Breathing Patterns

Breathing is an essential component of all forms of physical exercise. 

How can breathing be measured? Take a moment to write a list of variables relevant to breathing. 

Respiration rate (number of breaths per unit time), lung capacity, depth of respiration, and rate of airflow are all ways to measure breathing. 

A spirometer measures the rate of flow of air from breathing. Consider the graphs of spirometer readings below, excerpted from a book series by Schottenbauer Publishing.

Discussion Questions

1. In each graph above, what are the maximum and minimum flow rates?
2. In each graph above, what is the period of breath cycle? 
3. In each graph above, what is the frequency of breath cycle? 
4. Why is the first graph not a perfect sine wave?
5. Why is the second graph not showing the same shape as the first graph?

Additional Information

Schottenbauer Publishing

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Science of Yoga, Pilates, & Ballet: Volume 4

A new volume of The Science of Yoga, Pilates, & Ballet: Data & Graphs for Science Lab has arrived! Volume 4 features brightly colored graphs depicting a variety of complex moves. Examples include a yoga sun salutation, Pilates splits, backbend, and inverted bicycle, and a series of ballet leaps (Glissade, Sauté, Soubresaut, Pas Assemblé, Pas de Chat, Sissonne Fermée, Royale, Grand Jeté, and Cabriole). The book also contains graphs showing ballet jumps with a variety of axes options, as well as comparison data from the motion of a ball flying through the air, falling, and bouncing on a carpet.

The two sample graphs below are excerpted from Volume 4:

Discussion Questions

1. What is the minimum and the maximum for each variable in these graphs?
2. Which leg rises into the air first?
3. How high is the jump?
4. How long is the person in the air?
5. Does either ankle ever rise higher than either knee?
6. Is this correct technique for glissade?
7. Draw a sketch of the person's movement at five (5) points during the move, to show what the move looks like to an audience. Use a stick figure.
8. Where should the arms be for the glissade? Draw the ideal position of the arms on each of your sketches from #7. Then, draw a graph showing the ideal movement of the arms. Use a separate graph for the right and left arms. Include Shoulder, elbow, and wrist in your graphs.

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Schottenbauer Publishing

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New Book Series Provide Direct Access to Science of Yoga, Pilates, Dance, & Ballet

The science of exercise has now become even more accessible to the public, with new educational books by M. Schottenbauer, Ph.D. Written for students from grades 7 through high school, college, and university, these lab manuals feature graphs of the physics and biophysics of yoga, Pilates, dance, ballet, and other popular sports. The data can be used to supplement traditional curricula in a variety of classes, including math, science, health, and physical education.

The following two graphs, excerpted from one of the books, compare electrical signals in the left bicep during two yoga positions.

Discussion Questions:

1) How much variation in electrical activity is present in Graph 1? In Graph 2?
2) Which graph shows a greater increase in electrical activity during the pose?
3) Which pose requires greater effort to produce?
4) What is the activation pattern of the forearm muscles during each pose?
5) Which yoga pose is more relaxing during the pose? 
6) Which yoga pose is more relaxing after the pose?
7) Does this scientific data suggest which yoga pose should come first, in a good routine?


Graphs such as the ones above can be found in the following book series:

Graphs & Data for Science Lab: Multi-Volume Series

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

Anthologies of 28 Graphs

• The Science of Yoga
• The Science of Dance & Ballet

Related books, appropriate for younger students, include the following:

Geometry Workbooks

• The Geometry of Yoga
• The Geometry of Ballet 

Additional information on these and related book series is available on the author's blog on Sport Science Education.


Additional Information

Schottenbauer Publishing

Free Education Resources

The Science of Yoga, Pilates, Dance, & Ballet

The science and math of yoga, pilates, dance, and ballet are topics of new books from Schottenbauer Publishing. Presenting data from real exercises collected by the science writer and publisher M. Schottenbauer, Ph.D., these books bring the "high tech" end of stretching, holding, moving, and leaping to audiences everywhere!

In these books, students can enjoy learning about common moves from yoga, pilates, dance, and ballet. One series of books, written for elementary school students, focuses on geometry. Two series of science books feature graphs and data, illustrating common mathematical functions, plus a variety of concepts from physics and biophysics. 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. 

Books include the following:

Geometry Workbooks

• The Geometry of Yoga
• The Geometry of Ballet 

Graphs & Data for Science Lab: Multi-Volume Series

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

Anthologies of 28 Graphs

• The Science of Yoga
• The Science of Dance & Ballet

These books are complemented by a series of science books on other popular sports topics, including Olympic sports, athletic training, exercise equipment, gymnastics, and more. Relevant topics include:

Geometry Workbooks

• The Geometry of Gymnastics

Graphs & Data for Science Lab: Multi-Volume Series

• The Science of Athletic Training 
• Volume 1: Force & Acceleration
• Volume 2: Biophysics
• Volume 3: Video Analysis
• 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

Anthologies of 28 Graphs

• The Science of Physical Fitness
• The Science of Gymnastics

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
• Ballet Book Available in 3 Languages (English, German, & Chinese)

Graphs & Data for Science Lab: Multi-Volume Series

• Print Editions
• Available in English & German

Anthologies of 28 Graphs

• Print Editions
• English Only

Additional Information

Schottenbauer Publishing

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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.