July 5, 2020

When I tried to draw a circle in the software R, I made an all-star trignometric mistake by initiating a sequence of 200 angles from 0 to 360 so that any two adjacent angles are about¹ 1.8 apart, which makes a 200-edge polygon look smooth enough to be a circle. However, I forgot the trigonometric functions are radians speakers. They interpret 1.8 as radians, which equals² 103.1324031∘. That is a lot of travel on a circle (farther than the latitudes between Ushuia and Quebec City, or the longitudes between Honolulu and San Juan). Had I used 2π, the radians equivalency of 360∘, it would be a perfect circle. Nevertheless, it turns out to be a beautiful mistake.

t = seq(0, 360, length.out = 200) # An arithmetic sequence of 200 angles between 0 and 360
plot(cos(t), sin(t), type = 'l') # 'l' means line

This inspired me to create an app to explore other possible cool designs. The app pins down a sequence of points on a circle. Two adjacent points are apart by θ∘ along the circle and connected by a line segment. So, for example, 120∘ and four points draw a perfect triangle, while 120.3∘ and 40 points draw an artistic triangle. Try it yourself. Happy drawing!

PS: See? Math is beautiful and simple! Except, on the tests, you are always asked “what is the radius of the inner circle if the outer circle has a radius of 1”. Good luck.