The Geometry of Ice Skating

Geometry is essential for ice skating. Take a moment to write down a few ways in which geometry affects the precision of the sport. 

Discussion Questions

1. What data is necessary to collect in order to understand the role of geometry in figure skating, hockey, and speed skating? 
2. What spatial perspectives and/or mathematical planes are important for precision? 

The cover of The Geometry of Figure Skating, to the right above, features a skater in action. 

Discussion Questions

1. What angles can be measured on the diagram, in order to understand the accuracy of technique?  
2. Is any essential information missing from the picture? What is necessary in order to measure that information?

Geometry diagrams featuring ice skating are available in the following books from Schottenbauer Publishing:

Geometry Workbooks

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

Additional Information

Schottenbauer Publishing

Free Education Resources

Video Analysis of "Cool Skating Move"

As with any sport, ice skating can be analysed in graphs. Consider the following graph below, excerpted from the upcoming Volume 9 of Glide, Spin, & Jump! The Science of Ice Skating by Schottenbauer Publishing. 

Discussion Questions

1. What body parts are moving in this example?
2. Which body part moves the most in the x direction? In the y direction?
3. What is the name of this move?

Now, consider the following pictures, excerpted from the video. (This move is shown in the YouTube Video Cool Skating Move.) 

Discussion Questions

1. Is this move in the first or second half of the graph?
2. What is the primary motion which occurs between these two pictures?
3. What concept(s) from physics are relevant for this move?
4. Is this move found in (a) figure skating, (b) ice hockey, or (c) both?

The diagram below highlights the move on the graph.

Discussion Questions

1. Which body part moves the most during this segment of the graph?
2. Which body part moves the most in the x direction? In the y direction?

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

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

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