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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.

Four Integers

Given four integers which, if added together three at a time, their sums are: 20, 22, 24, and 27. What are the integers?

Four Companies

There are four companies, in one of which there are 6 men, in another 8, and in each of the remaining two, 9 men. How many ways can a committee of 4 men be composed by choosing one man from each company?

Maya Calendar Conversions

The authors provide descriptions of Maya calendar systems, photos of artifacts, examples of calendar conversions, and exercises for classroom use.

Four Circles in a Square

In a given square, inscribe 4 equal circles so that...

Tools of American Mathematics Teaching, 1800-2000

A survey of the use of technology in American mathematics teaching over the past 200 years.