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

- Describe the approximate position of the hilt during this series of moves.
- Describe the approximate motion of the tip of the sword during this series of moves.
- Approximately which part of the graph shows the circling motion?
- 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?
- 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.)

Physics divides motion into two general types: translational (straight) motion and rotational (curved) motion. Understanding these two types of motion is essential to the science of fencing.

The graphs below (Copyright 2014, All Rights Reserved), excerpted from the book series The Science of Fencing from Schottenbauer Publishing, show a toy sword first in translational motion, then in rotational motion.

Discussion Questions

- Describe the shapes of the lines in Graph 1.
- Describe the shapes of the lines in Graph 2. Why are they different than Graph 1?
- On a separate piece of paper, sketch the physical location of the sword at the beginning, middle, and end of its trajectory, using the data provided in Graph 1.
- On a separate piece of paper, sketch the physical location of the sword at the beginning, middle, and end of its trajectory, using the data provided in Graph 2.
- In Graph 1, is the toy sword moving parallel to the plane of the camera? What information provides clues to the answer?
- In Graph 2, is the toy sword moving parallel to the plane of the camera? What information provides clues to the answer?
- Is it common in fencing to have either pure translational motion or pure rotational motion, without combining the two? Give several examples.

The science and math of fencing are topics of new books from Schottenbauer Publishing. Presenting data from real and simulated conditions collected by the science writer and publisher M. Schottenbauer, Ph.D., these books bring the "high tech" end of fencing to audiences everywhere!

In these books, students can enjoy learning about common aspects of fencing. One series of books, written for elementary school students, focuses on geometry. Another series of science books features graphs and data; these illustrate common mathematical functions, plus a variety of concepts from physics. The science books can be integrated into classes such as math, physical science, physics, physical education, and health, anywhere from 7th grade through high school, as well as some introductory college and university classes.

The books directly pertaining to fencing include the following:

Geometry Workbooks
Graphs & Data for Science Lab: Multi-Volume Series
Anthologies of 28 Graphs

These books are complemented by a series of science books on other popular sports topics, including Olympic sports, athletic training, exercise equipment, gymnastics, yoga, ballet, and more. Topics related to track and field include:

Geometry Workbooks
- The Geometry of Gymnastics
- The Geometry of Yoga

Graphs & Data for Science Lab: Multi-Volume Series
- The Science of Exercise Equipment
- Volume 1: Force & Acceleration
- Volume 2: Biophysics
- Volume 3: Video Analysis

- The Science of Gymnastics
- Volume 1: Force & Acceleration
- Volume 2: Biophysics
- Volume 3: Video Analysis

- The Science of Yoga, Pilates, & Ballet
- Volume 1: Force & Acceleration
- Volume 2: Biophysics
- Volume 3: Video Analysis

Anthologies of 28 Graphs
- The Science of Gymnastics
- The Science of Yoga

Most of the books above are available in both English and German translation. The books pertaining to the geometry of Olympic sports are also available in 15 world languages.
The same publisher offers similar books on additional popular topics, including sports, transportation, construction, environment, music, entertainment, and general physics. All of these book series are available in several formats and languages, including the following:
Geometry Workbooks
- Print & E-Book Editions
- Available in English & German
- Olympics Books Available in 15 Languages

Graphs & Data for Science Lab: Multi-Volume Series
- Print Editions
- Available in English & German

Anthologies of 28 Graphs
- Print Editions
- English Only

**Additional Information**
MusicaNeo Digial Sheet Music
__Unbeatable Specials__
With Kindle Unlimited ($9.99/month) at Amazon.com, you can read all e-books from Schottenbauer Publishing for no extra charge! Amazon offers Free 30 Day Trials of Kindle Unlimited. With this deal, trial members can read all Schottenbauer Publishing e-books free! This includes all the geometry workbooks, plus "The World in a Graph," "Alphabets of the World," textbooks on the science of music, all the e-book puzzles, and the educational novels by M. Schottenbauer, Ph.D.