The Goal Angle Problem

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These sketches arose from the following post:

Date: Thu, 14 Oct 1993 09:51:05 -0700 (PDT)
From: Philip Mallinson 
Subject: Re: dshs-period two geom. class
To: Dover-Sherborn High School 

There's a great classic problem about geometry and hockey, football,
soccer that was recently explored by Jon Choate in the Modeller's Corner
in CoMAP's Consortium.  As you are tearing down the wing with the ball
towards the goal the angle subtended by the goal increases for a while and
then decreases. When is the angle at its maximum?
By the way, the difference between a good problem and a great problem is
that in a great problem I know the answer and you don't.

Three sketches were submitted by Ken Koedinger of Carnegie Mellon. Two are solutions to the problem, and one is an illustration of the quadrature of a rectangle.

Solution 1

Download Solution 1

Solution 2

Download Solution 2

Quadrature of a Rectangle

  • Download Quadrature of a Rectangle
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