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Convergence articles

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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.

Isoceles Trapezoid

Given the dimensions of an isosceles trapezoid, find the length of the transversal drawn parallel to the bases that divides the trapezoid into 2 equal areas.

Robert Recorde's Pathway to Knowledge
The first page of Pathway to Knowledge by Robert Recorde (1510-1558). A version of Euclid's Elements, with commentary by Recorde to make it easier to understand. This page includes Euclid's first three postulates.
The Art of the Infinite

This book is a collection of mathematical ideas organized around the themes of infinity and the illumination of the nature of mathematical thought.

The Pythagorean Theorem: A 4,000 Year History

A survey of this theorem's 4000 year history, with applications to many fields.

Leonard Euler's Solution to the Konigsberg Bridge Problem

A survey of the famous Konigsberg Bridge Problem and its connection to graph theory, by an undergraduate student.

Silver Cups

A lady has two silver cups, and only one cover for both. The first cup weighs 16 oz, and when it is covered it weighs 3 times as much as the second cup; but when the second cup is covered, it weighs 4 times as much as the first.

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