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Convergence articles

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Square Battalions

A general formed his men into a square, that is, an equal number in rank and file, and he found that he had an excess of 59 men.

Perpendicular Curves

Show that the curves x2 - y2 = a2 and 2 xy = b2 cross at right angles.

An Apple a Day

A man entered an orchard through 7 gates, and there took a certain number of apples. When he left the orchard, he gave the first guard half the apples he had and 1 apple more.

A Radical Approach to Real Analysis

A historically minded textbook designed to teach real analysis by considering some of the problems faced by 19th century mathematicians.

To Know a Little

To find three quantities x.y, and z...

Horses and Stalls

It is required to determine whether 30 horses can be put into 7 stalls; so that in every stall there may be, either a single horse, or an odd number of horses.

Review of The Music of Pythagoras
Subtitled How an Ancient Brotherhood Cracked the Code of the Universe and Lit the Path from Antiquity to Outer Space, this is a book of entertaining stories more so than scholarly research.
Small Fish

There is a fish whose body weighs 8 ounces. How much does the whole fish weigh?

A Serious Series

Given the fraction ax/(a-x), convert it into an infinite series.

But What's in the Flasks?

Thirty flasks—10 full, 10 half-empty, and 10 completely empty—are to be divided among 3 sons so that flasks and contents should be shared equally. How may this be done?

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