The word Geometry comes from the Greek “Geo”, Earth, and “metron”, a measure; “metron” comes from the Indo-European root, “me”, to measure. This can been seen as measurement of space and position.

Geometry involves the use of angles and shapes, can be used to form tools and structures and understanding movement and stability. Martial arts adapt a variety of geometric principles to fighting: The movement in a circle, the angles of the triangle, and the stability, or lack thereof, of structure.

As you can see pictured here, represented are the 90 and 45 degree angles on a circle; as pictured, they are the angles on a triangle, which is part of the circle. The 90s are straight lines to the four sides, and the 45s are diagonal lines to the corners. Understanding this will aid the martial artist in movement, direction, and position.

Illustrated above are the degrees on a full circle. As you can see, to the first corner is 45 degrees; if you add another 45 degree (turn), you hit 90 degrees which is directly to the right. In practical terms, if you were facing a wall in front of you, you will have turned to the right corner and then to the wall to the right. The right corner would be a 45 degree turn and the wall to the right would be a 90 degree turn. As you can see from the illustration, this process can be continued all the way to 360, which would be turning in a complete circle. 180, of course, would be an about-face, turning to the back wall.The other angles are to the sides or corners.

So, the arms, feet, foot maneuvers, legs, kicks, strikes and punches can move along these degrees as well.

Angles are important in defense, particularly in stance. Stances are important because it is from your stance that you derive stability, mobility, protection, and projection of your technique. Pictured below is what is called in Kenpo, the Neutral Bow Stance or Fighting Stance. Notice that the feet are angled at 45 degree angles which root the stance and cover the center-line; the body is angled to provide the ability to use both lead and rear weapons, but also to cover the center-line, to avoid having your targets hit, as much as possible without sacrificing mobility.

Angles are important in terms of footwork too. Obviously you can move along these angles, to avoid, to strike, to throw and grapple. In addition, moving at these angles can present you with openings on the opponent. This video illustrates rather well the principle of “triangular footwork”, moving at the 45s mainly, but also to the 90s, each case presenting different opportunities and ways of evading attack and use angles in which you can get a line of attack at your opponent.

 

One way that angles are used in Kenpo is by taking away your opponent’s bracing angle or attacking them where they have no base. A bracing angle is an angle at which there still is a base. Here we will look at a couple of Kenpo techniques in which the idea is to go to a position in which the opponent has no bracing angle and so no base, so that you can attack his center-line, where he’s vulnerable, or take him off his feet where he has no mobility or base and you have an advantage.

The first technique is called “The Back Breaker”, which is against a sneak attack (punch) from the side. You move to the back of the opponent, take him down and strike him in various ways. The position in back of him and in his center-line is where he has no bracing angle and can be taken down.

Attacker approaches defender from the side

Defender slips the punch and inserts an eye poke

Using footwork, defender maneuvers to the back of the opponent where he has no bracing angle

Defender drives a knee into the opponent’s back

Pulling him off his base, defender puts his opponent on his knee

Defender strikes his opponent’s jaw and wrenches his neck

Defender strikes.

Defender claws the face and eyes.

Defender shuffles back to pull the table out from under his opponent while striking his clavicles.

Knee drop on attacker’s face.

Another example of maneuvering to where the opponent has no bracing angle and to his center-line is a Kenpo technique called “Circling Destruction”.

Defender slips and parries a left punch.

Stepping with his right foot into the attacker’s center-line (from rear), defender strikes and hooks the chin.

Sliding his left foot into a position giving him a good stance to work the center-line, defender strikes the attacker’s neck.

Defender scoop kicks the groin while checking the attacker’s upper body.

Using gravity as an ally, defender lands with an inward elbow to the attacker’s kidneys.

Still in the center-line and where the attacker has no bracing angle, defender grabs the ankles and bumps the waist with his shoulders to pull the attacker off his feet.

Defender delivers a kick to the groin.

The fighter can also use foot maneuvers to position himself in the opponent’s center-line where he has access to targets; here we show how this is done.

Kenpo technique called Broken Gift, against an unfriendly handshake in which the handshake is a pretext for an attack.

Defender uses his arm to hyper-extend the attacker’s elbow joint and to cancel or check his back-up weapon.

Defender strikes.

Defender moves into the attacker’s center-line and controls the head which controls the rest of the body.

Controlling the attacker’s dimensional zones and having access to his center-line, defender attacks.

In the Kenpo technique “Thrusting Salute”, the defending gains access to the opponent’s center-line by blocking the kick, which opens the center-line, and by stepping back at a 45 degree angle which puts him in a position to kick to the groin. The opponent’s center-line, after the kick is blocked, is at a 45 degree angle from the path of the defender’s kick.

Beginning of Kenpo technique “Thrusting Salute”

As attacker kicks, defender blocks.

Defender kicks attacker in the groin.

This concludes our examination of Martial Arts Geometry. As you can see knowledge of angles is instructive for understanding proper position and execution of technique in martial arts.