Fencing requires skill not only for manipulating a foil, sabre, or épée in hand, but also with physical fitness and positioning of the entire body. The subject of relative body position can be studied in graphs, just as easily as the position of any sword.
A sample graph from The Science of Fencing: Volume 2 from Schottenbauer Publishing is shown below:
Discussion Questions
- Which body part is furthest right? Furthest left?
- Which body part is highest? Lowest?
- Sketch the initial position of shoulder, elbow, and hand.
- Sketch the final position of shoulder, elbow, and hand.
- Sketch the position which is most extremely distant from either the initial or final position.
- Describe the motion in-between initial and final position.
A new volume of The Science of Fencing has arrived! Volume 2 contains new data showing the position of a moving toy sword, from different perspectives and angles. New features include graphs of the position and motion of the fencer, in addition to the sword itself. The data collected are relevant to common forms of competitive Olympic fencing, including épée, sabre, and foil.
These data can be used for lesson plans by teachers and parents as supplements for traditional classes, as well as for special school projects, after-school enrichment activities, homeschool, and special science camps.
A sample graph from The Science of Fencing: Volume 2 from Schottenbauer Publishing is shown below:
Discussion Questions
- What do the two lines represent in the graph?
- What is the maximum of the blue line? The minimum?
- What is the maximum of the red line? The minimum?
- Describe the shape of each line in words.
- Sketch the sword's pattern of motion in real space, indicating at least 10 points.
- Describe the sword's pattern of motion, focusing on the tip only.
- Redraw the graph, using a different origin.
- In this graph, what is the perspective of the viewer? Is this graph showing the front of the fencer, the side of the fencer, or another angle?
- Where is the hilt during this motion? Is there more than one possibility for the location? Can the position of the hilt be determined from the graph?
Additional Information
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.
