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Problems from Another Time

Individual problems from throughout mathematics history, as well as articles that include problem sets for students.

A series of circles have their centers on an equilateral hyperbola and pass through its center. Show that their envelope is a lemniscate.
Divide 100 loaves of bread among 10 men including a boatman, a foreman, and a doorkeeper, who each receives double portions. What is the share of each?
How a translation of Peano's counterexample to the 'theorem' that a zero Wronskian implies linear dependence can help your differential equations students
Three people buy timber together. One pays the merchant 5 coins, another 3 coins, and the last 2 coins.
If a ladder, placed 8 ft. from the base of a building 40 ft. high, just reached the top, how far must it be placed from the base of the building that it may reach a point 10 ft. from the top?
An oracle ordered a prince to build a sacred building, whose space would be 400 cubits, the length being 6 cubits more than the width, and the width 3 cubits more than the height. Find the dimensions of the building.
Discussion of 15th century French manuscript, with translation of its problems, including one with negative solutions
Given right triangle ABC where C is the right angle, ellipse O (a,b) is inscribed in it, with its major axis parallel to BC. Calculate the semi-major axis, a, in terms of AC, BC and b.
In a right triangle, the hypotenuse is 13 and the sum of the sides around the right angle is 17. Find the lengths of the sides around the right angle.
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?

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