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Problems from Another Time

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

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 man bought a number of sheep for $225; 10 of them having died, he sold 4/5 of the remainder for the same cost and received $150 for them. How many did he buy?
A barrel has various holes in it. The fist hole empties the barrel in three days...
In a rectangle, having given the diagonal and perimeter, find the sides
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.
Determine the different values of x, when a certain function hits a minimum.
Given a door and a measuring rod of unknown dimensions, the rod is used to measure the door.
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.
Two ants are 100 paces apart, crawling back and forth along the same path. The first goes 1/3 pace forward a day and returns 1/4 pace; the other goes forward 1/5 pace and returns 1/6 pace. How many days before the first ant overtakes the second?
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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