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Problems from Another Time

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

A set of n disjoint, congruent circles packs the surface of a sphere S so that each region of the surface exterior to the circles is bounded by arcs of three of the circles.
A wooden log is encased in a wall. If we cut part of the wall away to a depth of 1 inch...
An oracle ordered a prince to build a sacred building, whose space would be 400 cubits, the length being 6 cubits more than the width, and the width 3 cubits more than the height. Find the dimensions of the building.
Discussion of 15th century French manuscript, with translation of its problems, including one with negative solutions
Now a good horse and an inferior horse set out from Chang'an to Qi. Qi is 3000 li from Chang'an.
Having been given the lengths, a and b, of two straight lines drawn from the acute angles of a right triangle to the middle of the opposite sides, determine the length of those sides.
The steamer, Katie, leaves the wharf at New Orleans and runs an average speed of 15 mph. When Katie had gone 25 miles, the steamer R.E. Lee leaves the wharf and runs the average speed of 18 mph. How far will the Lee go before she overtakes the Katie?
A mouse is at the top of a poplar tree 60 braccia high, and a cat is on the ground at its foot. The mouse decends 1/2 a braccia a day and at night it turns back 1/6 of a braccia.
A farmer sold a team of horses for $440, but did not receive his pay for them until 1 yr, 8 mo after the sale. He had at the same time another offer of $410 for them. Did he gain or lose by the sale and by how much, money being worth 6%/yr?
Prove geometrically that the hypocycloid is a straight line when the radius of the rolling circle is one-half the radius of the fixed circle.

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