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Convergence articles

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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.

A vessel is anchored in 3 fathoms of water and the cable passes over a sheave in the bowsprit which is 6 ft above the water.

A translation of and commentary on Frans van Schooten's work on constructions using only a straightedge. Van Schooten's postulates for use of the straightedge, however, allow the copying of one line segment onto another.

A man, woman, and two boys desire to cross a river, but their boat has weight restrictions!

A man has four creditors. To the first he owes 624 ducats; to the second, 546; to the third, 492; and to the fourth 368.

History of Maya calendars, including the modified base 20 number system used in them.

A rifle ball is fired through a three-inch plank, the resistance of which causes an unknown constant retardation of its velocity.

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.

Find the two numbers such that multiplying one by the other makes 8 and the sum of their squares is 27

This is a collection of plates that Leonardo da Vinci created to illustrate De divina proportione of Luca Pacioli.