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Convergence articles

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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.

Japanese Temple Problem 2
The triangle ABC has a right angle at C. Show that 1/ED=1/AC+1/AB
A Circular Problem

Determine the dimensions of the least isosceles triangle ACD that can circumscribe a given circle.

Wooden Be Board

Given a wooden log of diameter 2 ch'ih 5 ts'un from which a 7 ts'un thick board is to be cut, what is the maximum possible width of the board?

Log Stuck in a Wall

Now given a cylindrical log of unknown size buried in a wall...

Grain and Camels

A certain gentleman ordered that 90 measures of grain were to be transported from his house to another, 30 leucas distant.

Ladder Problem

If a ladder, placed 8 ft. from the base of a building 40 ft. high, just reached the top, how far must it be placed from the base of the building that it may reach a point 10 ft. from the top?

Kepler: The Volume of a Wine Barrel

In his analysis of volumes of wine barrels, Kepler used ideas that would become important in differential and integral calculus. Use this article's animated visual imagery to help share Kepler's ideas with your students.

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