Jigsaw Puzzles and Footballs

Jigsaw puzzles are made up of pieces which are regular repeating shapes. This kind of recurring pattern is known as tessellations , and the maths and geometry that define such shapes is fundamental to the software and websites that rely on such repeating patterns, including those offering free online jigsaw puzzles.

But tessellations are not just a feature of this kind of free jigsaw puzzles. They occur throughout nature and the physical world, often in the most common of places, and an example of this is the football (or if you’re in the US – Soccer Ball).

The challenge for manufacturers of the balls is to produce as near a spherical shape as possible, with as few pieces of material as they can manage, and which moves through the air in a reliable and predictable way. Many designs have been tried over the years, and it was during the 1976 World Cup that a now familiar style of ball appeared, which went on to became the standard international game-ball for almost thirty years.

The balls are made from flat sections of material (often leather) that are stitched together. The spherical shape is then achieved when the ball is inflated and the internal pressure forces out the flexible fabric. The geometrical description of the shape is a type of spherical polyhedron called a truncated icosahedron, and in the case of the football comprises a pattern of regular pentagons and hexagons. So it varies a little from online jigsaw puzzles, which tend to use a single repeating shape, and is more accurately described as a semi-tessellation. The classic icosahedron has 20 triangular faces, 30 edges and 12 vertices, and the football design is development on the theme.
The key factor for the design is that it must achieve the balance of a certain degree of flexibility while retaining a good shape in flight. This is needed because if the ball were too solid, it would injure the player’s feet when it was kicked, but if it was too soft, it would distort when kicked hard and the irregular shape would make the path of the ball unpredictable once it was in flight. The combination of hexagons surrounded by pentagons was found to have this combination strength and excellent aerodynamics, making it very popular with players.

The design also has the advantage of being visually attractive. While this may not seem particularly relevant as it is the physical characteristics of how a ball behaves once it has been kicked that are crucial to the success of a ball during a game, it does have great commercial significance. The modern game is big business, with merchandising raising millions for clubs and manufacturers as fans rush to buy the products they see their footballing heroes use. By being the official World Cup match ball, this design became the standard shape that both players and fans wanted to use around the world, creating a large and lucrative market for the designers of the ball.

So, while a modern football may not seem to have much to do with free jigsaw puzzles, the maths behind the shapes that are fundamental to both are, in fact, more similar than you may think.

 

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