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Great Moments in Mathematics Before 1650

A collection of short lectures by Howard Eves giving details on 20 important happenings in the history of mathematics before 1650.

Apollonius's Ellipse and Evolute Revisited

Apollonius found how to draw normals to an ellipse from points in the ellipse by using hyperbolas. A modern version is presented here.

Euler's Analysis of the Genoese Lottery

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.

Gardening

An oblong garden is a half yard longer than it is wide and consists entirely of a gravel walk...

Area of Elliptical Segment

Find the area of the elliptical segment cut off parallel to the shorter axis;

The Nodding Sphere and the Bird's Beak: D'Alembert's Dispute with Euler

An introduction to the priority dispute between Euler and D'Alembert relating to several mathematical ideas that both worked on in the 1740s and 1750s.

Agenda items

Here are some things I don't want to forget to ask.

Points in a Semicircle

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

Apples and Oranges and Peaches

If 40 oranges are worth 60 apples, and 75 apples are worth 7 dozen peaches, and 100 peaches are worth 1 box of grapes and three boxes of grapes are worth 40 pounds of pecans, how many pounds of pecans can be bought for 100 oranges?

A History of Abstract Algebra

A history of the various algebraic structures that came together to give us "abstract algebra" by early in the twentieth century.