# CoMac

## A Nines Multiples Problem

CoMaC shares a problem on the sum of digits adapted from one that appeared in an online column on the Math Forum site.

## Two Combinatorial Problems

Here are some problems that were posed in a recent mathematics contests...

Take a look at some number problems from ancient India...

## Ramanujan and Pythagoras!

An interesting extract from Ramanujan’s notebooks which makes for a great classroom exercise in geometry, with a dash of algebra thrown in. An enterprising teacher could do this proof in stages — starting from showing students the figure and asking them to prove the theorem; if they can’t, providing them with enough scaffolding to help them complete the proof.

Here are other links, suggested by Rajkishore from APF,  that can be referred to as well (Click on the image):

## Viviani’s Theorem...And A Cousin

Viviani’s theorem is one of those beautiful results of elementary geometry that can be found experimentally
even by young children...

## Complete Family of Pythagorean Triples - Part 2

In Part I of this article we presented a few methods for generating Primitive Pythagorean Triples (PPTs). You will recall that they were all ‘piece meal’ in character. Now we present two more approaches which offer complete solutions to the PPT problem. Both are based on straightforward reasoning and simple algebra. And no PPT is left out: we capture the complete family in each case.

## A Surprising Fact about Triangles with a 60 degree Angle

Is the converse of a statement always true?...
Ever posed this question to a class and then scanned your memory for good
examples to clinch your argument? Here is one you could use.

## How Many Primitive Pythagorean Triples in Arithmetic Progression?

A simple investigation and a convincing proof based on a novel connection between two topics — the Pythagorean Theorem and Sequences — taught in middle and high school.

## The Pythagorean Theorem

Taking note of a collective of contributors...
How do I prove thee? Can I count the ways? A look at the wide variety of methods used to prove the theorem of Pythagoras.

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