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11:27
Khan Academy
Sal Khan
Khan Academy
Euler's Formula, e^(ix) = cos(x) + i*sin(x), and Euler's Identity, e^(iπ) + 1 = 0, are incredible math discoveries. They connect e, i, and pi through Maclaurin series of cos(x), sin(x), and e^x. These formulas reveal a deep, mysterious connection between important numbers in math.
Aug 14, 2016
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Euler’s formula for polyhedra reveals a universal truth hidden within the architecture of shapes. It states that for any convex polyhedron, the number of vertices minus the number of edges plus the number of faces always equals two (V - E F = 2). This simple equation highlights the balance and symmetry in the design of polyhedra, proving that even in complexity, there’s a fundamental simplicity guiding the structure of our universe. Through Euler’s formula, we glimpse the meticulous order govern
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