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Problems from Another Time

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

Difference of Squares
Having been given the sum of two numbers, a, and the difference of their squares, b, find the numbers.
A Tree with Branches, Nests, Eggs and Birds
There is a tree with 100 branches. How many nests, eggs and birds are there?
Height and Distance
An erect pole of 10 cubits has its base moved 6 cubits. Determine the new height and the distance the top of the pole is lowered.
Why It Pays to Learn Math
In order to encourage his son in the study of arithmetic, a father agrees to pay him 8 pennies for every problem solved correctly and to charge him 5 pennies for each incorrect solution.
The Size of a City
A square walled city of unknown dimensions has four gates, one at the center of each side.
Tomato Can
A cylindrical tin tomato can is to be made which shall have a given capacity. Find what should be the ratio of the height to the radius of the base that the smallest possible amount of tin shall be required.
Area Problem
Three equal circles with radii 12 feet are tangent to each other. Compute the area enclosed between them.
Peano on Wronskians: A Translation - On the Wronskian Determinant
How a translation of Peano's counterexample to the 'theorem' that a zero Wronskian implies linear dependence can help your differential equations students
Arbelos
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.
Disjoint Congruent Circles
A set of n disjoint, congruent circles packs the surface of a sphere S so that each region of the surface exterior to the circles is bounded by arcs of three of the circles.

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