Who Said Math Isn't Beautiful?

Who said math couldn't be beautiful? Math comes in various shapes and sizes that are very attractive: triangles, squares, prisms, parabolas, waves, spirals, and even flowers! Actually, mathematicians don't call them flowers; they call them rose curves. Here take a look!

This is a rose curve that follows this equation r = cos(4θ). The reason why the curve appears like this is because of polar coordinates. Polar coordinates spice up the Cartesian plane by replacing rectangular coordinates--x and y--with θ and r. θ is the angle from the positive x-axis to any given point; on the other hand, r is the length measured from the pole (or the origin) to the given point. As you can see functions like these are cyclic which causes the curve to repeat patterns; in this case a rose petal repeats itself as θ increases from 0 to 2π radians (or 0 to 360 degrees). Pretty cool, huh?

For more generalized equations to make rose curves, follow these formulas: r = ksin(nθ) or r = kcos(nθ). The constant, n, determines how many petals the rose curve will have. If n is an odd number, the curve will have n petals. If n is an even number, the curve will have 2n petals. The other constant, k, determines how long the petals will be from the origin. Before drawing rose curves on graphing calculators, be sure that your calculator is in radian mode and using polar coordinates!

Polar coordinates can create more wild shapes, but I'll save those for future blogs.

These curves alter people's perception toward math. People see math as black and white, and they don't see its true color. Hopefully, these petals pretty-up the conventional y = mx+b. Truly, math is full of boring (most may think) equations, but it's these boring equations that make the world beautiful. Just take a second and look around you. You don't just see a computer screen, a desk, a table lamp, you also see math's product. Look outside. Our whole world is governed by mathematics: fractals, bell curves, infinite series, parabolas, inverse square laws, derivatives, integrals, geometry etc. Take the time to look at math, analyze math, and soon you will lift the veil of boredom and find a beautiful figure underneath it.