# Convergence articles

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A certain man had in his trade four weights with which he could weigh integral pounds from one up to 40. How many pounds was each weight?
Classrom suggestions for integrating Leonardo's ideas in several different classes
A man and his wife drink a barrel of wine at different rates. Find the rate it takes both of them together to drink the wine.
Two men starting from the same point begin walking in different directions. Their rates of travel are in the ratio 7:3.
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.

Images from Frans van Schooten's 1659 edition of The Geometry of Rene Descartes

Determine the greatest cylinder that can be inscribed in a given cone.
Of a collection of mango fruits, the king took 1/6; the queen 1/5 the remainder, and the three princes took 1/4, 1/3 and 1/2 (of the same remainder); and the youngest child took the remaining 3 mangoes.
A cliff with a tower on its edge is observed from a boat at sea; find the height of the cliff and the tower.
A castle has n rooms each of which has 7 samurai in it.