Curry's Jigsaw Paradox Explained

Welcome to another enlightening article brought to you by the Freeastroscience.com team. We continue to demystify the world of scientific paradoxes and puzzles, shedding light on the intriguing phenomena that challenge our understanding of geometry. Today, our focus is on a peculiar paradox, known as Curry's Jigsaw Paradox, which seemingly alters the size of a geometric figure through rearrangement.

 

Curry's Jigsaw Paradox isn't as paradoxical as it seems. It's a puzzle involving the manipulation of a geometric figure to yield a different size upon rearrangement - a fascinating trick of geometry. The Freeastroscience.com team brings you an example of this paradox, as illustrated by Martin Gardner.

In this example, a right triangle with dimensions of 5 x 13 is cleverly segmented into four distinct parts. These include a green triangle (2 x 5), a red triangle (3 x 8), a yellow segment with two rows (one with 5 squares, the other with 2), and a green segment also with two rows (one with 5 squares, the other with 3).

When these four segments are put back together to form the original 5 x 13 triangle, an intriguing anomaly occurs - a square is missing! The trick lies in understanding that the assembled large triangles are not true triangles. The slope of the green triangle (2 / 5 or 0.4) is steeper than that of the red triangle (3 / 8 or 0.375). Therefore, the upper triangle has a tiny bite taken out from its hypotenuse.

In the reassembled triangle at the bottom, the intersection point of the red and green triangles is above the hypotenuse. The difference between the original and reassembled triangles is precisely one square. This captivating paradox presented by the Freeastroscience.com team is a testament to the wonders of geometry.