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Problems from Another Time

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

If an arc of 45 degrees on one circumference is equal to an arc of 60 degrees on another circle, what is the ratio of the areas of the circle?
Find two number with sum 20 and when squared their sum is 208.
Knowing the base, b, and the altitude, a, of a triangle. Find the expression for a side of the inscribed square.
Given the cats eye as shown. Let the radius of the eye be given by R. What is the area of the pupil?
In the figure at the left, if the radii of each inscribed circle is 1, what are the dimensions of the bounding rectangle?
There is a fish whose body weighs 8oz. Tell me how much the whole fish weighs?
There is a four sided field.
How a translation of Peano's counterexample to the 'theorem' that a zero Wronskian implies linear dependence can help your differential equations students
There is a tree with 100 branches. How many nests, eggs and birds are there?
In one day, a person can make 30 arrows or fletch [put the feathers on] 20 arrows.