Research Links

A 24-by-60 rectangle is covered with ten 12-by-12 square tiles, where 12 is the GCD of 24 and 60. More generally, an a-by-b rectangle can be covered with square tiles of side-length c only if c is a common divisor of a and b. So the task is to find the largest square that tiles the rectangle completely.  See below:

Subtraction-based animation of the Euclidean algorithm. The initial rectangle has dimensions a = 1071 and b = 462. Squares of size 462×462 are placed within it leaving a 462×147 rectangle. This rectangle is tiled with 147×147 squares until a 21×147 rectangle is left, which in turn is tiled with 21×21 squares, leaving no uncovered area. The smallest square size, 21, is the GCD of 1071 and 462.

So the example compiled down to arithmetic steps would be as follows:

1071 = 2*462 + 147

462 = 3*147 + 21 

147 = 7*21 + 0   Thus 21 is the GCD of 1071 & 462

Categories: Math

Fudgy McFarlen

Woo hoo.

Leave a Reply

Your email address will not be published. Required fields are marked *

Related Posts

Jordan Peterson

Jordan Peterson on Prices Law

Price’s Law says that 50% of work at a company is done by the square root of the number of employees.  As an example take a company with 100 employees.  In that company 10 people Read more…

Math

Reason for using Base 60 or 360 for Angles

Babylonian Triangle Table Research Links Wikipedia: Plimpton 322 Tablet Forget trigonometry, 'cos Babylonians did it better 3,700 years ago – by counting in base 60! Ancient Babylonian use of the Pythagorean Theorem and its Three Read more…

Math

The Inevitable Knot in Your Long Extension Cord

This knot in my extension cord occurred inadvertently and thus I assumed with the highest likelihood it could be undone with a single pass through a cable end through a loop or loops with the loops Read more…