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Convergence articles

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Find two numbers, x and y, such that their sum is 10 and x/y + y/x = 25
Given a rectangle, find the line through one vertex of minimum length that passes through the extensions of the two opposite sides.
In how many ways can a vowel and a consonant be chosen out of the word "logarithms?"

Problems from a 15th century French manuscript, including one with negative solutions

This website devoted to miscellanea about Archimedes contains much interesting material about his life and times.
This is page 167 from the Exercitationes mathematicae (1657) of Frans van Schooten (1615-1660). This book contained a collection of mathematical construction problems, among much else. It was one of the books read by Isaac Newton while he was a student at Cambridge University and helped to introduce him to modern mathematics. On this page we see a construction enabling one to find the distance across a river.
A survey of the attempts to prove Kepler's conjecture over the past 400 years.
Prove geometrically that the hypocycloid is a straight line when the radius of the rolling circle is one-half the radius of the fixed circle.
Fibonacci gave a practical rule for approximating the area of an equilateral triangle.
Given the frustum of a circular cone with height h.

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