Problems from Another Time

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

I have two fields of grain. From the first field I harvest 2/3 sila (a measurement of grain volume) per sar (a unit of area); from the second, 1/2 sila per sar.

Logarithms: The Early History of a Familiar Function

The authors recount the 'great tale' of Napier's and Burgi's parallel development of logarithms and urge you to use it in class.

The Door is Ajar

A two door gate of unknown width is opened so that a 2 ts'un gap exists between the two doors.

Rifle Ball Through a Three-Inch Plank

A rifle ball is fired through a three-inch plank, the resistance of which causes an unknown constant retardation of its velocity.

Two Circles

Two circles of radii 25 feet intersect so that the distance between their centers is 30 feet. What is the length of the side of the largest square inscribable within their intersecting arcs?

Peano on Wronskians: A Translation - On the Wronskians

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

Gardening

An oblong garden is a half yard longer than it is wide and consists entirely of a gravel walk...

The Speculator's Buy

A speculator bought stock at 25% below par and sold it at 20% above par. He gained $1560. How much did he invest?

Contractors

A carpenter has undertaken to build a house in 20 days. He takes on another man and says; "If we build the house together, we can accomplish the work in 8 days!" How long would it take this other man to build the house working alone?

'He Advanced Him 200 Lambs of Gold': The Pamiers Manuscript - A Source of the Two-Trains Problem?

Discussion of 15th century French manuscript, with translation of its problems, including one with negative solutions