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Problems from Another Time

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

How a translation of Peano's counterexample to the 'theorem' that a zero Wronskian implies linear dependence can help your differential equations students
In a certain lake, swarming with red geese, the tip of a lotus bud was seen to extend a span [9 inches] above the surface of the water.
A square circumscribed about a given circle is double in area to a square inscribed in the same circle. True of false? Prove your answer.
What proportions of sugar at 8 cents, 10 cents and 14 cents per pound, will compose a mixture worth 12 cents per pound?
Fibonacci gave a practical rule for approximating the area of an equilateral triangle.
What number which being increased by 1/2, 1/3, and 1/4 of itself, the sum shall be 75?
A gentleman has bought a rectangular piece of land whose perimeter is to be 100 rods.
The dimensions of a rectangular box in inches are expressed by three consecutive numbers. The surface of the box is 292 square inches. Find the dimensions.
Given two circle tangent at the point P with parallel diameters AB, CD, prove that APD and BPC are straight lines.
A copper water tank in the form of a rectangular parallelopiped is to made. If its length is to be a times its breadth, how high should it be that for a given capacity it should cost as little as possible?

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