The Simple Geometry of Lacrosse Goalie
Math Project By Tony Spizzirri June 4th, 2004
Table of Contents
Table of contents Introduction Basic layout explanation Shot 1 Shot 2 Shot 3 Shot 4 Going further Conclusion
Introduction
This PowerPoint is a math project showing how far out a goalie would need to go in order fully cut off the angle. The rest will become clear as we move along.
And yes, that was me making a sick save on the Title Page… Note the useless picture
Basic Layout
What we’re going to have is four different slides showing shots from different places on the lacrosse field. The goal/goalie is at the top, represented by the . The goal posts are two of the vertices of the triangle, while the shooter is at the other vertex of the triangle. The net is always 6 feet wide. The goalie is 2 feet wide. The bisector is always 14 feet (totally arbitrary).
Shot 1
This shot is from directly in front of the net. This is by far the easiest shot to work with mathematically, because it isosceles, and we know the median, so we can make a right triangle.
Shot 1
-1
This means that the total angle is 24.2° We can use the original angle to find the triangle with a base of 2 feet.
Shot 1
The new triangle will have a base of two, but we again are making a right triangle, making the base of our triangle 1.
Eventually we will find out that the longer leg of this triangle is 4.66.
This means that the goalie would have to come out 9.34 feet to cover completely. This is 67% of the distance.
Shot 2
This shot is a little bit different: it will not make a right triangle (which is a shame for anyone finding out the math involved). However, to save everyone some time, The math will be left out.
135°
Shot 2
When the goalie comes out of the net to cut off the offensiveman’s shot (who has a 15° angle to the net), 6.4 feet, ending up 7.6 feet away. This is 46% of the distance.
Shot 3
170°
Unless you’re Jack Forster, you won’t score here. Here’s why:
Shot 3
When calculated, we find that a 2-foot-wide goalie wouldn’t have to move out of the net at all. If the goalie was a rectangle, the shot can’t go in.
Shot 4
For the fourth shot I decided to find the biggest angle (at 14 feet away) that the goalie would not have to come out of the net.
Here are some Indians playing lacrosse. Wee.
Shot 4
??
Oh, how I wonder.
Shot 4
The smallest angle is about 10°
Shot 4
10°
So exciting.
Going Further
There are much more complicate geometrical ideas in playing goalie in the game of lacrosse. Looking at the shots in a 3D perspective, for example. The geometry involved in the mesh of a stick. The list goes on…
AHHHHHHHH
Thank You