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Four episodes in the history of geometry are discussed, where dynamic geometry helps in understanding the ideas.
In the middle of the 18th century, King Frederick the Great of Prussia became interested in creating a lottery to raise money. As was his custom when mathematical matters were involved, he called upon Leonhard Euler for counsel.
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.
The edge of a cloud is at an altitude of 20 degrees and the sun above it at 35 degrees. The shadow cast by the edge of the cloud fall on a object 2300 yards away, how high is the cloud?
A thorough study of Benjamin Franklin's mathematical accomplishments, in particular his work on magic squares.
Suppose that for every 4 cows a farmer has, he should plow 1 acre of land, and allow 1 acre of pasture for every 3 cows; how many cows could he keep on 140 acres?