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Convergence articles

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Given the cats eye as shown. Let the radius of the eye be given by R. What is the area of the pupil?
Prove that if the sums of the square opposite sides of any quadrilateral are equal, its diagonals interect at right angles.
A man bought a number of sheep for $225; 10 of them having died, he sold 4/5 of the remainder for the same cost and received $150 for them. How many did he buy?
This 1989 revision of the 1969 NCTM yearbook still provides wonderful suggestions for using the history of mathematics in the classroom.
Two travelers, starting at the same time from the same point, travel in opposite directions round a circular railway.
Find two number with sum 20 and when squared their sum is 208.

Review of Bertram's text on the history of Greek science.

If an equilateral triangle whose area is equal to 10,000 square feet be surrounded by a walk of uniform width, and equal to the area of the inscribed circle, what is the width of the walk?
Two pages from a 1650 manuscript of the Lilavati of Bhaskara II (1114-1185). The second photo is an illustration of the Pythagorean Theorem.
Show that the curves x2 - y2 = a2 and 2 xy = b2 cross at right angles.