Algebra: Feynman's Physics Explained
Mathematics is the language of physics and algebra is its grammar. Starting from simple counting and a few rules, we abstract them and demand they keep working even where the original meaning breaks down — which forces us to invent negative numbers, fractions, and finally complex numbers. The crowning result is Euler's formula, which reveals a stunning hidden link between exponential and trigonometric functions: they are two sides of the same coin.
The big idea
Pushing the rules of arithmetic to their limit reveals deep hidden unity.
Think about it
Why might mathematicians 'invent' a number for the square root of a negative — and why would physics ever need it?
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