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Problems from Another Time

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

Find two number with sum 20 and when squared their sum is 208.
A set of four congruent circles whose centers form a square is inscribed in a right triangle ABC where C is the right angle and serves as one corner of the square. Find their radius in terms of the sides; a,b,c, of the triangle.
In the figure at the left, if the radii of each inscribed circle is 1, what are the dimensions of the bounding rectangle?
Two ants are 100 paces apart, crawling back and forth along the same path. The first goes 1/3 pace forward a day and returns 1/4 pace; the other goes forward 1/5 pace and returns 1/6 pace. How many days before the first ant overtakes the second?
There is a four sided field.
Suppose a man had put out one cent at compound interest in 1620, what would have been the amount in 1824, allowing it to double once in 12 years?
How a translation of Peano's counterexample to the 'theorem' that a zero Wronskian implies linear dependence can help your differential equations students
A circle, a square and an equilateral triangle all have the same perimeter equal to 1 meter. Compare their areas.
In one day, a person can make 30 arrows or fletch [put the feathers on] 20 arrows.
Gun metal of a certain grade is composed of 16% tin and 84% copper. How much tin must be added to 410 lbs. of this gun metal to make a composition of 18% tin?

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