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

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.

I followed and went through the page more:

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

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:

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.

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!

1. Like!! I blog frequently and I really thank you for your content. The article has truly peaked my interest.

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2. Sohanpreet Kaur says:

Mathematics is language of nature.

Liked by 1 person

1. Aarnav Gupta says:

Absolutely!

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3. Saania2806 says:

Maths is my favourite subject π

Liked by 2 people

1. Aarnav Gupta says:

Saaame! Mine too!

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1. Saania2806 says:

High five β ππ

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1. Aarnav Gupta says:

βοΈβοΈ

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4. Sid says:

Truly amazing to see your amazing passion for maths. I personally hate that subject π. But the sheild you created was πππ

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1. Aarnav Gupta says:

Oh come on. Why would you hate something as beautiful as maths?

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1. Sid says:

I don’t know I just find it too hard. Or maybe I haven’t practiced as much.

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1. Aarnav Gupta says:

Yes, practice is a key element, if not the only, to do good in Maths.

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2. Riya Rajayyan says:

I have the same words!

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1. Riya Rajayyan says:

How did it come twice lol. Delete one of it please. Sorry for spam.

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1. Aarnav Gupta says:

Looool

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3. Riya Rajayyan says:

I have the same words to sayπ
The design is really amazing.

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1. Aarnav Gupta says:

Creater of Captain America designed that. Pretty iconic, no? π

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1. Riya Rajayyan says:

Yeah!π

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