Lesson 15 of 20 · about 17 min

Taylor series

The wave machine's controller chip can only add and multiply, yet it needs sin(x) hundreds of times a second. How do computers calculate sin, cos and eˣ at all? By polynomials that match the function's value, slope, bend and every higher derivative at one point. You'll add terms one at a time and watch a polynomial wrap itself around a wave, then build your own sin and exp from nothing but arithmetic.