Geometry and martial arts? Bah! you say? But wait. Geometry, if not at least some mathematics, are a part of all sorts of things around us in life that you may never even consider. Physics for example. Without mathematics, you'd never get through all those formulas like the rate of gravity: 9.8 meters per second per second, or acceleration, velocity, etc. That may seem like an obvious one. How about art? I know it may seem easy and not exactly math related to draw a picture, but in order to really make something look realistic, to actually draw or paint what you see with your eye, you have to be able to account for angles, vanishing points, horizon lines, the angles at which light and shadow fall, proportions for the human body for example.... and the list goes on.
Martial arts is also deeply rooted in mathematics and specifically geometry. We just don't usually think about it that way. Wing Chun, for example, utilizes the concept of a centerline and focusses a lot of attention on not crossing it if possible and at the same time forcing your opponent to cross their own. That is one example. Another would be Ba Gua Chan also know as Pa Qua in which you focus on walking a circle and on more circular movements. Kali is another excellent example of geometry in martial arts, because rather than teaching specific defenses to specific attacks, Kali teaches general defenses against different angles of attack. This is true for many weapons arts it would seem. I believe I first learned of this principle and that there are really only nine possible angles from which you can either attack or be attacked when training in sword fighting. It's something which is true no matter what the weapon is or even if you don't have any weapon at all though.
So, you can see the different elements of geometry showing themselves in lines of attack and even in footwork, but it's the same with grappling and striking techniques too. If you go to do a roundhouse kick for example, there is a certain angle at which you need to tilt your body and certain position you need for your feet to be at in order to maintain your balance while performing this type of technique. This is usually described as body mechanics, but it's all geometry. Just different ways of saying things. Jiu Jitsu is an excellent example of what I'm trying to say here. If you've ever applied a rear naked choke to someone, you know that there is a certain position you need for your arm to be in in relation to your opponent in order to get maximum efficiency out of the technique. My teacher used to tell us our elbow of the choking arm should be directly below the chin, parallel. Sounds like geometry to me.
So, why should you care that math is so involved in the martial arts? Well, I personally think it's kind of a neat and different way to look at it. But aside from that, there's also the fact that if you can see it and break it down into its mathematical and geometric form, you can start to see where what you're doing is right and efficient and where you're wasting effort or not connecting things the way you could be. Now, of course there's a lot more to martial arts than just knowing math and lines and whatnot. If that was all there was to it, people would have wanted to learn self defense from Albert Einstein instead of Bruce Lee. you have to train your body and you have to have a certain mental and emotional strength, but those are all things which you can develop. Knowing all the "ahem" anlges.... can help you to understand your art better and that could help you to improve in it more quickly. So, maybe just give a little thought to geometry and what a great mathematician you're becoming the next time you step out on a mat to train in martial arts. Want more tips and information to help with your martial arts training? Visit me here and check out our martial arts segment.