“[Mathematics] is the work of the human mind, which is destined rather to study than to know, to seek the truth rather than to find it.”

— Évariste Galois | Mathematician, who by age 20, solved the 350 year old problem of describing which polynomials are solvable by radicals (turns out there are only nice general formulas [like the quadratic formula] up to degree 4)

mathblab: The Pythagorean theorem can be exte…


The Pythagorean theorem can be extended to any number of dimensions. In 2D space, the Pythagorean theorem gives us the length of the diagonal of a rectangle. It turns out, a simple modification (adding another square term) to the formula gives the diagonal of a rectangular prism. In the same way, the formula can be further extended to apply to 4 dimensional situations, and give the diagonal of a hypercube (4D cube) or tesseract (yes that’s where Marvel got the name for that glowing blue cube, one of the infinity stones). Keeping with the pattern, the Pythagorean theorem can be generalized to any arbitrary whole number dimension to apply to finding diagonals of n-dimensional rectangle analogs. 

Okay, but is this 4th dimension, hypercube stuff even real? IDK, is any math real? It doesn’t matter. But I can tell you this type of mathematics is useful. For example, these formulas are used to calculate lengths of vectors and are used in statistics to calculate standard deviation. Also Einstein’s theory of general relativity relies on a 4-dimensional mathematical framework. Without knowing this, the GPS in your phone would not work (GPS relies on precise timing, so precise that the effects of earths mass on spacetime become necessary to consider). 

See also Weisstein, Eric W. “Tesseract.” From MathWorld–A Wolfram Web Resource.

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