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Mathematics is often referred to today as the "science of patterns." But has this always been true historically, or is this something that happened in recent times? The question is discussed here with reference to the work of Euclid and Jacob Steiner.
A seminar of faculty from colleges and universities in the Philadelphia area, meeting monthly at Villanova University.
Determine the dimensions for a right-angled triangle, having been given the hypotenuse, and the side of the inscribed square.
A horse, halving its speed each day, travels 700 miles in 7 days. How far does it travel each day?
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.
The perimeters of two similar triangles are 45 and 135 respectively. One side of the first triangle has length 11″ and a second side, 19″. Find the lengths of the sides of the second triangle.
Suppose General [George] Washington had 800 men and was supplied with provisions to last 2 months but he needed to feed his army for 7 months.
Three men wish to buy a horse but none have a sufficient amount of money for the purchase; to do so they must borrow from each other. How much money does each man have and what is the price of the horse?
A lady being asked how old she was at the time of her marriage replied that the age of her oldest son was 13; that he was born 2 years after her marriage...

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