# Problems from Another Time

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

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.
Now there is a wall 5 feet thick and two rats tunnel from opposite sides.
Suppose a man had put out one cent at compound interest in 1620, what would have been the amount in 1824, allowing it to double once in 12 years?
A circle, a square and an equilateral triangle all have the same perimeter equal to 1 meter. Compare their areas.