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Problems from Another Time

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

Money Makes the World Go Around
You have two sums of money, the difference of which is 2 dirhems; you divide the smaller sum by the larger and the quotient is equal to 1/2. What are the two sums of money?
Logarithms: The Early History of a Familiar Function - Conclusion
The authors recount the 'great tale' of Napier's and Burgi's parallel development of logarithms and urge you to use it in class.
Alphabet Challenge
In how many ways can a vowel and a consonant be chosen out of the word "logarithms?"
Horses and Stalls
It is required to determine whether 30 horses can be put into 7 stalls; so that in every stall there may be, either a single horse, or an odd number of horses.
Be Careful Where You Step!
A ladder has 100 steps. On the first step sits 1 pigeon; on the second, 2; on the third, 3; and so on up to the hundredth. How many pigeons in all?
'He Advanced Him 200 Lambs of Gold': The Pamiers Manuscript - Introduction
Discussion of 15th century French manuscript, with translation of its problems, including one with negative solutions
Heron's Formula
Heron of Alexandria (c. 10 - 75 CE) wrote on many aspects of applied mathematics.
Circle and Square
Prove that a square circumscribed about a given circle is double in area to a square inscribed in the same circle.
Circumscribed Circle #2
Find the isosceles triangle of smallest area that circumscribes a circle of radius a.
In the Gentleman's Garden
A gentleman has a garden of rectangular form and wants to construct a walk of equal width half way round to take up half the garden. What must be the width of this walk?

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