Introduction

Mathematics is the language of the universe! Ok that may seem weird at first but its true. Everything in the universe can be modled by mathematics. Our greatest developments in solving problems in science and life have come with mathematics. Even topics like complex numbers have helped us a lot!! There was a time when negitive numbers were seen as crazy. Now we use them to represent debt, height below a plane, any amount of loss or penalyty. Heck they even allow us to graph grazy shapes and the complete equations. Imaginary numbers are just a step up in complexity and are used to solve very complex problems. So what does this have to to with graphing? Well as you may know graphs are one of the best ways to represent problems. We can see the patterns in which something changes, we can analyze data. Sine and cosine waves are used in physics to represent wavelengths! Even the tangent function has uses in computer science. And there are so many more.
There are also graphs that are in some way beautiful and very cool. Here we will explore those ones!

Math is art

Math can be used creativly, and graphing is one of many, many different ways. If you think about it building a computer is a creative way of using math

To explore some of these yourself copy the equation into desmos:

Graph 1: sin(x^2+y^2) = cos(xy)

Graph 2: sin(x^2 + y^2) = cos(2xy)

Graph 3: sin(x^2 + y^2) = cos(3xy)

Graph 4:

Graph 5:

Graph 6:

Graph 7:

Graph 8:

Graph 9:

Graph 10:

Explanation - The ones with "t" in them

You were probably wondering what all that t stuff means, so I have decided to provide what I think is an easy to understand explanation! These are from something that is called a parametric equation

What is that exactly?

belive it or not parametric functions are actully really simple of an idea! Most often Parametric equations have x and y be functions of another parameter, t which represents time, However they can be used for all sorts of other things. They make really cool things when graphed too!

Play around with this one on desmos!

See what happens as you change a and b which are two constants that effect the equation in different ways

The Importance

Parametric functions are used to solve advanced problems often in complex branches of science such as physics. Complex things such as an objects trajectory involve multiple different independant variables, which form effectivly vectors, matrixes, or tensors.You can learn more about these in the calculus section of the website

An example

I belive that khan academy provides an excellent example of one way that these can be used. Check it out. We also have more examples in the calculus section as I mentioned. We also talk about it with physics. If you want to practice than visit the practice page for worksheets & 10 question reviews




I hope you enjoyed some of these examples!

I really think this shows kind of the beauty of math, and one of many ways it can be expressed as a form of art. I encourage you to research more. Some cool things are the mandlebrot set, collatz conjecture tree diagram art, fibbonachi sequence, DNA and genetic logic,and so much more!