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Problems from Another Time

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

Having been given the sum of two numbers,a, and the difference of their squares,b, find the numbers.
Two circles of radii 25 feet intersect so that the distance between their centers is 30 feet. What is the length of the side of the largest square inscribable within their intersecting arcs?
Find the greatest value of y in the equation a4 x2= (x2 + y2)3.
A circle is inscribed in an isosceles trapezoid. Find the relationship of the radius to the sides.
A square walled city of unknown dimensions has four gates, one at the center of each side.
A carpenter has undertaken to build a house in 20 days. He takes on another man and says; "If we build the house together, we can accomplish the work in 8 days!" How long would it take this other man to build the house working alone?
The authors recount the 'great tale' of Napier's and Burgi's parallel development of logarithms and urge you to use it in class.
A fellow said that when he counted his nuts by twos, threes, fours, fives and sixes, there was still one left over; but when he counted them by sevens they came out even. How many did he have?
There are two piles, one containing 9 gold coins, the other 11 silver coins.
A general formed his men into a square, that is, an equal number in rank and file, and he found that he had an excess of 59 men.