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Problems from Another Time

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

Squared Proof
Prove that if the sums of the squares of opposite sides of any quadrilateral are equal, its diagonals intersect at right angles.
Water Reeds
A pond has two water reeds, where the one grows 3 feet and the other 1 foot on the first day. The growth of the first becomes every day half of that of the preceding day, while the other grows twice as much as on the day before.
Logarithms: The Early History of a Familiar Function - Logarithms: A 'Great Tale' for Use in the Classroom
The authors recount the 'great tale' of Napier's and Burgi's parallel development of logarithms and urge you to use it in class.
Two Equal Parts of a Triangle
The three sides of a triangular piece of land, taken in order, measure 15, 10, and 13 chains respectively.
Series of Circles
A series of circles have their centers on an equilateral hyperbola and pass through its center. Show that their envelope is a lemniscate.
Breaking Bread
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?
Peano on Wronskians: A Translation - Conclusion
How a translation of Peano's counterexample to the 'theorem' that a zero Wronskian implies linear dependence can help your differential equations students
Buying Wood
Three people buy timber together. One pays the merchant 5 coins, another 3 coins, and the last 2 coins.
Ladder Problem
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?
Oracle for Rent
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.

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