Visualization of pi being irrational
2:25
Visualization of pi being irrational
Oct 22, 2023
redditaDazzlingDove
Pi won’t start repeating after a trillion digits. And it’s not because we checked the digits. We know π is irrational from a proof going back to Lambert in the 1700s. His result shows that if tan(x) is rational (and x ≠ 0), then x must be irrational. But tan(π/4) = 1, and 1 is rational. So π/4 is irrational → π is irrational. #pi #irrationalnumbers #mathreels #mathproofs | polymathematic
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Pi won’t start repeating after a trillion digits. And it’s not becaus…
53.8K views3 months ago
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Pi is the infinite ratio between a circle’s circumference and its diameter, but it never repeats and never ends. In this video we see a simple, but visually interesting, example of a complex exponential sum (a two-term Fourier series with incommensurate frequencies) where Pi shows up as one of the angular speeds. The function is: z(θ) = e^(iθ) e^(iπθ) The symbol we write as π ≈ 3.14159 is an irrational number, and its decimal expansion goes on forever without settling into a pattern. When the di
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