Convergence articles

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The Nodding Sphere and the Bird's Beak: D'Alembert's Dispute with Euler

An introduction to the priority dispute between Euler and D'Alembert relating to several mathematical ideas that both worked on in the 1740s and 1750s.

Agenda items

Here are some things I don't want to forget to ask.

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