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Convergence articles

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Horsing Around

One military horse cannot pull a load of 40 dan; neither can 2 ordinary horses, nor can three inferior horses...

Japanese Pentagon Problem

There is a regular pentagon. The length of its side is a. Find the area of the pentagon. Generalize your result for a nonagon.

Logarithms: The Early History of a Familiar Function

The authors recount the 'great tale' of Napier's and Burgi's parallel development of logarithms and urge you to use it in class.

The Amount of Time a Man Can Do Work

How long does it take a single man to do work when...

Pennies for the Poor

If I were to give 7 pennies to each beggar at my door, I would have 24 pennies left in my purse. How many beggars are there and how much money do I have?

Contractors

A carpenter has undertaken to build a house in 20 days. He takes on another man and says; "If we build the house together, we can accomplish the work in 8 days!" How long would it take this other man to build the house working alone?

An Inscribed Ellipse
Given right triangle ABC where C is the right angle, ellipse O (a,b) is inscribed in it, with its major axis parallel to BC. Calculate the semi-major axis, a, in terms of AC, BC and b.
Landscaping

A person has a circular yard that is 150 ft. in diameter, and wishes a walk of equal width made round it within the fence...

Poles

On a certain ground stands two poles 12 feet apart, the lesser pole is 35 ft. in height and the greater 40 ft. It is sought, if the greater pole will lean on the lesser, then in what part will it touch?

Review of L'algebre au temps de Babylone: Quand les mathematiques s'ecrivaient sur de l'argile

[Translation of title: Algebra in the Time of Babylon. When Mathematics Were Written on Clay.] A thorough review of Jens Hoyrup's revision, expansion, and French translation of his own 1998 book for Danish high-school students.

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