The term “musclebound” means more than just “overly muscular”. It has a technical meaning, too: a meaning that is based on gymnastics and geometry.

This is one of my favorite little pieces of trivia, because it involves both fitness and mathematics. I remember hearing it a long time ago from a gymnast friend of mine in college, but beyond that I can’t vouch for it being a historically accurate explanation of the word “musclebound”. But regardless of whether this is the real story of how the term came into being, it is still an interesting and important lesson about working out that also relates * directly* to high school level geometry.

In gymnastics, more so than in any other sport, your main goal is to move around your own body. You have to lift your own body into the air, support yourself, and move yourself around. As a result, there are two factors that are very important to your performance: your strength and your weight. These two factors are directly opposed: the stronger you are, the more you can lift and move; the lighter you are, the easier it is to lift and move your own body.

But of course these two things are also intrinsically tied to one another: the way that you get stronger is that you build up your muscles, which then in turn makes you weigh more.

When you first start building muscle, the amount of strength that you are gaining more than makes up for the amount of weight that you are gaining, so your overall performance improves. However, as you keep on building muscle, you eventually reach a tipping-point: the point where your weight gains overtake your strength gains.

Why? Because of geometry.

Think about muscles as spheres. Of course, in reality muscles are not exact spheres: they are deformed, usually very elongated spheres. But that doesn’t matter for what we are thinking about. Basically, muscles are mutated sphere shapes.

The strength of a muscle is proportional to the thickness of the muscle; in other words, the strength of a muscle is related to the area of its cross-section. For example, think about your bicep. The strength of your bicep is proportional to the area of the cross-section you get by cutting it in half at its thickest point. The strength of a muscle increases with the area of its cross-section.

The weight (mass) of a muscle, on the other hand, is proportional to the volume of the muscle. It is the overall bulk of a muscle that contributes to how much it weighs.

Now, remember your high school geometry:

The area of a circle is equal to pi times the radius squared.

The volume of a sphere is equal to four-thirds times pi times the radius cubed.

The important thing to compare here is this: As the radius is increasing, the area (which is related to your strength) is only increasing by a factor of the radius * squared*, but the volume (which is related to your weight) is increasing by a factor of the radius

*.*

**cubed**Because of this basic mathematical truth, **these two curves must cross**! At first, increases in the radius of your muscle give you more strength than weight, which is a good thing: this will increase your performance as a gymnast. But then, the additional benefit you get from adding more muscle decreases, because you are increasing your weight * faster* than you are increasing your strength.

Weight increases by the cube of radius, while strength only increases by the square of radius.

It is at the point where these two curves cross that you have the ideal amount of muscle for gymnastics. If you have less muscle, then you could still improve your performance a little bit by gaining. But if you go above that point, then your own muscles weigh so much that they actually detract from your performance.

If you go above that point, your own muscle weight is growing faster than your own muscle strength.

Your performance is * bound* by the weight of your own muscles.

You are musclebound.

The way this story was told to me, the term “musclebound” actually was originally a * technical* term in gymnastics with exactly this meaning, and it only evolved into the more general term in common usage later on.

Whether “musclebound” was originally intended to have this technical meaning or not, the basic analysis of the relationship between muscle strength and muscle mass is still true and very interesting. It is a fantastic application of basic geometry to sports and exercise.