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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 two circles tangent to each other and to a common line, determine a relationship between the radii and the distance between the tangent points.
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 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.
After a terrible battle it is found that 70% of the soldiers have lost an eye.
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?
Discussion of 15th century French manuscript, with translation of its problems, including one with negative solutions
A man plants 4 kernels of corn, which at harvest produce 32 kernels: these he plants the second year; now supposing the annual increase to continue 8 fold, what would be the produce of the 15th year, allowing 1000 kernels to a pint?
A wooden beam is stood vertically against a wall. The length of the beam is 30 units.
If an arc of 45 degrees on one circumference is equal to an arc of 60 degrees on another circle, what is the ratio of the areas of the circle?
Knowing the base, b, and the altitude, a, of a triangle. Find the expression for a side of the inscribed square.

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