Download NBA Court Redesign

First Step: Analyze
Existing Court Dimensions
We created a baseline court model using the
existing court dimensions in Google SketchUp.
The current 3-point line design uses straight
lines that intersect a circle with radius 23’ 9”.
We will show alternatives to the current
dimensions that will make the game more
challenging and interesting.
Alternative #1:
We created a new equation for the 3-point line using the
same endpoints in the original model.
We chose to center our new model on the y-axis with our
endpoints on the x-axis (our endpoints were -22.5’ and
22.5’).
Given those endpoints, we determined that coefficient b
should be 0, and coefficient c should be positive.
We wanted the furthest point of the 3-point line to be
472.5” from the hoop.
Factoring
Our first equation:
-0.006481481x + 472.5 = 0
472.5 - 0.006481481x = 0
2
2
( 21.73706512 - 0.0805076487x) ( 21.73706512 + 0.0805076487x) = 0
21.73706512 - 0.0805076487x = 0
21.73706512 = 0.0805076487x
21.73706512 + 0.0805076487x = 0
21.73706512 = -0.0805076487x
21.73706512
=x
0.0805076487
269.9999999 = x
21.73706512
=x
-0.0805076487
-269.9999999 = x
Quadratic Formula
Our first equation:
-0.006481481x + 0x+ 472.5 = 0
2
± 12.2499909
-0.012962962
±3.49999987
2
-0 ± 0 - 4 ( -0.006481481) 472.5 x =
-0.012962962
x=
2 (-0.006481481)
x = ±270.00001
-b± b2 - 4ac
x=
2a
x=
Alternative #2
We decided to keep the straight extensions of
169”, and change the arc that connects to them.
Since the points were still 22.6 points away from
the center, we decided to make our c value 22.6
also.
We then used what we knew to solve for a and
get our equation.
Factoring
Our second equation: -0.003703703x2 + 270 = 0
270 - 0.0037037037x2 = 0
(16.43167673+ 0.0608580619x)(16.43167673- 0.0608580619x) = 0
16.43167673+ 0.0608580619x = 0 16.43167673- 0.0608580619x = 0
16.43167673 = -0.0608580619x 16.43167673 = 0.0608580619x
16.43167673
16.43167673
=x
=x
-0.0608580619
0.0608580619
-270.000002 = x
270.000002 = x
Quadratic Equation
Our second equation:
-0.003703703x2 + 0x+ 270 = 0
± 3.999999996
x=
-0.0074074074
-0 ± 0 2 - 4 ( -0.003703703) 270
±1.99999999
x=
x=
2 ( -0.003703703)
-0.0074074074
x = ±270.0000001
-b± b2 - 4ac
x=
2a
Conclusion
Conclusion
We think that the NBA should use our second
model because it is closer to what the current
model is, and because it adds more area to the
inside of the 3-point line without taking away
from the current area.
Resources
http://www.sportsknowhow.com/basketball/dime
nsions/nba-basketball-court-dimensions.html
http://sketchucation.com/
http://www.lincoln.k12.or.us/Page.asp?NavID=25
37
http://sketchup.google.com/support/