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Convergence articles

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Perimeters of Similar Triangles

The perimeters of two similar triangles are 45 and 135 respectively. One side of the first triangle has length 11 and a second side has length 19. Find the lengths of the sides of the second triangle.

Benjamin Banneker's Trigonometry Puzzle

Benjamin Banneker solved some trigonometry problems in his extant notebooks. One of them is discussed here. The authors have also discovered the probable source of Banneker's trigonometry table.

Alphabet Challenge

In how many ways can a vowel and a consonant be chosen out of the word "logarithms?"

The Sagacity of Circles: A History of the Isoperimetric Problem

A summary of the history of the problem of finding the region of greatest area bounded by a given perimeter. This essay was a winner of the HOM SIGMAA student essay contest in 2006.

Learning Geometry in Georgian England

The copybooks of two young men reveal very different purposes in learning geometry.

Square

The square of a certain number multiplied by itself and by 200 is 446,976. What is the number?

A Locally Compact REU in the History of Mathematics: Involving Undergraduates in Research

A description of a Research Experience for Undergraduates conducted in 2007 at Hood College.

Abel's Proof

A discussion of the meaning of mathematical unsolvability in the context of the history of Abel's proof of the unsolvability of the quintic equation in terms of radicals.

Water Tank Minimization

A copper water tank in the form of a rectangular parallelepiped 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?

Brazen Lion

I am a brazen lion; my spouts are my 2 eyes, my mouth, and the flat of my foot. My right eye fills a jar in 2 days, my left eye in 3, and my foot in 4.

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