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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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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Explaining The Universe on Instagram: "@ExplainingTheUniverse teaches you something NEW everyday day 🧠💫 Pi (π) is a mathematical constant that represents the ratio of a circle’s circumference to its diameter. It is an irrational number, meaning its decimal expansion never ends or repeats, and its approximate value is 3.14159. Pi is one of the most important numbers in mathematics and science, appearing in countless formulas related to geometry, physics, and engineering. It is used to calculate
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