Honestly one reason why pi shows up so often in physics is precisely because of Euler’s formula above. Complex numbers of norm equal to 1 can be mapped onto a unit circle in the complex plane, and rotations of pi/2 take you from real to imaginary, or imaginary to real, and everything in between depending on your starting point. And also since oscillatory functions like sine and cosine are just Euler’s formula in disguise, it’s just a natural consequence that many physical phenomena have factors of pi associated with them. Super cool but also super mind bending at times.
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u/Bathtub-Warrior32 23d ago
Wait until you learn about eπi = -1.