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The coordinates of the corners of the unit squares are whole numbers. The two natural numbers are 40 and 15 in this case. This proves our original claim for for the case in which . Suppose we are given two positive whole numbers and , neither of which is a multiple of the other (the case where one is a multiple of the other is easy and is left to the reader). Given our two numbers and , none of which is a multiple of the other, start by forming a square with sides of length . The greatest common divisor of the two given numbers, we claim, is the distance from the starting point to the closest point of self-intersection, divided by . If , then we can rescale the whole figure by a factor : dividing and by their greatest common divisor, we obtain two positive integers whose greatest common divisor is . Have a look at the Geogebra animation below (the play button is in the bottom left corner) and try to figure out how the construction works. If you would like to play the animation again, double click the refresh button in the top right corner.

To do this, note that at least one of or must be odd, and that the end point of comes from repeatedly reflecting the top right corner of the rectangle . Keep going like this, reflecting rectangles across sides crossed by , until you reach the bottom left rectangle . Basically, the point here is that modelling impacts like these is a tricky business. Like I already said, it's not rocket science. When a foul is committed, the opposing player is awarded ball in hand, allowing them to place the cue ball anywhere on the table for their next shot. The goal is to make sure that you get awarded the most points. Losing Hazard: You score if you hit the other cue ball, What is billiards which should then hit the red ball and pocket the ball to get three points. Don’t forget the cue ball. It’s recommended to use a cue stick designed for billiards to ensure accurate shots and proper gameplay. Billiards and snooker share similarities but also have distinct differences in terms of table size, rules, and gameplay strategies.

Mathematical billiards is an idealisation of what we experience on a regular pool table. Angled rails of hardened rubber or synthetic rubber, known as cushions, rim the inner edge of the table. The pool table consists of six pockets, which split the cushions and are built into the rails. The path of the billiard ball consists of line segments. In pool, players use the cue stick to strike a white ball called the cue ball to hit other similar balls into semicircular holes called pockets along the inner edge of the table. Most of the time, you will use 16 balls (including the white ball). In this situation, if the cue ball hits a striped ball first and you pocket a solid, then the ball remains pocketed. A shot is legal if the cue ball makes contact with an object ball and a ball is potted, or if the cue ball hits an object ball directly.

The most widespread game of pool, also known as, stripes and solids, pocket billiards, and 8 ball pool. Eight-ball, sometimes called stripes and solids, or pocket billiards, is the most common game of pool played today. Because is the least common multiple of and our square is the smallest square that can be tiled by rectangles with sides of lengths and in this way. One fascinating aspect of mathematical billiards is that it gives us a geometrical method to determine the least common multiple and the greatest common divisor of two natural numbers. The last player with at least one ball still on the table, wins the game! What is required is that an object ball falls in the player’s "target" pocket. System for Aiming With Sidespin (SAWS) is a full-length instructional video by Dr. Dave that covers a new system to compensate your aim for cue ball (CB) deflection and object ball (OB) throw when using sidespin. Bank shots involve bouncing the ball off a cushion before potting it. Advanced players can perform trick shots that showcase their skill and control over the balls’ movement.