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Geometry in Games: Billiards

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Malik Jones

on 16 May 2011

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Transcript of Geometry in Games: Billiards

As we all know, math is in everything, and in this case, to be more specific, geometry. We know that on a simple level, it’s all about angles, shapes, and figures. Since math is in everything, geometry is too, and we can easily see it in thousands of games. A Presentation
By
Malik Jones What are some games we see geometry in? Golf:
-The area of the hole
-The volume of the ball, which affects the weight, which in turn affects how it flies when hit Soccer:
-Everyone knows that common
pentagonal and hexagonal pattern that we always see on soccer balls
-The ball IS a sphere Baseball:
The baseball field is the net of a cone
The bases are all squares, and the pitchers mound is a rectangle Geometry in Games
*Billiards* But, there is one game that is arguably one of the most mathmatical ever created... Billiards! So what's the History behind this awesome game? Fun Fact:
The analysis of math in games is called game theory. (Ex. the different
methods in which someone could win a game of chess or checkers using math.) So What's the History? Billiards originated sometime in the 15th century in Europe, coming from a game similar to lawn croquet (the game with the arches, balls, and mallet) and was meant to simulate the lawn game indoors. The first billiards game actually had their own arches on the tables as well Also, you know the green cloth on the pool tables? It's green to simulate the lawn grass!!! So who exactly played billiards way back then?
The game actually became extremely popular. Kings
played, peasants played, the impoverished played, the
nobility played, and unlike many elements of European society, women played just like men. Just to start things off, everyone should know that
Billiards isn't Pool, Pool is Billiards. Billiards is really
and umbrela term for a multitude of games played with
a cue ball, cue stick, and a table. Pool specifically is a
type of Billiards game, with most people referring to pool
as the Billiards game played with a six-pocket table,
7 solid color balls, 7 striped balls, and one solid, black, 8-ball
(The one most of you are all probably familiar with.) So where's all the Geometry!?! Well, there are plenty of different examples.
How about these geometric shapes? And if the shapes aren't good enough for you, there's always the hundreds of formulas associated with billiards:
Kinectic Energy: mass x velocity^2 / 2
Velocity: distance / time
Pythagorean Theorem: a^2 + b^2 = c^2
Distance Formula: sqrt of (x1 - x2)^2 + (y1 - y2)^2
Volume of a Sphere Formula: pi x r^3 x 4/3
Area of a Circle: pi x r^2
Area a Rectangle: base x height But anyone can say there's math in Billiards, lets actually see it! Although you've learned a few things about the world of Billiards and its relationship to math, the world of Billiards is still much more extensive than the few formulas and such that I've have showed you. It would be immpossible to show you all the math in Billiards because every aspect is literally ALL math. As time went on and the Industrial Revolution took place, the table and untensils of play evolved. The cue stick first resembled more of a croquet mallet, but when it became difficult to hit the ball with it near the rails of the table, the cue evolved into something a little more precise. Hexagon Circle Triangle In this diagram, we can see a few of the terms that we have become familiar with over the school year. A and B represent Billiard balls. Ball A has been hit and is traveling towards ball B, and we can see where the two collide. Point CP is the contact point of the two balls, and in a 2D perspective, is the point of tangency. Line L1 is tangent to both circles A and B. What happens when a ball collides with another on an angle? As the diagram illustrates,
when one ball hits another,
they take paths perpendicular
to each other. Since there is
a right angle formed and the balls don't
roll forever, there must be a hypotenuse
for the triangle that can me made here right?
Yes, and the hypotenuse is shown in gray. It
would be the distance between the
two balls after they would stop rolling. Now i'll demonstrate it for you with two foam balls. So what have we learned?
We have learned that: -Shapes
-Angles
-Areas
-Volumes
-Tangents
-And much more THE END Are all apart of Billiards. Another example:
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