Series at Work

Relativity and Euler’s formula

An interactive lesson with 7 steps, about 6 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Taylor expanding $\gamma mc^2$ gives $mc^2 + \tfrac12 mv^2$.
• Euler's formula $e^{i\theta} = \cos\theta + i\sin\theta$ follows from the series.
• $e^{i\pi} + 1 = 0$.

Steps

1. Hidden inside E = mc²
2. How good is it?
3. Euler’s formula from series
4. The series as a walk
5. Beyond Newton
6. How many terms?
7. The most beautiful equation