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Mathematics as the Science of Patterns

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 Linear Hypocycloid

Prove geometrically that the hypocycloid is a straight line when the radius of the rolling circle is one-half the radius of the fixed circle.

Water Reeds

A pond has two water reeds, where the one grows 3 feet and the other 1 foot on the first day. The growth of the first becomes every day half of that of the preceding day, while the other grows twice as much as on the day before.

Making Heads or Tails of It

Now there are six-headed four-legged animals and four-headed two-legged birds placed together.

Property Values

A gentleman has bought a rectangular piece of land whose perimeter is to be 100 rods.

Rifle Ball Through a Three-Inch Plank

A rifle ball is fired through a three-inch plank, the resistance of which causes an unknown constant retardation of its velocity.

'In these numbers we use no fractions': A Classroom Module on Stevin's Decimal Fractions

After completing this assignment on Simon Stevin's treatment of decimal fractions in his 1585 De Thiende, the author's preservice mathematics teachers understood why our usual procedure for multiplying such fractions works.

How Much to Buy a Horse?

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?

Ohio Section Short Course, Study the Masters
The Ohio Section Short Course will consider the use of original sources in teaching mathematics.
Round Pond in Rectangular Garden

A round pond sits in a rectangular garden. Its center is inaccessible; however, you know the distances from each corner of the garden to the circumference of the pond: 60, 52, 28, and 40 yards. What is the radius of the pond?

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