Schottenbauer Publishing

Friday, October 3, 2014

Changing Position, Changing Perspectives

Fencing provides a particularly relevant problem for math and physics, pertaining to the apparent size of the sword. As the angle of the sword changes with respect to the viewer's plane, the sword appears smaller or larger. This problem of the "shrinking sword" and "growing sword" can be solved by applying trigonometry to a visual analysis of sword motions.

The graph below (Copyright 2014, All Rights Reserved), excerpted from the book series The Science of Fencing from Schottenbauer Publishing, show a toy sword in various motions towards the video camera.

Discussion Questions
  1. Describe the approximate position of the hilt during this series of moves.
  2. Describe the approximate motion of the tip of the sword during this series of moves.
  3. Approximately which part of the graph shows the circling motion?
  4. As the sword moves, it appears to change size. What is the minimum length that the sword appears to be during this set of moves? What is the maximum length?
  5. What is the angle between the x-y plane and z axis which corresponds to the perceived shortest and longest lengths of the sword? (The toy sword used to make the graph is 65 cm in length.)