# Problems from Another Time

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

A series of circles have their centers on an equilateral hyperbola and pass through its center. Show that their envelope is a lemniscate.
Given the fraction ax/ (a-x ), convert it into an infinite series.
Given a wooden log of diameter 2 feet 5 inches from which a 7 inch thick board is to be cut, what is the maximum possible width of the board?
A two door gate of unknown width is opened so that a 2 inch gap exists between the two doors.
A man agreed to pay for 13 valuable houses worth $5000 each, what the last would amount to, reckoning 7 cents for the first, 4 times 7 cents for the second, and so on, increasing the price 4 times on each to the last. 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 father left$20,000 to be divided among his four sons ages 6, 8, 10, and 12 years respectively so that each share placed at 4 1/2 compounded interest should amount to the same value when its possessor becomes the age 21.
There is a circle from within which a square is cut, the remaining portion having an area of 47.6255 square units.
Given a right triangle where you know the length of the base and the sum of the perpendicular side and the hypotenuse.

How a translation of Peano's counterexample to the 'theorem' that a zero Wronskian implies linear dependence can help your differential equations students