How Does Geometry Affect Ice Skating?

On the surface level, both the technique and beauty of ice skating can be described by geometry, in terms of the angles of knee bends and arm positions. On a technical level, geometry is essential for understanding the science of ice skating, including the physics of force and motion.

The books The Geometry of Winter Olympic Sports and The Geometry of Figure Skating contain diagrams which introduce children and teens to the task of identifying angles in ice skating. Consider the diagram below, excerpted from page 25 of The Geometry of Winter Olympic Sports (Copyright 2014, All Rights Reserved).

Discussion Questions

1. How many angles are formed in this diagram?
2. From a casual analysis, what types of angles (Acute/Obtuse/Right) are located in the diagram? Indicate the location of each angle.
3. In order to analyze the angles in this diagram, where should the coordinate axis be placed? Why? Is it necessary to identify more than one coordinate axis? Why or why not? If so, where should the axes be placed?
4. Using a protractor, measure all the angles in the diagram that are relevant to the art or physics of skating.
5. Is it possible to identify the direction of motion from this diagram? Why or why not?
6. Is this a figure skater or a hockey player? Justify your answer.

Assistance answering some of these questions may be found by watching the video How to Use Geometry Workbooks on the publisher's YouTube channel.

The following books from Schottenbauer Publishing contain geometry diagrams relevant to ice skating, figure skating, and hockey. 

Geometry Workbooks

• The Geometry of Figure Skating
• The Geometry of Winter Olympic Sports 

Additional Information

Schottenbauer Publishing

Free Education Resources

Skater in Motion: x-y Plots of Movement

In elementary school, math students learn the graph-reading skills. How often do these same students enjoy applying math to real-life data? In books from Schottenbauer Publishing, students have the opportunity to decode graphs showing movement during popular sports.

The graph below (Copyright 2014, All Rights Reserved), excerpted from the book series Glide, Spin, & Jump: The Science of Ice Skating from Schottenbauer Publishing, shows an ice skater in forward motion.

Discussion Questions

1. What is the range of each variable in each graph? Include x, y, and t as variables in your analysis.
2. In this sample, which leg is used for pushing off? Which leg moves forward first? 
3. Use the information from the graph to draw the body in physical space, at a minimum of 4 time points.
4. Is the right knee ever in front of the right hip? Is the right ankle ever in front of the right knee or right hip? Describe the sequence of motion.
5. Is the left knee ever in front of the left hip? Is the left ankle ever in front of the left knee or left hip? Describe the sequence of motion.

Additional free graphs are available in a free pamphlet from the publisher's webpage. 

The following books from Schottenbauer Publishing contain similar types of graphs and data pertaining to the science of ice skating, figure skating, and hockey:

Graphs & Data for Science Lab: Multi-Volume Series

• The Science of Ice Skating 
• Volume 1: Translational Motion
• Volume 2: Rotational Motion (Curves)
• Volume 3: Rotational Motion (Spins)
• Volume 4: Jumps
• Volume 5: Ice Hockey
• Volume 6: Biophysics
• Volume 7: Video Analysis
• Volume 8: Reference Manual
• The Science of Hockey
• Volume 1: Force, Acceleration, & Video Analysis of Pucks & Balls
• Volume 2: Force & Acceleration of Sticks, plus Biophysics
• Volume 3: Video Analysis of Ice, Field, & Street Hockey Sticks

Anthologies of 28 Graphs

• The Science of Figure Skating
• The Science of Ice Hockey
• The Science of Winter Olympic Sports

In addition, the following books are suitable for younger children learning geometry:

Geometry Workbooks

• The Geometry of Figure Skating
• The Geometry of Winter Olympic Sports 

Additional Information

Schottenbauer Publishing

Free Education Resources

Pucks & Balls: The Physics of Motion

How does a ice hockey puck compare to a field hockey ball? This question is highly relevant for ice hockey players, who are eager to keep in shape over the warm summer months. According to physics, balls do not act like pucks. The graphs below (Copyright 2014, All Rights Reserved), excerpted from the book series The Science of Hockey from Schottenbauer Publishing, show an official field hockey ball and an official ice hockey puck in motion.

Discussion Questions

1. What is the range of each variable in each graph? Include x, y, and t as variables in your analysis.
2. Use the information from the graph to draw the trajectory of the ball and the puck on separate pieces of paper. Include beginning and ending time points in your drawing.
3. Using the information from Questions 1 and 2, compare the graphs. What is different about the motion of the ball and the puck?
4. Approximately how much energy from the ball is lost due to friction? 
5. Approximately how much energy from the puck is lost due to friction? 

Additional free graphs are available in a free pamphlet from the publisher's webpage. 

The following books from Schottenbauer Publishing contain similar types of graphs and data pertaining to the science of ice skating, figure skating, and hockey:

Graphs & Data for Science Lab: Multi-Volume Series

• The Science of Ice Skating 
• Volume 1: Translational Motion
• Volume 2: Rotational Motion (Curves)
• Volume 3: Rotational Motion (Spins)
• Volume 4: Jumps
• Volume 5: Ice Hockey
• Volume 6: Biophysics
• Volume 7: Video Analysis
• Volume 8: Reference Manual
• The Science of Hockey
• Volume 1: Force, Acceleration, & Video Analysis of Pucks & Balls
• Volume 2: Force & Acceleration of Sticks, plus Biophysics
• Volume 3: Video Analysis of Ice, Field, & Street Hockey Sticks

Anthologies of 28 Graphs

• The Science of Figure Skating
• The Science of Ice Hockey
• The Science of Winter Olympic Sports

Additional Information

Schottenbauer Publishing

Free Education Resources

Spinning on Ice

Physics divides motion into two general types: translational (straight) motion and rotational (curved) motion. Whether it is a figure skater, hockey skater, or puck rotating on the ice, the same laws of physics apply. 

The graph below (Copyright 2014, All Rights Reserved), excerpted from the book series Glide, Spin, & Jump: The Science of Ice Skating from Schottenbauer Publishing, shows a rod rotating around a central axis.

Discussion Questions

1. Describe the four variables contained in the graph. What is the range of each variable?
2. How is position measured in the graph? What is the unit of measurement?
3. How many times is force applied to the rod? 
4. When force is applied, what happens to the rod?
5. Why does the rod slow down, and motion stop?
6. What is the definition of acceleration? 
7. Why does acceleration change so much, when the velocity and position do not?

Additional free graphs are available in a free pamphlet from the publisher's webpage. 

The following books from Schottenbauer Publishing contain similar types of graphs and data pertaining to the science of ice skating, figure skating, and hockey:

Graphs & Data for Science Lab: Multi-Volume Series

• The Science of Ice Skating 
• Volume 1: Translational Motion
• Volume 2: Rotational Motion (Curves)
• Volume 3: Rotational Motion (Spins)
• Volume 4: Jumps
• Volume 5: Ice Hockey
• Volume 6: Biophysics
• Volume 7: Video Analysis
• Volume 8: Reference Manual
• The Science of Hockey
• Volume 1: Force, Acceleration, & Video Analysis of Pucks & Balls
• Volume 2: Force & Acceleration of Sticks, plus Biophysics
• Volume 3: Video Analysis of Ice, Field, & Street Hockey Sticks

Anthologies of 28 Graphs

• The Science of Figure Skating
• The Science of Ice Hockey
• The Science of Winter Olympic Sports

Additional Information

Schottenbauer Publishing

Free Education Resources

Real Ice Skating Data from Child Double Runner Skates!

Easy access to the science of ice skating is provided by several book series from Schottenbauer Publishing! Books contain graphs, data, and diagrams of ice skating, figure skating, and hockey.

The graphs below are excerpted from Volume 1 of Glide, Spin, & Jump: The Science of Ice Skating, as well as a free pamphlet from the publisher. These graphs show a child's double-runner skate being pulled along a piece of real ice with a force meter, while position, velocity, and acceleration are measured by a motion detector from the back.

Discussion Questions

1. For each graph, describe the motion of the skate in words. 
2. How far does the skate travel in each graph?
3. What is the maximum force on the skate?
4. Is the force on the skate similar to the forces incurred during real skating?
5. From these two graphs, can you determine the mass of the skate?
6. How much physical work is occurs during the movement of the skate? 
7. In which graph is the friction greater?
8. Can the friction be calculated from these graphs?
9. How accurate are these graphs? What is the margin of error, if any?
10. Are these graphs relevant for real skaters? If so, how? 

Additional free graphs are available in a free pamphlet from the publisher's webpage. 

The following books from Schottenbauer Publishing contain similar types of graphs and data pertaining to the science of ice skating, figure skating, and hockey:

Graphs & Data for Science Lab: Multi-Volume Series

• The Science of Ice Skating, Vol. 1-8
• The Science of Hockey, Vol. 1-3

Anthologies of 28 Graphs

• The Science of Figure Skating
• The Science of Ice Hockey
• The Science of Winter Olympic Sports

In addition, the following books are suitable for younger children learning geometry:

Geometry Workbooks

• The Geometry of Figure Skating
• The Geometry of Winter Olympic Sports 

Additional Information

Schottenbauer Publishing

Free Education Resources

Cool Figure Skating Move: Before and After Photos!

A new YouTube Video shows a cool figure skating move on synthetic ice. Here are the before and after photos! 

Let's think about the physics of this move. What happens in order for the skater to turn from one position to the other? How does the rotation begin? What stops the rotation? Watch the video on YouTube for more details!

Additional information on the science of ice skating is available on the Schottenbauer Publishing website. Books include the following:

Geometry Series

• The Geometry of Winter Olympic Sports
• The Geometry of Figure Skating

Graphs & Data for Science Lab (Book Series)

• The Science of Ice Skating
• The Science of Hockey

Anthologies of 28 Graphs

• The Science of Winter Olympic Sports
• The Science of Figure Skating
• The Science of Ice Hockey

Additional Information

Schottenbauer Publishing

Free Education Resources

Ice Skate Comparison

Ice skates are not all the same! Two extremes are hockey and figure skates. Because hockey skates have a smooth, curved blade on the front and the back, they can feasibly be tilted almost to a right angle while still gliding across the ice! In comparison, the blade of a figure skate has grooved teeth on the front, and a flat back blade. These features prohibit tilting of the figure skates during gliding. 

What are the angles of maximum tilt for each of these skates?

Hockey Skate (Left) and Figure Skate (Right)

Two additional types of skates are shown below: bob skates and child double-runner skates. These skates are for children and are not traditionally sharpened, so they do not glide over the ice. How far could these skates rotate upwards to the front or back, before hitting the plastic or tipping over?  

Bob Skate

 Child Double-Runner Skate

Additional information on the science of ice skating is available on the Schottenbauer Publishing website. Books include the following:

Geometry Series

• The Geometry of Winter Olympic Sports
• The Geometry of Figure Skating

Graphs & Data for Science Lab (Book Series)

• The Science of Ice Skating
• The Science of Hockey

Anthologies of 28 Graphs

• The Science of Winter Olympic Sports
• The Science of Figure Skating
• The Science of Ice Hockey

Additional Information

Schottenbauer Publishing

Free Education Resources

Learning to Glide, Spin, and Jump!

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

In these books, students can enjoy learning about common moves from figure skating and hockey. One series of books, written for elementary school students, focuses on geometry. Two series of science books feature graphs and data; these illustrate 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. 

The books directly pertaining to ice skating and hockey include the following:

Geometry Workbooks

• The Geometry of Figure Skating
• The Geometry of Winter Olympic Sports

Graphs & Data for Science Lab: Multi-Volume Series

• The Science of Ice Skating 
• Volume 1: Translational Motion
• Volume 2: Rotational Motion (Curves)
• Volume 3: Rotational Motion (Spins)
• Volume 4: Jumps
• Volume 5: Ice Hockey
• Volume 6: Biophysics
• Volume 7: Video Analysis
• Volume 8: Reference Manual
• The Science of Hockey
• Volume 1: Force, Acceleration, & Video Analysis of Pucks & Balls
• Volume 2: Force & Acceleration of Sticks, plus Biophysics
• Volume 3: Video Analysis of Ice, Field, & Street Hockey Sticks

Anthologies of 28 Graphs

• The Science of Figure Skating
• The Science of Ice Hockey
• The Science of Winter Olympic Sports 

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 ice skating include:

Geometry Workbooks

• The Geometry of Yoga
• The Geometry of Ballet
• 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 Yoga, Pilates, & Ballet 
• 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 Dance & Ballet
• 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

Schottenbauer Publishing

Free Education Resources

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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.