Fiddler on the Proof: Nov 1, 2024

David Ding

Nov 1, 2024

What’s the Area of a “Pseudo-Square”?

We have a "pseudo-square" here:

diagram of a pseudo-square

The pseudo-square pictured above has two straight sides, which run radially between arcs of two concentric circles.

Assuming this is a unit pseudo-square (i.e., each side has length 1), what is its area?

Area: \(\frac{1 + \sqrt{\pi^2 + 1}}{2\pi} \approx 0.68\) unit squared

Explanation:

This is a pen-and-paper solve:

Part 1 Part 2 Part 3 Part 4