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Convergence articles

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Steamboat

The cost per hour of running a certain steamboat is proportional to the cube of its velocity in still water. At what speed should it be run to make a trip up stream against a four-mile current most economically?

The Classic Greek Ladder and Newton's Method
Greek ladders for approximating square roots may be more ancient than the ancient Greeks. Students at any level can appreciate their beauty and simplicity. Those who have studied calculus can compare them with Newton's Method for approximating roots.
Purse of Denari

Four men already having denari found a purse of denari; each man has a different amount of denari before they found the purse. Find out how much denari each man has.

Annual Meeting of HPM Americas Section
This meeting will take place at the MAA Carriage House in Washington, DC on April 19, 2008.
Two Circles

Two circles of radii 25 feet intersect so that the distance between their centers is 30 feet. What is the length of the side of the largest square inscribable within their intersecting arcs?

Abel on Elliptic Integrals: A Translation

A translation of one of the seminal papers in the field of elliptic integrals, but one that can be read by an undergraduate.

Pearls of Wisdom

The third part of a necklace of pearls, broken in a lover's quarrel, fell to the ground...

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.

Extracting Square Roots Made Easy: A Little Known Medieval Method
A method for extracting square roots used in Italy through the 18th century was introduced in a manuscript by the 12th century mathematician al-Hassar. Appendix: When Was Fermat Born? (Not in 1601 ...)
The Time It Takes To Eat a Goat

A lion, a wolf and a fox each take a certain amount of time to eat a goat separately. How long would it take all these animals together to eat the goat?

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