Geometry and Exercise: The Shapes You’re In
– Without Geometry, Life is Pointless
It may seem like an odd topic to include in the study of exercise science. Few texts and paradigms devote much time to the subject. Many (ok, most) students saw Geometry as a subject invented by dudes named Pythagorus and Euclid, who concocted a few sadistic theorems which tortured students and caused centuries of test anxiety.
Geometry and Anatomy
But the truth is that the laws of geometry are wonderfully logical and elegant. Another fact is that geometry (translated: The study of the earth) is integral to much of our physical world, and very much essential to the form and function of the human body.
For example, several muscles are named for different shapes (trapezius, rhomboids, deltoid, etc.) Our joint actions of flexion and extension are described as respectively decreasing and increasing joint angle. We further define joint movements by identifying the plane in which they occur.
We turn our palms up or down by crossing the two bones in the forearm. Most specifically, one bone (the ulna) remains centered while a more mobile bone travels around it in a path similar to an arc. It is because of this “circle like” path that the mobile bone is called the radius.
There’s also a bone in your wrist called the trapezoid, and one in your ankle called the cuboid. By the way, the suffix “-oid” means “shaped like.” So the cuboid bone is so named because it is shaped like a cube. The deltoid muscle is shaped like the Greek letter delta, which is to say that is it roughly triangular.
Torque in Joint Rotation
If we delve into human movement a bit more, we see that many of our joint actions involve rotation. The force which creates rotation is called Torque, the study of which is defined as:
Here, Torque is equal to the magnitude of force (how hard a push or pull) multiplied by the Perpendicular distance between the line of action of the force and the Fulcrum.
In order to understand the notion of Torque, you must first appreciate the uncompromisingly geometric concepts of Line, Fulcrum and Perpendicular. Certainly kinesiology, the study of how humans move, consistently requires a strong grasp of geometry. Indeed it’s been known that a certain local professor, driven by obsessive curiosity (and lack of social engagement), has sketched geometric proofs supporting such thrilling phenomena as the shortening of the gastrocnemius muscle upon knee flexion, or the resistance curve created by a 45 degree back extension exercise.
A crucial factor which determines the strength of a muscle is its cross sectional area. It is important to note that overall muscle volume is less related to force production.
Even within muscles, the fibers can be arranged parallel, in which case a muscle can pull through a greater distance, or can lie along various angles of pennation, which allows for more force but limits distance of muscle shortening. Indeed the muscle itself is wrapped in a layer of tissue called the perimysium, so called because this thin sheath encapsulates the muscle and defines the perimeter, or outer measure. Even on a microscopic level, we now know that the muscle proteins (actin and myosin) are positioned so that they connect at 45 degree angles, optimizing their ability to contract quickly and efficiently.
Examples of applications of geometry in the human anatomy, physiology and movement are ubiquitous. Suffice it to say that the further you wish to study the body, the more important it becomes to understand Geometry. We even recognize that body shapes are correlated to risk of disease with the adage: It’s better to shaped like a pear than an apple.
About the Author:
James Menz earned his Master’s Degree in Exercise Science in 2005. He’s been a Certified Strength and Conditioning Specialist since 2000. He is currently the Director and author of the Senior Fitness Training Specialist Certification at the University of Delaware, and travels nationally to deliver continuing education seminars for allied health professionals.
His courses in the AthleticTraining.com catalog include Low Back Pain Treatment for Health and Fitness Professionals, Skeletal Muscle Function and Movement Analysis, and Exercises for Prevention of and Recovery from Back Pain.