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Convergence articles

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A fellow said that when he counted his nuts by twos, threes, fours, fives and sixes, there was still one left over; but when he counted them by sevens they came out even. How many did he have?
This book explores the history of mathematics from the perspective of the creative tension between common sense and the "impossible" as the author follows the discovery or invention of new concepts that have marked mathematical progress.


Two circles of radii 25 feet intersect so that the distance between their centers is 30 feet. What is the length of the side of the largest square inscribable within their intersecting arcs?

In this collection of essays on modern trends and issues in the history of mathematics, consideration of mathematics history in the classroom is often more theoretical than practical.

Given the fraction ax/ (a-x ), convert it into an infinite series.
There is a round fish pond of certain dimensions, and into the pond is dropped a marble column. How high will the water rise?

Having been given the lengths, a and b, of two straight lines drawn from the acute angles of a right triangle to the middle of the opposite sides, determine the lengths of those sides.

Curve sketching, tangent lines, and optimization, explored via interactive applets

A certain man says that he can weigh any amount from 1 to 40 pounds using only 4 weights. What size must they be?
Explain the geometric basis of "completing the square," the original method of solving quadratic equations, to your students.

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