That thing does not obey the laws of physics at all!

The most versatile substance on the planet… and they used it to make a frisbee.

Yep, I just used a graphing app, which can be used to understand Maths at a depth that I haven’t even studied yet, to design a frisbee!

November 2017 was the day my Maths teacher told me that in subsequent chapters we’ll learn how to plot any graph on a graph paper. That was also the day I came across Desmos, an app on iOS/Android which helps in plotting equations. Soon as I learnt differentiation, increasing-decreasing functions, concavity and more in calculus, I wanted to play with equations. Functions soon became my favorite chapter in entire JEE syllabus.

Then I came across this page on Instagram:

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Beyond the limits… Mathlover . . . #batman #bat #dc #comics #batman😎 #batmanbeyond #batmanfans #graph #math #mathgraphs #circles #art #mathart #mathematician #mathdesign #art #mathcurves #graphs #geometry #maths #mathematics #mathematician #trigonometry #sin #cos #tan #mathclass #mathteachers

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I followed and went through the page more:

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Save nature #save #lives . Save animals save #nature . "Until one has loved an #animal a part of one's #soul remains unawakened." . 44 equations. . Trying to spread #love towards nature. . Nature gave us everything what we are it in return???? Pollution and destruction. . ''Each and every animal on earth has as much right to be here as you and me. . Go green. . Comment your views about nature. . . Follow @_the_grapher__ . . #logo #fox #animals #forest #natural #endangered #endangeredspecies #trees #pack #wolf #jack #maths #tail #green #earth #foxes #carnivore #amazon #logodesinger

A post shared by THE GRAPHER (@_the_grapher__) on Nov 21, 2018 at 7:17am PST

This told me how beautiful maths can be, and how simply numbers and two variables (x,y) can create beautiful designs!

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39 equations. . . Follow @_the_grapher__ . Turn on post notification. . Tag a animal lover❤️. . . 👉All male deer have antlers, with the exception of the Chinese Water Deer, which have tusks. 👉This family classification include well known animal like the Moose, Red Deer, Reindeer, Roe and Chital among others. 👉Male deer are called bucks, females, are does, and the young are fawns. 👉The term is deer whether you are talking about one of them or more. Many people say “deers” as the plural but that is incorrect. 👉Deer are found to live in every region around the world except for Australia and Antarctica. While it is understandable why deer wouldn’t survive in Antarctica it isn’t fully understood why they can’t survive in Australia. 👉Only one species of deer lives in Africa – the Red Deer. 👉Reindeer are the only species of deer where the females have antlers as well as the males. 👉Deer are the only animals in the world that feature antlers. Moose have the largest antlers of all the species. They are covered with velvet. 👉Deer where first identified by the Europeans and then taken by them into the area we know today as New Zealand. 👉Approximately 1.5 million vehicles are involved in accidents annually from hitting deer. The cost of these accidents is about $1 million per year. They also result in about 150 deaths per year. 👉All deer are classified as Artiodactyls because they have hooves and an even number of toes. 👉Deer have a homeland range and it can span about 30 miles. They will move around the area finding different places to sleep and food to eat. 👉Deer have lots of muscles in their ears. This allows them to turn the ears different directions but they don’t have to move their bodies as they do so. 👉In the fall deer will shed their summer coat. A thicker and fuller one will appear to keep them very warm in the winter time. 👉Due to their eyes being at the side of the head, they have a 310 degree view. #deer #deerhunting #deerseason #animal #animals #forest #forests #trees #green #horns #hoodfights #maths #art #artist #nature #love #nationalgeographic #prey #hunting #hunt #facts #fact #insta #instaart #facts💯 #animallovers

A post shared by THE GRAPHER (@_the_grapher__) on Dec 1, 2018 at 5:12am PST

So, I decided to play with the app too.

The first thing I designed was months back, and also the last till last week. It was a very simple, mindless thing to plot – the Deathly Hallows!

Now, it has been several months since I designed this. Recently, thanks to the Endgame craze, I came across this news article:

A group of MIT pranksters transformed the school’s Great Dome Saturday night into Captain America’s shield in celebration of the new “Avengers” movie. https://t.co/tDxQpxcEot pic.twitter.com/5dP9Ovyv16

— The Boston Globe (@BostonGlobe) April 29, 2019

This gave me an idea to design what I wanted to share today. I decided to design Captain America’s Shield on Desmos.

I faced a lot of challenges while making this.

Initially when I started with it, I was having trouble in separating the colors. Such as, I wasn’t able to get the white part of the disc, and there was a red layer above the blue one. And that point, I hadn’t even started thinking about the star in the middle. But, it didn’t take me long to understand how Desmos will accept two inequalities to shade one region. So, that got sorted out pretty fast.

The next challenge was getting the shape of that star, with the 5 points lying on the circle. I started out by drawing some variable lines and changing their slopes using sliders with precision to make them intersect at the perimeter. I kept trying, but I wasn’t getting a star that looked symmetric enough. I changed the radius of the inner-most circle, trying again with the similar method. I had started with a radius of 4 units, increasing it to 5, 8, 10 and eventually 16 for getting a neater scale. At the end, I made it a little less than 16, 15.9 units.

Eventually, I decided to change the way I’m approaching it. I first decided approximately where I want that horizontal part of the star to be. Once I had decided that, I drew the next line while adjusting the slope similarly with the slider where I felt it would set the theme for the last line accurately. Other lines just had to have the same slope, but negative.

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So, since I now I had the two intersection points for the line left, it wasn’t difficult to plot it. By simple math, they were going to intersect on the Y-Axis, if I gave them the same intercept. Eventually, this being the most time consuming part, I got a star I was satisfied with.

Next, it was being impossible to get blue color there and white inside the stars. For that, I had to break the circle into 5 inequalities, each with 2 conditions, representing one of those 5 regions.

Now, the challenge was to remove the parts of the lines of the star, which were ending up differentiating the star into triangles and pentagon. It would’ve been easy, just quite messy. Infact, the black boundary wasn’t even looking that good. So, I decided to get rid of the lines, and deleted those equations.

Now, I needed to decide the radius of the subsequent circles. For that, I searched online the dimensions of his shield, and came across this pic:

So, I took the ratio accordingly. Since by inner most circle had a radius of about 16 units, I gave the subsequent circles 28 units, 40 units & 52 units respectively. And, thus got the final image:

So, I’ll share with you the equations I used:

1. x^2 + y^2 <= 15.9^2 {y >= 5.35} {y >= -2.47142x + 15.9}
2. x^2 + y^2 <= 28^2 {x^2 + y^2 >= 15.9^2}
3. x^2 + y^2 <= 52^2 {x^2 + y^2 >= 40^2}
4. x^2 + y^2 = 40^2
5. x^2 + y^2 <= 15.9^2 {y >= 5.35} {y >= 2.47142x + 15.9} 
6. x^2 + y^2 <= 15.9^2 {y <= -0.6445x - 4.3} {y >= -2.47142x + 15.9}
7. x^2 + y^2 <= 15.9^2 {y <= -0.6445x - 4.3} {y <= 0.6445x - 4.3} 
8. x^2 + y^2 <= 15.9^2 {y <= 0.6445x - 4.3} {y >= -2.47142x + 15.9}  

Desmos has a very limited color choices, so I had to go with the variant of red and blue it offered. But, I gotta say, this has been one of the most fun things I’ve done.

If any math enthusiast is reading this, I hope I could give you an idea too to find some beauty in maths. Else, comment down more designs you’ll like me to try, and I’ll give them a shot!

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