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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.
Four episodes in the history of geometry are discussed, where dynamic geometry helps in understanding the ideas.
A horse, halving its speed each day, travels 700 miles in 7 days. How far does it travel each day?
A horse halving its speed every day runs 700 miles in 7 days.
How high above the earth must a person be raised that he [or she] may see 1/3 of its surface?
An image of the calendar, together with instructions for its use
Prove that the area of a regular polygon can be given by the product of its perimeter and half the radius of the inscribed circle.
This is the title page to the 1811 edition of the Descriptive Geometry of Gaspard Monge (1746-1818). This book deals with methods for representing three-dimensional objects in two dimensions. It was written to accompany Monge's courses at the Ecole Polytechnique in Paris.
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 thorough study of Benjamin Franklin's mathematical accomplishments, in particular his work on magic squares.

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