I am not a Freemason. I do not agree with the ideology of the Freemasons in general. I have nothing against the individuals and I am not going to get into the conspiracies surrounding the Freemasons.
However, there is something I must get out of the way since most people will immediately think of them because of what I'm talking about.
The Freemasons believe there is a sacredness to Geometry, mathematics, certain sciences, and the use of Symbols. I am focusing on the Geometry, which does get into mathematics and certain sciences. However, I am only doing it from a practical point of view. I'll respectfully refrain from getting into the metaphysical side of any of it as well as ideologies stemming away from the Martial Arts, mostly for those who have a strong dislike for the Freemasons.. Just as much for those who don't want to hear conspiracies about them.
Something I had found very interesting that was said by Master IP of Wing Chun was that he wished he had known the complexities of Geometry when he was younger. The nature of him saying it was the importance of the Triangle within the Wing Chun system. What really caught my attention was that Master IP also stated he wish he had learned more in geometry at a younger age because of the profound importance it later had in his development of technique.
I heard this in the onset of my fascination with the system many years back. What caught my attention when Master IP said that particular statement about the triangle was the intricate nature of all Martial Arts systems coming down to a complex yet intuitive understanding of the Human Anatomy. Anyone who is training in Martial Arts comes to respect the weakness and strength of the Human body; if they don't, they haven't stepped away from the fanciful and foolish imagination of being Super Human.
I must admit that it was not a fascination with being a fighter that led me into any study of Martial Arts, it was the extremely docile outward demeanor of Masters coupled with their fierce aura within any situation which caught my attention. Growing up, I always found the real-life videos of Bruce Lee to be interesting, because he seemed so calm and so nice.. Yet he was nothing to be trifled with with fists or with brains.
That same fascination extended to many others caught on tape as well as ones I met face to face. Naturally, in those childhood years, I just couldn't help but wonder if there really was a deeper side to Martial Arts than a good ol' fashioned ass kicking (stupid Hollywood).
In my endeavors of enlightenment, I started to appreciate this understanding of mathematics. Even though I personally can care less about learning math concepts for scholarly purposes. In fact, I am very adverse to mathematics in all forms for some indescribable reason. It's not even that I have low confidence in my ability or just outright struggle with it.. I literally just don't like it. I am more quick to grab a calculator for the reason of not letting formulas go through my head than to speed up the process itself (No offense to those who find math to be fun, I have nothing against you guys).
Over time I started to realize that there was no need for me to get into mathematics in a linear fashion. My intuition could make sense of a lot of principles and I was resolved that the use of math is a matter of inevitability in one form or another even if complex formulas aren't. What became a matter of necessity in physical training, became a necessity in other forms of my life. Such as my visual creativity in the arts. Somehow.. That translated into my literary pursuits.
I noticed that there was a sort of beauty to certain aspects of mathematics as my curiosity for Quantum mechanics grew, though I also noticed a surreal nature to it all because of having to throw out my understanding of conventional physics. It's unfortunate to me that I couldn't throw out mathematics as well.
Fortunately, physics is a springboard to the understanding of many things and is nothing short of helpful in Martial Arts, as well as mathematical computation/analysis.
Since I'm getting deep into my personal enlightenment, I'll express what I learned from this whole idea of Sacred Geometry. I also believe that the triangle is a very useful concept when dealing with the basics of physical defense and offense. From stances, to combatives, and to energy flow.
For example: Something that most people will teach their students early on, never fully extend the forearm and elbow when punching; they'll also teach to quickly pull back. Some teach this purely as a way to increase reflex time to counterattack, while others purely teach it as a safety maneuver to keep from causing injury during an attack. Both are exceptionally true and both should be taught as a matter of safety. Also, some teach that excluding centrifugal motion (twisting) can yield faster motion even though it may not be as strong; such as the vertical punch (for someone like me, who doesn't have the size to use, I love vertical punches because they go well with my agility/speed and they have devastating potential when chained together).
It is worth noting the intuitive nature of bent knees in fighting stances, which is a matter of angles like a triangle. It may be understood that the spreading of the feet to shoulder length is also a matter of angles like a triangle as well. In fact, when you look at all the different positions that are taught for stances, you see triangles all over the place.. The geometry of them playing a big role in defense and offense capabilities, as well as proper placement to keep from being overpowered by a weak defense or having little power in a weak offense.
It is absolutely amazing how much training goes into understanding the application of stances and combatives because most people get the form yet they don't get the idea. That may sound like it is no big deal, but I'm expressing someone who knows the basics of how to make a fist to punch yet doesn't know to use their entire body and proper footing to make that fist into a good punch.
In my own pursuit, I have tried very hard to keep away from focusing on an idea before focusing on my form. The only reason is because I get carried away in creating variations because I have the idea, which keeps me away from every grasping good form. However, I eventually switch up when I have confidence in basic principle. This is because my body-memory serves my instincts well once I understand the capabilities of a form yet retain the idea. This is especially true with weapon handling, because it is a lot easier to recognize how much damage you can inflict and why you may have had a variation that yields weakness.
How anyone else learns may vary greatly, I am not trying to suggest my method is necessary or even to my own benefit over any other idea. What I've noticed remain constant is a respect for the complexities of the geometry of my form within the expression of an idea. It is simply how I process things, as I am a kinesthetic thinker and very intuitive.. So I'm better off making the mistakes of bad form to better grasp the idea as a whole.
Ok, so that bit is just what I've noticed in hand-to-hand combat. When we look at weapons, they are the greatest form of geometry and physics that I can think of in Martial Arts. You can say that the weapon itself is a testament to the power of geometry as well as the ambidexterity of the weapon itself.
The geometry of a weapon decides if and even how an edge of a blade cuts and it determines a weapon's weaknesses as well as special attributes against other weapons. To the laymen, there is no coincidence to the shape of a Katana, a shuriken, or the bo staff. A wonderfully malicious weapon that uses physics and shape is the morning star. I consider the Nunchaku to be very similar, just without the penetrating effect of a spike to pierce armor. Some weapons are developed to suit specific needs and many are very versatile in their uses. An Ax is a good example of something so formidable in combat, useful in everyday use, yet hard to understand just by looking at it.. However, the understanding of how any weapon (tool) can be used is the only practical way to successfully use them to your advantage while they are in the hands of your enemy. Just another reason why I value the pursuit of increasing my ambidexterity (for those who don't know, stances reveal a lot of what you are about to do or can't do. That is the reason why Hakama were made).
Now let's clear one thing up..
When we refer any shape as "Sacred Geometry", we are specifying certain attributes of specific shapes. The human anatomy doesn't have these specific shapes in their raw form, though the human anatomy easily conforms to these shapes in various ways. I have yet to see a weapon that functions extremely well that doesn't conform to these shapes. Moreover, the more simple the understanding of how these shapes interact with conventional physics then the better their versatility.
Eastern Philosophy focuses on Sacred Geometry in various ways. To my dismay, it is Western Civilization that keeps these things out of schools and doesn't allow it to take on different aspects of life. I am somewhat ashamed to see it perpetuated in Western Society when dealing with Eastern concepts..
Take a closer look at what you are taught in Martial Arts.. You might notice that the teachings are very much a "Hard Science". Meaning there is a consistency to it, can be tested with predictable results, and there's nearly no margin of error within these predictions. You may also notice that you can assimilate the basis of the knowledge to do many productive things around the house or labor jobs (which I'm sure many people can agree that they like studying Martial Arts because of how much it helps with everyday activities/chores).
If you didn't already know the significance of the role of Geometry in Martial Arts, I hope that opened your eyes a little bit. Maybe now you can look at your math test as a practice in a Dojo or even a matter of life and death.