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Vedic Sutra is one of many ancient Indian sutras which involves a cross subtraction method. Can you give a good explanation of WHY it works?

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Archimedes and Numerical Roots

The problem is how did Archimedes calculate the lengths of the sides of the polygons which needed him to be able to calculate square roots?

Triangle Incircle Iteration

Age 14 to 16
Challenge Level

Have you noticed that, whatever triangle you start with, the nested triangles get more and more like equilateral triangles? In fact this convergence is very rapid.

The question tells you how to show why this happens by considering iterative sequences.