured-parabolic-constant-by-4').innerHTML = gph1.displayAverage(upc/4)
})
}
gph1.onMoveOverParagraph();
gph1.sampledPointsOnSquare = []
function upcMeasurementSetup() {
graphH = document.getElementById('upc-measurement-graphHolder')
viewX.addGraph(graphH, "upc-measurement-graph", defaultGraphOptions)
graphH.addEventListener("mousemove", viewX.getCoordinatesOfEvent("upc-measurement-graph", "upcMeasurementGraphMouseMove"))
rectOptions = { x: 0, y: 1, w: 1, h: 1, stroke: "var(--lightYellow)", strokewidth: 0.4, rectcolor: "hsla(190, 100%, 50%, 0)"};
viewX.addRectangle("upc-measurement-graph", "upc-measurement-unit-square", rectOptions);
pointOnSquare = pickAPointOnSquare([0.7, 0.6])
gph1.sampledPointsOnSquare.push(pointOnSquare)
averageSoFar = calculateAverageOfPoints(gph1.sampledPointsOnSquare)
document.getElementById("parameter-measured-parabolic-constant-by-4").innerHTML = gph1.displayAverage(averageSoFar)
distanceText = viewX.distF([0.5, 0.5], pointOnSquare).toFixed(3);
lineOptions = { x1: 0.5, y1: 0.5, x2: pointOnSquare[0], y2:pointOnSquare[1], strokedasharray: "4,4", strokewidth: 0.7, linecolor: "var(--lightPink)"};
viewX.addLine("upc-measurement-graph", "upc-measurement-distance-line", lineOptions);
pointOptions = { x: 0.5, y: 0.5, pointsize: upcApp.graphPointSize, pointcolor: 'var(--lightBlue)'};
viewX.addPoint("upc-measurement-graph", "upc-measurement-center-C", pointOptions);
textOptions = {x: 0.5 + 0.05, y: 0.5 - 0.08, text: "C", textAlign: "center", fontSize: upcApp.graphFontSizeLarge, fontFamily: "Raleway", textcolor: "var(--lightBlue)"};
viewX.addText("upc-measurement-graph", "upc-measurement-center-C-label", textOptions);
pointOptions = { x: pointOnSquare[0], y: pointOnSquare[1], pointsize: upcApp.graphPointSize, pointcolor: 'var(--lightPurple)'};
viewX.addPoint("upc-measurement-graph", "upc-measurement-randomPoint-Q", pointOptions);
textOptions = {x: pointOnSquare[0] + 0.05, y: pointOnSquare[1] - 0.08, text: "Q", textAlign: "center", fontSize: upcApp.graphFontSizeLarge, fontFamily: "Raleway", textcolor: "var(--lightPurple)"};
viewX.addText("upc-measurement-graph", "upc-measurement-randomPoint-Q-label", textOptions);
textOptions = {x: (0.5 + pointOnSquare[0])/2, y: (0.5 + pointOnSquare[1])/2, text: distanceText, textAlign: "center", fontSize: upcApp.graphFontSizeSmall, fontFamily: "Nunito", textcolor: "var(--lightPink)"};
viewX.addText("upc-measurement-graph", "upc-measurement-distance-label", textOptions);
}
upcMeasurementSetup()
function upcMeasurement(givenPointOnPlane) {
pointOnSquare = pickAPointOnSquare(givenPointOnPlane)
gph1.sampledPointsOnSquare.push(pointOnSquare)
if (gph1.sampledPointsOnSquare.length > 1000) {
removeRandomPoint(gph1.sampledPointsOnSquare)
}
averageSoFar = calculateAverageOfPoints(gph1.sampledPointsOnSquare)
document.getElementById("parameter-measured-parabolic-constant-by-4").innerHTML = gph1.displayAverage(averageSoFar)
lineOptions = {x2: pointOnSquare[0], y2:pointOnSquare[1]};
viewX.updateLine("upc-measurement-graph", "upc-measurement-distance-line", lineOptions);
viewX.updatePointXY("upc-measurement-graph", "upc-measurement-randomPoint-Q", pointOnSquare[0], pointOnSquare[1]);
textOptions = {x: pointOnSquare[0] + 0.05, y: pointOnSquare[1] - 0.08};
viewX.updateText("upc-measurement-graph", "upc-measurement-randomPoint-Q-label", textOptions);
distanceText = viewX.distF([0.5, 0.5], pointOnSquare).toFixed(3);
textOptions = {x: (0.5 + pointOnSquare[0])/2 + 0.05, y: (0.5 + pointOnSquare[1])/2 - 0.08, text: distanceText};
viewX.updateText("upc-measurement-graph", "upc-measurement-distance-label", textOptions);
}
function upcMeasurementGraphMouseMove() {
givenPointOnPlane = viewX.cursorCoordinates["upc-measurement-graph"]
upcMeasurement(givenPointOnPlane)
}
function upcRandomMeasurement() {
index = viewX.randomChoice([0, 1, 2, 3])
startingPoints = [[0,0], [1,0], [1,1], [0,1]]
startingPoint = startingPoints[index]
translateDirections = [[1,0], [0,1], [-1,0], [0,-1]]
translateDistance = Math.random()
translateVector = [translateDistance*translateDirections[index][0], translateDistance*translateDirections[index][1]]
givenPointOnPlane = viewX.addVec(startingPoint, translateVector);
// givenPointOnPlane = [Math.cos(2*Math.PI*Math.random()), Math.sin(2*Math.PI*Math.random())]
upcMeasurement(givenPointOnPlane)
}
gph1.loopinterval = setInterval(frame, 500);
gph1.animLoopCount = 1
function frame() {
gph1.animLoopCount = gph1.animLoopCount + 1
if (gph1.sampledPointsOnSquare.length < 5) {
if (gph1.animLoopCount % 5 == 0) {
upcRandomMeasurement()
}
}