Problems from Another Time

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

A vessel is anchored in 3 fathoms of water and the cable passes over a sheave in the bowsprit which is 6 ft above the water.

Flying High

How high above the earth must a person be raised that he [or she] may see 1/3 of its surface?

Small Fish

There is a fish whose body weighs 8 ounces. How much does the whole fish weigh?

Perpendicular Curves

Show that the curves x2 - y2 = a2 and 2 xy = b2 cross at right angles.

A Hole in One?

A barrel has various holes in it. The first hole empties the barrel in three days...

Out to Pasture 2

X, Y and Z hired a pasture for the season for $90.00. Each has a different number of mules and are on the pasture for a different number of days. How much is each to pay?

Fields of Grain

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.