Convergence articles

Displaying 661 - 670 of 723

Filter by subject

In this fascinating and accessible book, the author devotes one lively, informative page of description and one striking, full-page illustration to each of 250 milestones in mathematics.

Water in a Fish Pond

There is a round fish pond of certain dimensions, and into the pond is dropped a marble column. How high will the water rise?

Feline Geometry

Given the cats eye as shown. Let the radius of the eye be given by R. What is the area of the pupil?

The Ant Race

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?

Mystery Numbers

Find two numbers such that multiplying one by the other makes 8 and the sum of their squares is 27.

The Door and the Rod

Given a door and a measuring rod of unknown dimensions, the rod is used to measure the door.

Nuts Over Counting

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. What is the smallest number of nuts he could have?

When Nine Points Are Worth But Eight: Euler's Resolution of Cramer's Paradox

How Euler resolved the paradox first noted by Maclaurin that nine points should determine a curve of order three, yet two such curves can intersect in nine points

Walk Around the World

Suppose a person whose height is 5 feet 7 inches travels 10000 miles in the arc of a great circle. How much further will the person's head have gone compared to their feet, the circumference of the Earth being 21600 miles?

Lilavati of Bhaskara

Two pages from a 1650 manuscript of the Lilavati of Bhaskara II (1114-1185). The second photo is an illustration of the Pythagorean Theorem.