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MAT 220
Dr. Ritter
Stephanie Lee

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Math is found everywhere in the world and all throughout our daily lives. It can be found in nature, business, while driving, in stores, in sports, etc. The game of pool is one sport that utilizes math, particularly angles. The angles of pool are important to winning the game!

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While there are many ways to play pool, most people are familiar with the game of 8 ball. It is played on a rectangular table that has 6 holes (or pockets), using 16 balls and a stick (the cue). The object of the game is to "sink" all 7 of your object balls (stripes or solids) into the pockets using the "cue" (both the stick and white ball) and then "sink" the 8 ball last for the win.

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The object is very simple, however, making it happen is a different story. There are many angles that help to make a win in this game more possible. Let's start with the "set-up." This refers to where you "leave" the cue ball after you make a shot. During play, thinking about the next shot is a great strategy and key to winning. You should plan ahead in order to ensure that you don't leave yourself behind another ball, making it more difficult to sink your next ball. To do this it is important to realize that the white ball will move away from the object at a 90 degree angle if hit straight with no manipulation.

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English is a term used in pool to refer to the spin that is placed on the cue ball. Depending on where the tip of the cue stick hits the cue ball, it can manipulate the cue ball with a spin and change its "normal direction."

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If you need the cue ball to be in a different location in order to make a shot on the next ball, you can manipulate the white ball by putting a forward spin on it in order to make the degree of the angle less than 90 degrees, or an acute angle.

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Another way to manipulate the cue ball in order to set up for the next shot is to use a reverse spin. When a reverse spin is applied, the cue ball will reflect off of the object ball  at an angle that is greater than 90 degrees, or an obtuse angle.

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A "bank shot" is when you hit your object ball into the cushion in order to sink the object ball into a pocket on the opposite side of the table. A "kick shot" is when the cue ball hits the rail before making contact with the object ball. Typically these are needed in the event of a failed set up or when there are obstacles (or other balls) in the way. Given there is no manipulation to the cue ball, the cue ball or the object ball (depending on a kick or bank shot) should make two right triangles.

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Another way to manipulate the cue ball for a set-up is to use velocity. If the cue ball is hit with a higher velocity, the angle of the triangle will be smaller (acute). And just the same, if the cue ball is hit softer, the angle of the triangle will be bigger (obtuse).

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Another way to use angles to win in a game of pool is to utilize the diamond system on the edges of the table. These markers help the shooter to determine the appropriate angles needed to execute a bank or a kick shot. The key to using the diamond system is to "see" the almost parallel lines that are made using the markers. If the cue ball is hit at a diamond straight, with no manipulation, the ball should move around the table hitting relatively close to the same diamonds on the other sides of the table.

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Pool is my favorite hobby when I am not busy with school, working at one of my two jobs or taking care of my children. Although you can use math and equations to figure out the angles and where the balls are going to end up, practice and playing the game are much more fun. Even if you know the equations and exact angles needed, making it happen is a whole other "ball game!" Literally...

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Playing Pool with Professor Edward (a.k.a. Angles)

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Playing Pool with Professor Edward (a.k.a. Angles)

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This reminded me of Dr. Ritter in more than one way. First because she likes the little "comic bits" to do with math. And second it reminded me of the story told about her wanting to do all the math while remodeling with her husband.

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It is possible to use equations to figure out where exactly the cue ball and object ball will go. Here is one example of a mathematical equation to figure this out!

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1.     The Angle on Pool. (n.d.). Retrieved April 29, 2017, from https://www.pbslearningmedia.org/resource/rttt12.math.anglepool/the-angle-on-pool/#.WQUHGTxHaEc

2.     Introduction to the Pool Diamond System by Liberty Games. (n.d.). Retrieved April 29, 2017, from https://www.libertygames.co.uk/pool-diamond-system

3.     Kurtz, R., & Tutor, E. P. (n.d.). Diamond System Simplified - Easy Pool Tutor. Retrieved April 29, 2017, from http://www.easypooltutor.com/articles/56-ron-kurtz-articles/179-diamond-system-simplified.html

4.     Tutor, E. P. (n.d.). Understanding English - Easy Pool Tutor. Retrieved April 29, 2017, from http://www.easypooltutor.com/articles/3-how-to-use-sidespin/60-understanding-english.html

5.     The Math and Physics of Billiards. (n.d.). Retrieved April 29, 2017, from http://archive.ncsa.illinois.edu/Classes/MATH198/townsend/math.html