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The player must first pocket a red ball and then try to pocket any colour he may choose, scoring the value of the ball that he has pocketed. In play, the object is to stroke the cue ball so that it hits the two object balls in succession, scoring a carom, or billiard, which counts one point. The other principal games are played on tables that have six pockets, one at each corner and one in each of the long sides; these games include English billiards, played with three balls; snooker, played with 21 balls and a cue ball; and pocket billiards, or pool, played with 15 balls and a cue ball. At the centre of Chaos Theory is the fascinating idea that order and chaos are not always diametrically opposed. How can order on a small scale produce chaos on a larger scale? Finally, the six coloured balls must be pocketed in the order of their values.

In a variety of the game called three-cushion billiards, the cue ball must also touch a cushion or cushions three or more times to complete a carom. But we know from the aforementioned definition of the ellipse that any such path must have exactly the same length! 1. If one of the two given numbers is a multiple of the other, what is the shape of the arithmetic billiard path? 2. For which numbers does the arithmetic billiard path end in the corner opposite to the starting point? The small end of the cue, with which the ball is struck, is fitted with a plastic, fibre, or ivory reinforcement to which is cemented a leather cue tip. The game is played with 22 balls, made up of one white ball (the cue ball), 15 red balls, and six numbered coloured balls including one yellow 2, one green 3, one brown 4, one blue 5, one pink 6, and one black (valued at 7 points). All billiards games require the basic equipment of a table, cue sticks, and balls. Each red ball when pocketed remains in the pocket, while the colours when pocketed, as long as any reds remain on the table, are placed on their respective spots.

Chaotic systems are an intimate mix of the two: from the outside they display unpredictable and chaotic behaviour, but expose the inner workings and you discover a perfectly deterministic set of equations ticking like clockwork. The best we can do for three bodies is to predict their movements moment by moment, and feed those predictions back into our equations … In 1887, the French mathematician Henri Poincaré showed that while Newton’s theory of gravity could perfectly predict how two planetary bodies would orbit under their mutual attraction, what is billiards adding a third body to the mix rendered the equations unsolvable. What if we change things slightly and have the ball initially pass between the two foci? Regardless of the initial direction, after passing through one focus, the billiard ball reflects off the ellipse and passes through the other focus. What happens if when you hit the billiard ball, it passes through one of the focus points of the elliptical table? The traditional mahogany billiards table is still in use, but tables are now generally made of other woods and synthetic materials. To prove our claims above, we are going to exploit this simple idea, the mirror being one side of the billiard table.

This means that the ball will bounce infinitely many times on the sides of the billiard table and keep going forever. The cost of a new pool table on whether you buy a 7ft or 8ft pool table can be anywhere around the $2000 mark and up. We can see that after many bounces, the trajectory of the ball converges to the horizontal. In mathematical billiards the ball bounces around according to the same rules as in ordinary billiards, but it has no mass, which means there is no friction. What happens after the ball bounces off the elliptical table a second time? The large rectangular table typically is twice as long as it is wide. The game of pocket billiards, or pool, which uses six large pocket openings, is primarily the game played on the American continents and, in recent years, has been played in Japan. The game of English billiards is played on a relatively large table, usually 6 feet 1.5 inches by 12 feet (1.9 by 3.7 m); it is played with three balls as in carom-a plain white, a white with a spot, and a red.