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Convergence articles

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Points in a Semicircle

Given a semicircle, prove that if O is the circle's center, DO=OE.

Long Time to Fill the Tub

A water tub holds 73 gallons; the pipe which fills it usually admits 7 gallons in 5 minutes; and the tap discharges 20 gallons in 17 minutes.

Cow Dilemma

Suppose that for every 4 cows a farmer has, he should plow 1 acre of land, and allow 1 acre of pasture for every 3 cows; how many cows could he keep on 140 acres?

An Introduction to the History of Mathematics
Howard Eves' sixth edition is still worth considering for a textbook.
Difference of Squares

Having been given the sum of two numbers, a, and the difference of their squares, b, find the numbers.

Coins

A boy gives 11 coins of equal denomination to a man, and the man finds that their total value in yen is 4 less than his age.

Servois' 1814 Essay on the Principles of the Differential Calculus, with an English Translation

The authors provide an analysis and English translation of the argument by a little known French mathematician that calculus should be based on series rather than on infinitesimals.

The Magic Squares of Manuel Moschopoulos

A translation from the original Greek of a manuscript on magic squares by the Byzantine scholar Manuel Moschopoulos, written about 1315

Chuquet's Rule of Average Numbers

Prove Chuquet's rule of average numbers.

Numbers Game #2

Given a number, take 1/3 of the number away from itself and also remove 2. If this result is multiplied by itself, it equals the number plus 24. What is the number?

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