Basic arithmetic and geometry formed the basis of what the mathematical world had to offer at its very beginnings. ... This theory incorporates the idea that musical sounds have mathematical tones of energy which ultimately allow them to relate with patterns of proportion dealing with angles, shapes, and movements. ... As mentioned in the Stanford Encyclopedia, "Pythagoras is said to have transformed the philosophy of geometry into a form of liberal education, to have investigated its theorems in an immaterial and intellectual way and specifically to have discovered the study of irrationa...

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• Grade Level: Undergraduate