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Problem Set 4

How could the Pythagorean Theorem possibly translate from two and three dimensions into four dimensions?

1. Is it possible to create a Pythagorean Quintuplet with Plato’s method described in Problem Set 2 for creating Pythagorean Triples? Make a conjecture and test it. Prove or disprove it.

2. Could we go further with the Pythagorean Theorem into more dimensions? What type of application would that have?