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Problems from Another Time

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

The Length of a String
Two circles, the sum of whose radii is a, are placed in the same plane with their centers at a distance 2a...
Neither Rain nor Sleet nor Snow
If two Post-Boys, A and B at 59 miles distance from one another, set out in the morning in order to meet...
Swinging Pendulum
Given a pendulum as shown. The height of the pendulum is two units and its horizontal width is 2 units. What is the area of the pendulum?
Four Numbers
Given four numbers whose sum is 9900; the second exceeds the first by 1/7 of the first...
Sides of a Rectangle 2
In a rectangle, given the diagonal and perimeter, find the sides
Cow Dilemma
Suppose that for every 4 cows a farmer has, he should plow 1 acre of land, and allow 1 acre of pasture for every 3 cows; how many cows could he keep on 140 acres?
Peano on Wronskians: A Translation
How a translation of Peano's counterexample to the 'theorem' that a zero Wronskian implies linear dependence can help your differential equations students
The Rat Race
Now there is a wall 5 feet thick and two rats tunnel from opposite sides.
The Incircle of a Triangle
The incircle O(r) of triangle ABC touches AB at D, BC at E and AC at F. Find r in terms of AD, BE and CF.
 
Numbers Game #2
Given a number, take 1/3 of the number away from itself and also remove 2. If this result is multiplied by itself, it equals the number plus 24. What is the number?

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