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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.

Surveying a Field

I was employed to survey a field, which I was told was an exact geometrical square, but by reason of a river running through it, I can only obtain partial measurements.

Johannes Kepler's Astronomia Nova

Three images from Kepler's 1609 Astronomia Nova, the text in which he introduced his first two laws of planetary motion

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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