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Problems from Another Time

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

Find the greatest value of y in the equation a4 x2= (x2 + y2)3.
Given a pyramid 300 cubits high, with a square base 500 cubits to a side, determine the distance from the center of any side to the apex.
A square walled city of unknown dimensions has four gates, one at the center of each side.
In a rectangle, having given the diagonal and perimeter, find the sides
The authors recount the 'great tale' of Napier's and Burgi's parallel development of logarithms and urge you to use it in class.
Given two circles tangent to each other and to a common line, determine a relationship between the radii and the distance between the tangent points.
There are two piles, one containing 9 gold coins, the other 11 silver coins.
A set of four congruent circles whose centers form a square is inscribed in a right triangle ABC where C is the right angle and serves as one corner of the square. Find their radius in terms of the sides; a,b,c, of the triangle.
How a translation of Peano's counterexample to the 'theorem' that a zero Wronskian implies linear dependence can help your differential equations students
A certain man says that he can weigh any amount from 1 to 40 pounds using only 4 weights. What size must they be?

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