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Problems from Another Time

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

What is the perpendicular height of a cloud when its angles of elevation were 35 degrees and 64 degrees as taken by two observers at the same time...
When knowing the sum of their ages along with another equation, determine how old a father and son are.
Show that the curves x2 - y2 = a2 and 2 xy = b2 cross at right angles.
The highest point of the Andes is about 4 miles above sea level.
A California miner has a spherical ball of gold, 2 inches in diamter, which he wants to exchange for spherical balls 1 inch in diameter. How many of the smaller spheres should he receive?
In order to encourage his son in the study of arithmetic, a father agrees to pay him 8 pennies for every problem solved correctly and to charge him 5 pennies for each incorrect solution.
The sum of two numbers is 10 and their product is 40. What are the numbers?
There is a round town 8000 feet in circumference.
In baking a hemispherical loaf of bread of 10" radius, the crust was everywhere of an equal thickness, and the solidity of the crust was equal to half the solid content of the whole loaf. What were the dimensions of the interior soft part?
How a translation of Peano's counterexample to the 'theorem' that a zero Wronskian implies linear dependence can help your differential equations students

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