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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 a Bowsprit?
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 - Introduction
The authors recount the 'great tale' of Napier's and Burgi's parallel development of logarithms and urge you to use it in class.
Landscaping
A person has a circular yard that is 150 ft. in diameter, and wishes a walk of equal width made round it within the fence...
Woodcutter
A woodcutter starts to fell a tree 4 feet in diameter, and cuts half way through. One face of the cut is horizontal, and the other face is inclined to the horizontal at an angle of 45 degrees. Find the volume of the wood cut out.

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