ἀγεωμέτρητοσ μηδεὶσ εἰσίτω

let no-one ignorant of geometry enter here

Proof of the Pythagorean Theorem

{{< mthm >}} For a right-angled triangle, the square of the length of the hypotenuse (\(c\)) is equal to the sum of the squares of the lengths of the other two sides (\(a\) and \(b\)). This can be represented as: \[ c^2 = a^2 + b^2 \] {{< /mthm >}}

{{< mproof >}} Consider two squares, each of side length \(a + b\). We can place four congruent right-angled triangles inside each square, with side lengths \(a\), \(b\), and \(c\).

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The Dowel Problem

Given that we have a circular dowel as such

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