# Problems from Another Time

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

A certain man says that he can weigh any amount from 1 to 40 pounds using only 4 weights. What size must they be?
The authors recount the 'great tale' of Napier's and Burgi's parallel development of logarithms and urge you to use it in class.
In Archimedes' Book of Lemmas (ca 250), he introduces a figure that, due to its shape, has historically been known as "the shoemaker's knife" or arbelos.
A man plants 4 kernels of corn, which at harvest produce 32 kernels: these he plants the second year; now supposing the annual increase to continue 8 fold, what would be the produce of the 15th year, allowing 1000 kernels to a pint?
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?
Problems from a 15th century French manuscript, including one with negative solutions
Now a pile of rice is against a wall, it has a base perimeter of 60 feet and a height of 12 feet.
Having been given the lengths, a and b, of two straight lines drawn from the acute angles of a right triangle to the middle of the opposite sides, determine the lengths of those sides.
There is a fish whose body weighs 8oz. Tell me how much the whole fish weighs?
What number which being increased by 1/2, 1/3, and 1/4 of itself, the sum shall be 75?