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Convergence articles

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Area of a Polygon

Prove that the area of a regular polygon can be given by the product of its perimeter and half the radius of the inscribed circle.

Gaspard Monge's Descriptive Geometry
This is the title page to the 1811 edition of the Descriptive Geometry of Gaspard Monge (1746-1818). This book deals with methods for representing three-dimensional objects in two dimensions. It was written to accompany Monge's courses at the Ecole Polytechnique in Paris.
Purse of Denari

Four men already having denari found a purse of denari; each man has a different amount of denari before they found the purse. Find out how much denari each man has.

What is 0^0?
The expression 0^0 is usually called an indeterminate form. This article details the history of the meaning of this expression and concludes that, in some cases, we should evaluate it as 1.
Round Pond in Rectangular Garden

A round pond sits in a rectangular garden. Its center is inaccessible; however, you know the distances from each corner of the garden to the circumference of the pond: 60, 52, 28, and 40 yards. What is the radius of the pond?

Making Heads or Tails of It

Now there are six-headed four-legged animals and four-headed two-legged birds placed together.

A Triangular Problem

In a right triangle, having been given the perimeter, a, and the length of the perpendicular from the right-angled vertex to the hypotenuse, b, it is required to find the length of the hypotenuse.

The Incircle of a Triangle

The incircle O(r) of triangle ABC touches AB at D, BC at E and AC at F. Find r in terms of AD, BE and CF.
 

Mathematics in India

A survey of over two thousand years of the history of mathematics on the Indian subcontinent.

The Time It Takes To Eat a Goat

A lion, a wolf and a fox each take a certain amount of time to eat a goat separately. How long would it take all these animals together to eat the goat?

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