# Geometry in the Martial Arts?



## grappling_mandala (Jul 30, 2004)

I have a general question: 

Have any fellow forum members noticed any reoccuring patterns or geometry in their respective arts? 

For example in Kali i have seen mutliple diagrams of triagular footwork or box drills aka squares and triangles. Also the stickwork "box drills" literally traces the outline of a box because of the stick.

In WC there is a centerline and quadrants.

In BJJ there are fig 4's, and triangles everywhere

In Escrima there is killer patterned stick work that goes good with drums! (music is geometry)

Tai chi has the yin yang, and even has exercises where the hands and feet trace the tai chi. Tai chi has many principles that are direct reflections of the yin/yang in different mediums of movement.

Aikido uses the sphere a lot.

I see almost EVERY school has some sort of symbols they are using to represent an idea or truth.

What kind of geometric concepts does your art teach? For anything movement related! For strategy, movement, sparring, self-defense, posture, allignment, I think it would be VERY cool to see what universals are connecting all of us together in this way. 

Dave in Oregon

PS_ Heres one to kick it off. The significance of 45, 90 and 180 degree angles. I been finding them everywhere.


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## Han-Mi (Jul 30, 2004)

Triangles and domes are the strongest shapes for structures, so it shouldn't be too surprising that we also use these principles in MAs. Circles are used a lot for redirection and triangles for a lot of stances. Squares for basic patterns and basic footwork. Straight lines for many strikes. just a few observations off the top of my head. There is a lot of physics in the MAs. I go into that stuff every once in a while with my students.


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## Han-Mi (Jul 30, 2004)

grappling_mandala said:
			
		

> PS_ Heres one to kick it off. The significance of 45, 90 and 180 degree angles. I been finding them everywhere.


I missed the PS. Those seem to be the easiest angles for us to recognize and use. there might have been other angles used more if we could gauge them as well as we can these angles.


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## 8253 (Jul 30, 2004)

We use a lot of circular and rotational movements for displacements to gain tactical advantage.  Then it is linear to strike, and if nessissary back to circular or rotational movements.  We dont really study squares or anything, pretty much all of our studies is based on circular patterns.


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## DeLamar.J (Jul 30, 2004)

This is about the closest thing I could find.

A vector is a straight line from point A to point B, such as the line your fist travels when moving from your hip to an opponent's chin. Any deviation from the straight line will result in a loss of power.

Displacement is how far the fist is displaced from the hip to the chin along a vector. 

Distance is how far the fist actually travels during the punch, which includes any stray movements from the vector and its return travel back to the hip.

Speed of the fist is measured using the distance it moves, which includes any extraneous movements away from the vector. Velocity is measured using displacement of the fist, which only uses travel along the vector and in only one direction.

Velocity of the fist = displacement of the fist / time required to complete the displacement

Acceleration of the fist = change in velocity of the fist / time required to achieve the final velocity.

Force of the fist = mass of the fist (including arm and some of torso) x acceleration of the fist. As it applies to the punch, force is of no concern if it misses the chin. If it strikes the chin, then an important consideration is the amount of pressure the fist applies to the chin.

Pressure of the punch = force of the fist / striking area of the fist. Thus the smaller the striking area of the fist, such as the first two knuckles versus the entire front of the fist, the greater striking force.

Actually, the equation for force involves more than just mass and acceleration. The full equation is F=ma+cv+kx. This longer equation takes other variables into consideration, such as wind resistance, gravity, friction within joints, muscle tension, and energy lost through heat. This longer equation for force contains 6 parts: (mass x acceleration) + (velocity x displacement) + (damping x stiffness) 

Mass is basically the fist's weight. 
Acceleration is how quickly the fist increases in velocity. 
Velocity is how fast the fist is moving. 
Displacement is how far the fist moves. 
Damping accounts for force that is dissipated by flexible surfaces and structures contacting each other. Damping occurs when there is weakening in the structure of the punch. When the fist impacts the chin, skin, muscles, and joint collapse somewhat, which dampens, or reduces, the force of the punch. If the fist is covered in boxing glove, the striking force is reduced by dampening effect of the glove's padding. Some damping also occurs when the body oscillates. Since the body is mostly water, it oscillates when shaken by the reaction to the action of the punch. Damping is also caused by friction. Muscles generate heat by the friction of rubbing against each other, which uses up energy. Energy is also wasted by other types of friction, such as the arm rubbing against the body during a punch. 
Stiffness is how rigid the fist and arm are at impact. The stiffer the fist and arm are on impact, the greater the striking force. The hardness of the striking surface increases the force delivered because reaction force will not be absorbed, thus, the knuckles of the hand strike harder than the knife hand. 
Mass of the punch may be increased by using muscle tension to add the masses of the shoulder, torso, legs, and feet to the mass of the punching arm. Generally, speed decreases as effective mass increases, but, by using a sequential application of forces, such as arm, then shoulder, then hip snap, and then leg thrust, the fist is snapped out similar to a whip, without adding mass that may slow speed of the punch. Then, at moment of impact, the body tenses and adds the mass to the punch.

Focus is when a full-power, full-speed technique is aimed to terminate a point in space. Focus is not just terminating the technique at the point in space, it is also a simultaneous contracting of all muscles to add all the power and mass of the body to the technique. Maximum power occurs when all muscles of the body contract at impact. Since the impact force of a technique equals the mass times the acceleration of the attacking weapon, to reach maximum force, you must be loose and relaxed as a technique starts and progresses so you may achieve maximum acceleration, and then contract all the muscles to achieve maximum mass. Since the technique stops at the point of focus, maximum force of the technique occurs at a point just millimeters before the point of focus. After maximum power point, the fist is decelerating. Without the contraction, maximum power is not reached, therefore, if an opponent moves into a technique that was intended to stop just short of contact, the attacker can lessen the force of the impact by not contracting into the technique. When sparring, the point of focus is just short of the surface of the chin, so the opponent is not harmed. In an actual attack, the focus point is internal of the chin, so that fist is at maximum velocity when if strikes the surface of the chin and thus strikes with maximum force. 

Taking all this into consideration, which punches harder, a large person or a small person? The large person has bigger muscles and more mass, but it requires more muscle power to move the greater mass so acceleration and velocity of the punch is reduced. The smaller person has smaller muscles and less mass, but the acceleration and velocity of the punch is greater. This, striking pressures of the two punches may actually be equal. The striking force of a speeding bullet and speeding locomotive may be equal, but which would you rather be hit by?

A larger person has more reach, more mass to absorb blows, and more strength. The farther a punch travels, the more time it has to accelerate, so a larger person with longer arms may generate more power. However, it takes more time to cover the longer distance, which may give the smaller person time to avoid or block the punch. John Jerome, in his work The Sweet Spot in Time, states that large, muscular athletes are generally faster than smaller, thinner people when moving about. So, in general, a large person hits with more force than a small person.

The momentum of an object is its mass multiplied by its velocity. By adding up the momentum of all individual objects in a system, the system's total momentum can be calculated. In a "closed" system, the net momentum never changes. This is a useful fact when analyzing an impact, because we know that the total momentum of the system will be the same after the impact as it was before the impact, even though the momentum of its parts may have changed. Momentum is a "vector" quantity, which means that two equal masses moving in opposite directions with the same velocity have zero net momentum.

Energy takes many forms, such as the kinetic energy of a moving mass. Energy is a "scalar" quantity, which means that two equal masses moving at the same velocity have the same total kinetic energy, regardless of their direction of movement. The kinetic energy of an object is equal to half its mass times the square of its velocity.

Energy, like momentum, is always conserved. But, sometimes it changes from kinetic energy, which is easily observed by measuring velocities and masses, to other forms that are harder to measure, most notably heat. The process of changing kinetic energy to heat is usually damaging to the material being heated. If the material is human tissue, it can be crushed, torn, or broken by the conversion of kinetic energy to heat. If the material is wood, it will break. A process that slowly or gradually converts kinetic energy to heat is usually called friction. A process that suddenly converts kinetic energy to heat is called an inelastic collision.

Example 1: When billiard balls collide at normal speeds they suffer no measurable damage because their collisions are almost perfectly elastic. All collisions conserve momentum, but only elastic ones conserve kinetic energy. So, if one ball with a certain velocity strikes a stationary ball on-center, it will transfer all of it's momentum and kinetic energy to the stationary ball, stop, and cause the other ball to move away at the same velocity as the striking ball. If a perfectly elastic Taekwondo student struck a perfectly elastic target, the target would fly off undamaged, but with lots of kinetic energy, perhaps sustaining damage when it hits the floor. 

Example 2: If, instead of hard balls, we use balls made of soft clay, then, when one ball strikes a stationary ball, both balls will mush together and move away with half the velocity of the striking ball. The kinetic energy before the collision is MV2/2. The kinetic energy after the collision is MV2/4. Half of the kinetic energy has gone into damaging the balls. Since both balls are equally damaged, each ball got damaged in the amount MV2/8.

Example 3: If a hard ball strikes a stationary clay ball, only the clay ball will be damaged. Therefore all of the lost kinetic energy MV2/4 went into damaging the clay ball.

Example 4: If a clay ball strikes an anchored hard ball, all the momentum of the clay ball will be transferred to the earth, and all of its kinetic energy MV2/2 will be expended in damaging the clay ball. This is twice the damage of example 3, and four times the per-ball damage of example 2.

So, as a Taekwondo student, you should be as elastic as possible as protection against damage. Proper focus unites the bones, muscles, tendons, and ligaments into a structure that is better able to distribute forces elastically (non-destructively), such as pre-stressed concrete does in buildings. It also means that an onrushing opponent who is impaled on a well-rooted reverse punch will sustain more damage than a stationary opponent. The effect of having a firm stance is most important when the opponent is stepping toward you, therefore, your best strategy for causing damage is to wait for the opponent to step toward you with an attack, deflect the attack, and then use a well-rooted reverse counter punch. Colliding elastically does not transfer any kinetic energy, so it should be be avoided. An inelastic collision with the target transfers kinetic energy that damages the target rather than your striking limb. You want your victim to be damaged, not pushed backward. To cause maximum damage to an opponent, targets should be chosen for their inability to respond elastically. The ability of a target to respond elastically depends on its structure, the speed of the impact, and the area of impact pressure.

All tissues have a range of pressures over which they are capable of responding elastically. The transition from elastic response to inelastic response is called "yielding." As pressure builds in a collision between two objects, both objects are initially elastic. A striker strives to have a larger elastic domain than the target. Once the target yields, the pressure between the two objects stops increasing and starts decreasing. When we consider momentum rather than pressure, the speed at which your technique travels has a greater effect upon the collision than the mass of the technique. Therefore, maximize speed to maximize damage . If purpose of a technique is to break bone, then use a high velocity impact with a small target area. If purpose of a technique is to cause internal damage, then use a technique that will transfer momentum


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## Brother John (Jul 30, 2004)

YES:
The Tear drop shape!

Kenpo is replete with geometric patterns though.

Your Brother
John


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## Baytor (Jul 30, 2004)

Hapkido, like Aikido, seems to use a lot of circular movement.


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## Ippon Ken (Jul 30, 2004)

No doubt that this is universal amongst styles that use preset forms or drills. In Japanese this geometry or shape of a form/kata is called "embusen". The Japanese MAs, most especially kendo and kenjutsu, place great emphasis on doing the kata with the correct embusen. It helps you to remember the lessons of the form and teaches one attention to detail. When karate was "Japanized" the Okinawan kata, already significantly changed, also adopted this idea of perfect embusen. Especially of beginning and ending kata on the same spot. 

The Okinawans used embusen or geometrical shape, for example the "I" form of kata like Pinan Shodan, the linear form of kata such as naihanchi, and the more complicated geometric shapes produced when doing kata like Kusanku or Passai/Patsai Dai, but I think the intention was to give karate-ka options and techniques based on the systems strategies and tactics. The student then worked the analysis and application based on their individuality. Where one starts and stops doesn't matter. That one does everything as perfect as possible (within your styles philosophies and methods), with the right focus, was closer to the original embusen of Okinawan kata.

In many instances throughout history "memory" was ingrained in the architecture and monuments of mankind. This "sacred geometry" is present in many ancient civilizations as well as modern ones. Washington D.C.'s core is built to mimic the astrological sign of Gemini as it appears in the heavens. Just food for thought. These eternal mnemonics not only tell you something of the culture, but of the specifics of the architects and designers. As with kata, the significant memories and the "spirit" imbued in these mnemonics and patterns help the initiated decipher some of the intent of the builders and planners. Things were also structured this way so as to mimic the powers of the heavens and the gods themselves, or to gain favor with some higher power or purpose.

The value of kata goes beyond normal views. It's a mystery in many respects. This is one of the "secrets" that folks often speak of. It's not really anything that is truly secret. Most people just don't know the details. It is a refined training process that works only if you understand the message its creators are trying to convey. It definitely works and enhances, if there is not too much drift from the original form. The more intact it is the more power and knowledge one can gain from executing the kata. For example, doing an "I" form ShuriTe kata the common modern way where you move at 90 degree angles at the top and bottom horizontal lines of the "I" ("-") versus moving at a 45 degree angle ("v" or "^") at each end of the kata. What lost knowledge would that subtle change do for your kata training and understanding, or for the understanding of your style and its antecedents? Maybe kata is sacred geometry for the traditional martial arts?

"Keep lookin', searchin', seekin', findin..."- Afrika Bambaata and the Soul Sonic Force "Lookin' For the Perfect Beat" (c.1983)


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## Chrono (Jul 30, 2004)

I've noticed a lot of this, too. But, then, I think there's a lot more physics than geometry.


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## Firona (Jul 30, 2004)

I cry every time DeLamar makes a post like that, it's just beautiful. Anyway I think most of what I wanted to say has been said lol. Circular movements are focused on a lot in martial arts without many really realizing it. Aside from the redirection of force there is also the hand and foot movments you do for extra power (rotating the wrist as you punch, twisting the hips for kicks etc.) one thing that I have noticed in the basics of sparring is the drawing of lines. You draw a line from you to your opponent and when they strike you try to step off of it and strike along a different line. Finally, if we are talking about geometry I have to bring up fencing (rapier) When fencing with a rapier almost everything you do is based on geometry I think that's why i was never really in to fencing (stupid shapes and stuff) hehe.


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## kenpo tiger (Jul 30, 2004)

Brother John said:
			
		

> YES:
> The Tear drop shape!
> 
> Kenpo is replete with geometric patterns though.
> ...


"Rap on, Brother, rap on."

Kenpo is based upon the 'web of knowledge'.  Ever looked at a spider's web?  Very geometric.  Not to mention the angles our forms take.  Plus, the system itself is based on the clock.  Rife with geometry!

Hey Jason.  Good post!  KT


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## Trent (Jul 30, 2004)

Our silat from Pentjak Silat Serak is extensively based upon geometric patterns to take advantage of levers, the force of gravity, structure integrity, force vectors, torque and momentum.  It is most visually evident to new students in the pantjar. Our Kun Tao relies heavily on circles, spirals, triangles, ellipses and short arcs to generate power, evasion, grappling, etc. when meeting resistance or to more efficiently use your mass efficiently.

In fact, both use a myriad of similar geometric patterns and the overlapping is very large, but the approach of each is distinctly different.


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## Chronuss (Jul 30, 2004)

Brother John said:
			
		

> YES:
> The Tear drop shape!
> 
> Kenpo is replete with geometric patterns though.
> ...


I think replete is an understatement, but definately correct.


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## mj-hi-yah (Jul 30, 2004)

In Ed Parker's American Kenpo we have the Universal Pattern. It is totally geometric and representative of any possible way in which we can move in combat. The pattern contains both straight and curved lines, quarter, half and full circles including circles that touch and overlap each other. It also contains squares, diamonds, rectangles, triangles, crosses, crisscrosses, hearts, figure eights, and overlapping and elongated figure eights, octogons, etc., As I am learning form a wise Kenpo dude  ...when the Universal Pattern is repeated and meshed on seven different intersecting planes, your Universal Pattern of how we move in combat is complete. We are encouraged to use movement within this pattern that is useful to us in our self defense. 

*




*


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## Flatlander (Jul 30, 2004)

I wanted to post to this thread, but I need to draw pictures to make my point, and I can't.


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## kenpo tiger (Jul 30, 2004)

mj-hi-yah said:
			
		

> In Ed Parker's American Kenpo we have the Universal Pattern. It is totally geometric and representative of any possible way in which we can move in combat. The pattern contains both straight and curved lines, quarter, half and full circles including circles that touch and overlap each other. It also contains squares, diamonds, rectangles, triangles, crosses, crisscrosses, hearts, figure eights, and overlapping and elongated figure eights, octogons, etc., As I am learning form a wise Kenpo dude  ...when the Universal Pattern is repeated and meshed on seven different intersecting planes, your Universal Pattern of how we move in combat is complete. We are encouraged to use movement within this pattern that is useful to us in our self defense.
> 
> *
> 
> ...


Glad you read my post mj.


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## MichiganTKD (Jul 31, 2004)

Not only is traditional Tae Kwon Do full of geometry, I use geometry (angles, shapes, Pythagoran Theorem etc) to explain how movements should be performed, where the hands and feet should be placed, and what techniques should look like.

1. Front stance-feet should be in a triangular pattern.
2. Side kick-cocked leg should be parallel to the floor.
3. Side block-arm is 45-degrees, fist at eye level.
4. Wheel kick-your hip rotator traces a full circle in front of you.


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## Phoenix44 (Jul 31, 2004)

Also, you can poke attackers in the eye with those compass things.:knight:


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## MichiganTKD (Jul 31, 2004)

Finger works quite well for that as well. Throat too.


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## pete (Jul 31, 2004)

circles, diamonds, hearts, moons, clovers...*always after me lucky charms~*


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## kenpo tiger (Jul 31, 2004)

pete said:
			
		

> circles, diamonds, hearts, moons, clovers...*always after me lucky charms~*


Pete, you slay me!


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## Brother John (Jul 31, 2004)

pete said:
			
		

> circles, diamonds, hearts, moons, clovers...*always after me lucky charms~*


They're magically
Destructive...


Your Brother
John
PS: IS Tony the Tiger's "THeirrrrr  GREAT!" Actually a Kiai or what???


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## Brother John (Jul 31, 2004)

Phoenix44 said:
			
		

> Also, you can poke attackers in the eye with those compass things.:knight:


Yeah, my grandpa, the "Master Mason" taught me that one.
You can all so trip them up with your square, beat them over the head with your 24 inch guage and strangle them with your apron strings.
Just be sure not to leave the body in the middle of the Lodge. 
The older brothers tend to trip over it.







Your Brother
John


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## kenpo tiger (Jul 31, 2004)

Bro,

It's a tiger thing.  You wouldn't understand.  KT


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## GAB (Aug 7, 2004)

Hello:

I see that Brother John has brought forth the Masonic Mon.

In my humble opinion. The Masonic tradition has been one of the main movers regarding the martial arts. 

Kenpo as we know it today is only about 60+ years old, Kempo goes back further. The Chinese arts and some of the FMA (masonic influence FMA) goes back further.

Okinawan and Japanese are quite intertwined. The Chinese and the Okinawan are also intertwined.

If you study the origins of Geometry and the influence it has had into Western Culture in the last 500 years+ you will find, much has to do with Masonic influence.     

The Universal Pattern that is so much apart of AK/EPAK. Comes directly from that teaching (masonic).

Regards, Gary


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## MichiganTKD (Aug 8, 2004)

In my opinion, one of the things that separate traditional from so called "freestyle" arts is this adherence to geometric and physical laws. Geometry brings order to nature. And by using geometric principles in martial arts, you bring a sense of stability and beauty as well as art and science.
For instance, it is one thing to say "a front stance should be done about like this...". However, an isosceles triangle (a triangle with three equidistant sides) is very stable and strong. Using this model provides a known and stable method of doing this stance. You can visualize exactly where to place your feet. Using a concept like parallel also helps students better understand chambering certain kicks, as opposed to dropping the knee because they don't know how to keep their leg.


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## cdhall (Feb 16, 2008)

mj-hi-yah said:


> In Ed Parker's American Kenpo we have the Universal Pattern. It is totally geometric and representative of any possible way in which we can move in combat. The pattern contains both straight and curved lines, quarter, half and full circles including circles that touch and overlap each other. It also contains squares, diamonds, rectangles, triangles, crosses, crisscrosses, hearts, figure eights, and overlapping and elongated figure eights, octogons, etc., As I am learning form a wise Kenpo dude  ...when the Universal Pattern is repeated and meshed on seven different intersecting planes, your Universal Pattern of how we move in combat is complete. We are encouraged to use movement within this pattern that is useful to us in our self defense.
> 
> *
> 
> ...



I was going to bring this up.
But I have been away for a long time and I see this is an old thread and that most of the users have been closed out.

Hmmm...

But I've used the Universal Pattern as illustrated to show students how we are trying to execute a certain move. I've found it a very handy teaching aid.


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## Balrog (Feb 18, 2008)

All of the forms in Songahm Taekwondo fit on what we refer to as the Songahm Star.  There's a brief discussion and a picture of it at http://www.ataonline.com/taekwondo/songahm.asp


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