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Billiards and Pool – the Geometry of Motion

September28

The pool table is a great battlefield for training the mind to read angles, in order to sink the balls into the appropriate pocket. There is actually a very real geometry behind billiards and pool. My Dad was a skilful billiards player as well as a good mathematician and I am sure his math was behind his success in this sport. Try you hand at the game of pool in this online version from cool math and try to figure out the angles behind this game:
pool

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NCEA Level 2 Algebra Problem. Using the information given, the shaded area = 9, that is:
y(y-8) = 9 –> y.y – 8y – 9 =0
–> (y-9)(y+1) = 0, therefore y = 9 (can’t have a distance of – 1 for the other solution for y)
Using the top and bottom of the rectangle,
x = (y-8)(y+2) = (9-8)(9+2) = 11
but, the left side = (x-4) = 11-4 = 7, but rhs = y+? = 9+?, which is greater than the value of the opp. side??
[I think that the left had side was a mistake and should have read (x+4)?]

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