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Problems from Another Time

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

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.
'He Advanced Him 200 Lambs of Gold': The Pamiers Manuscript - Acceptance of Negative Solutions
Discussion of 15th century French manuscript, with translation of its problems, including one with negative solutions
An Inscribed Ellipse
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.
Viete: Triangle II
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.

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