# Convergence articles

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Page 12: Dilworth to Doob

Determine the dimensions for a right-angled triangle, having been given the hypotenuse, and the side of the inscribed square.

This is the title page of the Summa de arithmetica, geometrica, proportioni et proportionalita, published by Luca Pacioli in 1494. This was the most comprehensive mathematical text of the time and one of the earliest printed mathematical works. It contained not only practical arithmetic, but also algebra, practical geometry and the first published treatment of double-entry bookkeeping.

Given a semicircle, prove that if O is the circle's center, DO=OE.

Relationships between Architecture and Mathematics

The radius of a circle is 3.20 meters. Compute to within .001 square meters the areas of the inscribed and circumscribed equilateral triangles.

A fox, a wild-cat, and a hound pass through customs and together pay 111 coins.

Suppose General [George] Washington had 800 men and was supplied with provisions to last 2 months but he needed to feed his army for 5 months.

The cavity of our chimney is an upright parallelepiped, the diagonal of whose base is 60"; and the height of the lower side of the lintel above the plane of the floor is 40".

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