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# Triangle Incircle Iteration

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### Vedic Sutra - All from 9 and Last from 10

### Tournament Scheduling

### Archimedes and Numerical Roots

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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.

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?

Scheduling games is a little more challenging than one might desire. Here are some tournament formats that sport schedulers use.

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?