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Problems from Another Time

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

Inscribed Square
Knowing the base, b, and the altitude, a, of a triangle, find the expression for a side of the inscribed square.
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?
Snowdrift on the Tracks
A railway train strikes a snowdrift which creates a constant resistance. How long does it take the snow to stop the train?
A River Runs Through It
Wanting to know the breadth of a river, I measured a base of 500 yards in a straight line close by one side of it.
Travelling Men 2
Two men start walking at the same time and travel a distance. One is walking faster and completes the journey sooner. How fast did each man travel?
Chuquet's Rule of Average Numbers
Prove Chuquet's rule of average numbers.
Look Out Below!
Suppose a ladder 60 feet long is placed in a street so as to reach a window 37 feet above the ground on one side of the street...
Radii of Three Circles
Determine the radii of three equal circles described within and tangent to a given circle, and also tangent to each other.
Numbers Game #1
The sum of two numbers is 10 and their product is 40. What are the numbers?
Logarithms: The Early History of a Familiar Function - Bibliography
The authors recount the 'great tale' of Napier's and Burgi's parallel development of logarithms and urge you to use it in class.

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