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A father wills his estate valued at $40, 000 to his three children. Before the settlement one of the children dies. What should the other two receive?
Imagine an urn with two balls, each of which may be either white or black. One of these balls is drawn and is put back before a new one is drawn.

Problems from a 15th century French manuscript, including one with negative solutions

Having been given the lengths, a and b, of two straight lines drawn from the acute angles of a right triangle to the middle of the opposite sides, determine the lengths of those sides.

The expression 0^0 is usually called an indeterminate form. This article details the history of the meaning of this expression and concludes that, in some cases, we should evaluate it as 1.
This is page 167 from the Exercitationes mathematicae (1657) of Frans van Schooten (1615-1660). This book contained a collection of mathematical construction problems, among much else. It was one of the books read by Isaac Newton while he was a student at Cambridge University and helped to introduce him to modern mathematics. On this page we see a construction enabling one to find the distance across a river.
Explain the geometric basis of "completing the square," the original method of solving quadratic equations, to your students.
In one day, a person can make 30 arrows or fletch [put the feathers on] 20 arrows.
Poster of Banneker, with a brief description of his life and work.

As is the case with a great deal of interesting mathematics, the conic sections are believed to have been discovered in an attempt to solve a problem, a problem which on the surface seems to have nothing to do with conic sections.