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Problems from Another Time

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

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.
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?

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