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Convergence articles

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In a rectangle, having given the diagonal and perimeter, find the sides
Make of 10 three parts such that one part multiplied by 3 makes as much as the other multiplied by 4 and as the other multiplied by 5.
A creative expression combining text, design and illustrations, originally designed for the International Congress of Mathematicians in Madrid.
Given a number, take 1/3 of the number away from itself and add 2. If this result is multiplied by itself, it equals the number plus 24. What is the number?
Find a number having remainder 29 when divided by 30 and remainder 3 when divided by 4.

A math history class visits the 'Beautiful Science' exhibit at the Huntington Library in Southern California.

One says that 10 is divided into three parts and if the small part is multiplied by itself and added to the middle one multiplied by itself the result is the large one multiplied by itself...
Find the greatest value of y in the equation a4 x2= (x2 + y2)3.
If in a circle ABDC, circumscribe an equilateral triangle ABC; the straight line AD is equal to the sum of the two straight lines BD and DC: required a demonstration.
A father wills his estate valued at $40, 000 to his three children. Before the settlement one of the children dies. What should the other two receive?