# Convergence articles

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There are a number of wonderful mathematics websites that readers of Convergence should be aware of. We describe some of them here.

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 1640 printing of Galileo's Operation of the Geometrical and Military Compass, originally published privately in 1606. Galileo had invented a version of this geometrical compass a few years earlier and evidently gave copies of this manual to those who bought the compass. The compass had many uses, from performing square root calculations to determining ranges of cannons to solving surveying problems.

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

A man bought a number of sheep for $225; 10 of them having died, he sold 4/5 of the remainder for the same cost and received$150 for them. How many did he buy?

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

Three people buy timber together. One pays the merchant 5 coins, another 3 coins, and the last 2 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".

A detailed study of the cycles of the Mayan calendar, along with some other ancient calendars.