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Convergence articles

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Area of Elliptical Segment

Find the area of the elliptical segment cut off parallel to the shorter axis;

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.
The Secret Life of Numbers

Short sketches on how mathematicians work and think.

A Successful Businessman

A certain merchant increases the value of his estate by 1/3...

Four Congruent Circles and an Inscribed Square

A set of four congruent circles whose centers form a square is inscribed in a right triangle ABC where C is the right angle and serves as one corner of the square. Find their radius in terms of the sides; a,b,c, of the triangle.

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