The Area of an Infinite Batwing
July Livestream Challenge
I’ll present this diagram in the form of an algorithm.
FOR n = 0 TO INFINITY
PRINT [(1/2)^n]sin[(2^n)x]It’s an infinitude of sine waves. The first function, sin x, runs from 0 to π. We take a bite out of the area above the x-axis. We do this with a sine wave having half the amplitude and twice the frequency.
Create a third sine wave, half the amplitude and twice the frequency of the previous. Use it to take a bite out of the remaining area.
Repeat.
Forever.
The remaining shaded area looks like a batwing. What is the size of the batwing?
Have fun with this. We’ll have a look during the MathAdam YouTube Livestream: Sunday, July 25, 9 A.M. Pacific Time. If you miss the livestream, the link will take you to the replay.
Cheers!
Adam
