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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.

Long Time to Fill the Tub

A water tub holds 73 gallons; the pipe which fills it usually admits 7 gallons in 5 minutes; and the tap discharges 20 gallons in 17 minutes.

Cow Dilemma

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?

An Introduction to the History of Mathematics

Howard Eves' sixth edition is still worth considering for a textbook.