# The mathematics of Kenpo



## Thesemindz (Feb 2, 2004)

I was trying to make a list of the points,

Point of Origin
Point of Execution
Point of Interception
Point of Oblivion

and angles,

Bracing Angle
Angle of Cancellation
Angle of Protection
Angle of Execution
Angle of Incidence
Complimentary Angle
Angle of Disturbance

in my notebook. I was thinking of the use of mathematics in our understanding of combat and teaching.

Now I think most people know "point x, angle y" but what other angles and points do you feel are important. How do angles and points relate? What is the point of understanding all this stuff? Am I hitting this from the wrong angle?

As long as were talking math, what geometric concepts do you use as teaching aids? Do you use the universal pattern? Mr. Parker discussed using squares, circles, and triangles, are the other useful patterns?

-Rob


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## Nick Ellerton (Feb 2, 2004)

im not claiming to no but i think that was the main reason behind for the universal sphere being a majorly recognised part of the art.


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## arnisador (Feb 2, 2004)

> _Originally posted by Thesemindz _
> *Complimentary Angle*



This isn't actually a _mathematical_ concept.


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## Michael Billings (Feb 4, 2004)

So let's look at both, especially since the number of "angles" we look at, whether with footwork, blocks, parries, or strikes are almost infinite.  Mr. Parker put a tremendous amount of effort into the study of the structure of the body, then of bodies interacting.  He created a nomenclature whereby these concepts could be communicated orally, and obviously felt they were of value. 

Let's not limit ourselves about whether it is mathematic or geometric, as it also intersects with the discipline of physics, and physiology.  

Mathematic symbolism can be used as exemplified in Infinite Insights.  I start the students immediately on understanding adding & subtracting moves in a technique (or rearranging), but the plus sign (+), minus sign (-), times sign (X), and equal (=) sign I use in teaching foot maneuvers, strikes, and blocks from the first day.

-Michael


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## gman (Feb 7, 2004)

> _Originally posted by arnisador _
> *This isn't actually a mathematical concept. *




Mathmatically 2 angles are complementary when their sum is 90 degrees. Now I'm not any kind of expert on the universal pattern but intuitively I would think that in kenpo that would be the angle that would move you to a right angle to your opponents circle. That's how I visulize it.


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## Rainman (Feb 7, 2004)

> _Originally posted by gman _
> *Mathmatically 2 angles are complementary when their sum is 90 degrees. Now I'm not any kind of expert on the universal pattern but intuitively I would think that in kenpo that would be the angle that would move you to a right angle to your opponents circle. That's how I visulize it. *



Interesting and a workable expansion of the concept-  Here is another definition of complementary angle:

A strike or block that follows a path or angle that parallels an attacking weapon a defensive posture the contour of an opponent or a given line.  Following these angular paths allows clear entry to desired targets.  Taking advantage of these angular oppertunities helps to produce maximum results as well as cause greater damage.


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## arnisador (Feb 7, 2004)

> _Originally posted by gman _
> *Mathmatically 2 angles are complementary when their sum is 90 degrees. *



Agreed. Now _that's_ a mathematical concept!


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## younglearner (Feb 16, 2008)

What would be some examples of classic techniques that employ complimentary angles?  I am looking for at least 10 of them.


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## ChadWarner (Feb 17, 2008)

Complimentary angles exist throughout the system.   Five swords:  after the step into the opponent to cut his depth of penetraition with the 2 handswords the right handsword to the carotid artery compliments the angle of the attacking right round punch from the bicept if you use that version of said targets.   Just one example of how the term can be used... Now you try one!


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## profesormental (Feb 18, 2008)

Greetings.

It is important to note that the language and definitions of American Kenpo are mostly geometrical in nature. They define spaces, points, paths and relations between bodies.

These have analytical geometrical definitions. They are too technical to go into here (I'm a mathematical physicist), yet the technicalities are unnecessary to teach effective self defense.

So you have points, angles, zones and geometrical theories. You use these concepts to direct the execution times, paths and effects.

A small warning before continuing: while many of these concepts are validated backed up by biomechanical and physiological facts, some are not. Also, many of them are teaching tools that tell you what to do, yet not how specifically to do it optimally.

Now with that out of the way, you have to remember that these angles are relations with your personal geometry and the body geometry of your attacker. Also note that they are NOT dynamic concepts, but snapshots in time describing a positional relationship in space.

It is like seeing photographs with a prescribed path of execution as the action arrows describing the way you move for the next photograph.

The are normally used in the following manner.

Example: Incoming attack from attacker--> you survive the attack and block at Point of X to create an Angle of Y that gets you in a Zone of Z.

Unfortunately, I have to go... family duty. So I have to interrupt the post. I hope to come back later and add more to answer your questions.

Sincerely,

Juan M. Mercado


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## younglearner (Feb 18, 2008)

I appreciate your responses very much.  This is an exciting and engaging subject for me and the insights are very useful.  I will be checking the posts often.

Peace.


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## arnisador (Feb 18, 2008)

ChadWarner said:


> Complimentary angles exist throughout the system.



I don't doubt it. I'm sure those angles are very polite to one another.



profesormental said:


> These have analytical geometrical definitions.



What does this mean?



> A small warning before continuing: while many of these concepts are validated backed up by biomechanical and physiological facts, some are not.



Sounds like you have studied Anatomical Physics?

I do not believe the physical techniques to which you are referring could possibly support this level of mathematical analysis, even if the analysis were to be performed by knowledgeable scientists using correct technical language.


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## profesormental (Feb 19, 2008)

Greetings.


> Quote:
> Originally Posted by *profesormental*
> 
> 
> ...



Imagine that you are standing against a wall that has a grid drawn upon it, like graphing paper.

You could assign coordinates to every point in that surface, like a map. (longitude and latitude)

So you could do analysis using those coordinates and use mathematical equations to describe or approximate certain positions, relations and movements.

That is a small application of analytical geometry.

Yes, I've studies anatomical physics. While there are postures that can be analyzed using several methods, it also has to be taken into account that the body has parts of different densities and elasticities and such, plus that the nervous system has preference for certain movements which it makes much stronger than others... this makes for very interesting dynamic phenomena!

And they are not always obvious, and some are hard to find, least of all explain.

The thing is that it is easier to explain how to do stuff than it is to explain why it works with scientific rigor.

To be clear, I've been referring to the concepts of Points, Angles, Zones and Paths as used in American Kenpo, as found in the Encyclopedia of Kenpo.

While it is easy to see that if I change someone's width with a grab/pull to the right shoulder I can cancel the attacker's ability to strike with the left arm (create an Angle of Cancellation), it is not that easy to see why a strike to certain parts of the right arm at a certain angle can cause the cancellation of the use of the right leg to kick for a moment.

Also, there are movements and strikes that are NOT stronger and/or faster if executed from point of origin to point of penetration in a straight path.

That was the point in my earlier post for noting a warning.

Hope that clarifies.

Juan M. Mercado


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## Doc (Feb 19, 2008)

profesormental said:


> Greetings.
> 
> 
> Imagine that you are standing against a wall that has a grid drawn upon it, like graphing paper.
> ...


It's clear to me, and quite correct.


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## Danjo (Feb 19, 2008)

I prefer the formula: _Fist + Face = KO_


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## Carol (Feb 19, 2008)

Two hits in Kenpo.  You hit them + they hit ground


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## ChadWarner (Feb 19, 2008)

I don't doubt it. I'm sure those angles are very polite to one another.

Uhmmmm yeah- The nicer things are to each other the better they work together...


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## Touch Of Death (Feb 19, 2008)

arnisador said:


> This isn't actually a _mathematical_ concept.


Why? I seem to remember learning that term in geometry.
Sean


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## arnisador (Feb 19, 2008)

Touch Of Death said:


> Why? I seem to remember learning that term in geometry.



The term is _complementary_, not _complimentary_. The first refers to completion, the second to appreciation. The notion of a 'complement' occurs frequently in mathematics.


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## profesormental (Feb 21, 2008)

Danjo said:
			
		

> I prefer the formula: _Fist + Face = KO_





			
				ChadWarner said:
			
		

> I don't doubt it. I'm sure those angles are very polite to one another.
> 
> Uhmmmm yeah- The nicer things are to each other the better they work together...



That was really funny!!!


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## donald (Feb 21, 2008)

Owww you guys make my head hurt...


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## Touch Of Death (Feb 21, 2008)

donald said:


> Owww you guys make my head hurt...


Just like math!


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## ChadWarner (Feb 21, 2008)

arnisador said:


> The term is _complementary_, not _complimentary_. The first refers to completion, the second to appreciation. The notion of a 'complement' occurs frequently in mathematics.


 
But of course it was the context the term was used in that implied its usage was for a  particular angle of movement and not just saying something nice... Then again I did not know angles could be nice to each other.   Is there something youre not telling me Arnisador exceptin my proof reading is non existent?


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## TaiChiTJ (Feb 24, 2008)

Michael Billings said:


> Mr. Parker put a tremendous amount of effort into the study of the structure of the body, then of bodies interacting. He created a nomenclature whereby these concepts could be communicated orally, and obviously felt they were of value.


 
I suspect this is why Mr. Parker will live on in history for quite awhile. He actually made an attempt to analyze martial geometry and physics using the english language, and while that analysis can certainly evolve and develop, the fact remains he initiated it.


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## Ray (Feb 24, 2008)

Complementary as defined in Infinite Insights is: ...strike or block that follows a path or angle that parallels an attacking weapon, defensive posture, the countour of an opponent..."


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