Trajectories of human motion can be analyzed in several ways. Most often, scientists are interested in measuring the simple velocity or speed of a human walking, jogging, or running forward on a track. A closer analysis of human motion shows a complex pattern of movements, however. As the torso moves forward, the legs and arms move back and forth relative to the torso. In addition, the entire body bounces slightly up and down. The force of breathing can also distort the shape of the torso.
What does human movement look like in a graph? Consider the graph below, excerpted from the book series Walk, Jog, & Run: The Science of Athletic Training from Schottenbauer Publishing.
Discussion Questions
- In which direction is the walker moving?
- How many steps are shown in the graph?
- How can the speed of the walker be measured on the graph?
- Describe the movement of the knee, ankle, and toes relative to the hip, as if the hip were stationary.
- Which body part moves the most in the x direction?
- Which body part moves the most in the y direction?
- What is the velocity of the walker?
Additional Information
Geometry is essential for physical fitness. Take a moment to write down a few ways in which geometry affects the precision of sport.
Discussion Questions
- What data is necessary to collect in order to understand the role of geometry in physical activity?
- What spatial perspectives and/or mathematical planes are important for precision?
The cover of The Geometry of Water Sports, to the right above, features a waterskier in action.
Discussion Questions
- What angles can be measured on the diagram, in order to understand the accuracy of technique?
- Is any essential information missing from the picture? What is necessary in order to measure that information?
Geometry diagrams featuring physical fitness activities are available in the following books from Schottenbauer Publishing, available in paperback and Kindle editions:
Geometry Workbooks
Additional Information
Repeating patterns are common both in math and in exercise science. Consider the following graphs, excerpted from the series The Science of Exercise Equipment from Schottenbauer Publishing:
Discussion Questions
- What type of motion is described the graph?
- What are the maximum and minimum x positions of the pedal? The y positions? Write these as coordinate pairs (x, y).
- Sketch the real motion of the pedal, indicating at least 8 equally-spaced points in time.
- What is the period (length) of the cycle?
Discussion Questions
- What type of motion is described the graph?
- What are the maximum and minimum angles of the arm?
- Sketch the real motion of the arm, indicating at least 8 equally-spaced points in time.
- What is the period (length) of one cycle?
Discussion Questions
- What phenomenon is described in the graph?
- What are the minimum and maximum values of potential?
- Is a cycle described in the graph? If so, describe the cycle in words, relating potential to exercise activity.
- What is the period (length) of one cycle?
Discussion Questions
- What phenomenon is described in the graph?
- What are the minimum and maximum values of flow rate?
- What is the average minimum value of flow rate? The average maximum value?
- Is a cycle described in the graph? If so, describe the cycle in words, relating flow rate to behavior.
- What is the period (length) of one cycle?
The following books from Schottenbauer Publishing contain a more extensive collection of graphs and data pertaining to the science of athletic training:
Graphs & Data for Science Lab: Multi-Volume Series
- The Science of the Athletic Training
- Volume 1: Force, Velocity, Acceleration
- Volume 2: Biophysics
- Volume 3: Video Analysis
- Volume 4: Video Analysis
- The Science of Exercise Equipment
- Volume 1: Force, Velocity, Acceleration
- Volume 2: Biophysics
- Volume 3: Video Analysis
- Volume 4: Video Analysis
- The Science of Gymnastics
- Volume 1: Force, Velocity, Acceleration
- Volume 2: Biophysics
- Volume 3: Video Analysis
- Volume 4: Video Analysis
- The Science of Yoga, Pilates, & Ballet
- Volume 1: Force, Velocity, Acceleration
- Volume 2: Biophysics
- Volume 3: Video Analysis
- Volume 4: Video Analysis
Additional Information
How much sport science can be crammed into only 28 graphs? This question inspired a series of anthologies by Schottenbauer Publishing, spanning 10 popular Olympic and common sport topics.
Sport Science Anthologies
- Physical Fitness
- Summer Olympic Sports
- Winter Olympic Sports
- Gymnastics
- Track & Field
- Ball Sports
- Dance & Ballet
- Yoga
- Figure Skating
- Ice Hockey
Video Analysis
- Jumping Jack
- Pedaling on Bike
Goniometer
- Seated Knee Extensions
- Jogging in Place
Spirometer
- Normal Breathing
- After 5 Minutes Jogging (& Continuing to Jog)
Electromyogram
- Arm Relaxed
- Arm Held Straight Up
- Arm while Jogging
- Arm during Bicep Curls
- Quadricep During Vertical Squat
Electrocardiogram
- Before Cycling
- After 5 Minutes Cycling
- 4 Minutes After Ending Cycling
Discussion Questions
- What comparisons and contrasts can be made with this data?
- What additional data would be useful to obtain?
The following books from Schottenbauer Publishing contain a more extensive collection of graphs and data pertaining to the science of athletic training:
Graphs & Data for Science Lab: Multi-Volume Series
- The Science of the Athletic Training
- Volume 1: Force, Velocity, Acceleration
- Volume 2: Biophysics
- Volume 3: Video Analysis
- Volume 4: Video Analysis
- The Science of Exercise Equipment
- Volume 1: Force, Velocity, Acceleration
- Volume 2: Biophysics
- Volume 3: Video Analysis
- Volume 4: Video Analysis
- The Science of Gymnastics
- Volume 1: Force, Velocity, Acceleration
- Volume 2: Biophysics
- Volume 3: Video Analysis
- Volume 4: Video Analysis
- The Science of Yoga, Pilates, & Ballet
- Volume 1: Force, Velocity, Acceleration
- Volume 2: Biophysics
- Volume 3: Video Analysis
- Volume 4: Video Analysis
Additional Information
