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Convergence articles

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God Created the Integers: Mathematical Breakthroughs that Changed History

Original source material from seventeen mathematicians, with commentary by Stephen Hawking.

A River Runs Through It

Wanting to know the breadth of a river, I measured a base of 500 yards in a straight line close by one side of it.

The Chinese General and the River

An old Chinese general led his army to a river with a steep bank. Standing atop the bank, he held a stick 6 feet long perpendicular to himself.

Euclidean and Non-Euclidean Geometries: Development and History

This textbook seamlessly combines the history of non-Euclidean geometry with the mathematical ideas.

Prove the Straight Lines

Given two circles tangent at the point P with parallel diameters AB and CD, prove that APD and BPC are straight lines.

Conic Contents

Determine the greatest cylinder that can be inscribed in a given cone.

Tree and Vine

A tree is 2 zhang tall and has a circumference of 3 chi. There is a vine that winds seven equally spaced times around the tree and reaches the top. What is the length of the vine?

Lotus in the Lake

In a certain lake, swarming with red geese, the tip of a lotus bud was seen to extend a span above the surface of the water.

Two Numbers

Find two numbers with sum 20 and when squared their sum is 208.

Sick Leave

A teacher agreed to teach 9 months for $562.50 and his board. At the end of the term, on account of two months' absence caused by sickness, he received only $409.50. What was his board worth per month?

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