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Convergence articles

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Greek ladders for approximating square roots may be more ancient than the ancient Greeks. Students at any level can appreciate their beauty and simplicity. Those who have studied calculus can compare them with Newton's Method for approximating roots.
Determine the dimensions for a right-angled triangle, having been given the hypotenuse, and the side of the inscribed square.
A merchant woman buys and sells apples and pears for Denaros. How much did she invest in apples; how much in pears?
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Two ants are 100 paces apart, crawling back and forth along the same path. The first goes 1/3 pace forward a day and returns 1/4 pace; the other goes forward 1/5 pace and returns 1/6 pace. How many days before the first ant overtakes the second?

An elementary introduction to Euler squares and how they can be used in teacher training

Suppose General [George] Washington had 800 men and was supplied with provisions to last 2 months but he needed to feed his army for 7 months.
The authors recount the 'great tale' of Napier's and Burgi's parallel development of logarithms and urge you to use it in class.
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.
In the figure at the left, if the radii of each inscribed circle is 1, what are the dimensions of the bounding rectangle?

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