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Home > Columns > Ross Robertson > June, 2005 - Ikkyo, Nikyo, and Sankyo as Geometric Principles
by Ross Robertson

Ikkyo, Nikyo, and Sankyo as Geometric Principles by Ross Robertson

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It is self-evident that the names we use for our aikido movement forms are not rigorous or systematic in any way. Some names are poetic, as with "tenchinage" (Heaven and Earth Throw). Some are descriptive, as with "kotegaeshi" (Forearm Twist). Some names refer to the morphological form, for example "jujinage" (Figure Ten Throw). Still others may refer to a simple direction of progression, as with "zenponage" (Forward Throw).

And then there is the numeric sequence of ikkyo, nikyo, sankyo, and so on (also called ikkajo, nikajo, sankajo... in some systems). These translate roughly as "First Teaching, Second Teaching, Third Teaching..." But what are the principles behind these teachings, exactly? Why these forms, in this sequence?

There is not, to my knowledge, a clear historical explanation as to how these forms acquired these designations. They all have in common that they refer to methods of manipulating the arm, or of a set of postures of the arm. But kotegaeshi and shihonage (Four Direction Throw) also suggest arm postures... why are they not similarly numbered? Some have suggested that the numbers refer to a possible sequence of execution, that is, nikyo may follow naturally from ikkyo, sankyo from nikyo. I have also heard the suggestion that the numbers refer to how many joints are being affected. None of these explanations seem particularly compelling.

The anatomical form of ikkyo is generally pronation of the entire arm. The wrist and elbow may or may not be flexed. Nikyo is typically pronation of the forearm, supination of the upper arm, and flexion of the wrist and elbow. Sankyo is mainly pronation of the forearm, usually manipulated indirectly via the hand and wrist. Again, there does not seem to be a logical progression to this ordered sequence.

This being the case, I would like to propose a new way of looking at these forms and why we might justify arranging them in this sequence. I specifically am not claiming any insights as to the historical reasons. Rather, this is an a posterori explanation which I find useful in communicating these teachings.

I propose that ikkyo, nikyo, and sankyo may be viewed not only as anatomical forms, but as the geometric principles of the Line, the Curve, and the Spiral.


Dr. Stephen McAdam, Chief Instructor of the University of Texas Aikido Club, observed that all variations of of ikkyo serve to accomplish one goal: to move the shoulder forward sufficiently such that it is no longer supported by the hips. Once the system has been moved beyond its support structures, a collapse is inevitable. This understanding is primary, and underlies all other attack and defense forms.

We see that gravity implies a straight line along which things must be arranged if they are to stand. This same line is the vector of a fall, where no support is present (and no other forces are in effect, such as forward momentum).

We could, if we wished, extend the Principle of the Line in other ways. For example, when an attacker has the intent to pursue a target, a straight line is established between the aggressor and their goal (regardless of which path they ultimately take to reach the goal). Defenders who recognize this line can then act upon it, before tactile contact has even been made.

So, the axis of attraction may be viewed as the first principle. Understanding this forms the basis for successive principles.

In its simplest variation, ikkyo the defense form is expressed as a straight arm leading the shoulder off its support and then straight down. It is not necessary to twist (pronate) the arm for this to be successful.

Ikkyo is idealized as aikido in a single dimension.


Nikyo, then, is the Principle of the Curve. The first perturbation of a line will create a curve, or a wave pattern. If the principle of ikkyo is applied, but obstacles or interferences are introduced along the way, the straight line is deviated. Water dripping down a window pane or a leaf falling through air illustrate this dynamic.

In an attack dynamic, the line of intent may similarly be manipulated favorably for the defender. The defender is an "attractive" force operating on the attacker (though of course it is really the attacker's motive and follow-through that are the true forces in play, the effect is much the same). So, if the target moves after an attack has been launched, course corrections must be made which result in deviations from the original path of intent. This can serve the purpose of destabilizing much of the attack, and new trajectories may be introduced. Again, all of this may take place before tactile contact.

As a defense form, nikkyo is made manifest in the arm. The straight arm is now bent into curves, and the sine wave is almost visible. Furthermore, nikyo is more easily applied when moving the arm in a falling leaf pattern, than when cutting straight down.

Nikyo is aikido expressed in two dimensions.


Sankyo is the Principle of the Spiral. More specifically, it is the type of spiral known as the Helix. The line and the curve now have a rotational component added around the original axis.

Many aikido dynamics have a whirlpool quality to them. The attacker follows the line of Ikkyo attraction toward a goal. The target is in motion, and so a curvature in space is in effect created. Like two bodies orbiting around a common center, an imaginary gravity well results. When the system is sufficiently destabilized, one of the bodies will succumb to actual gravity. In this case, a downward spiral describes the trajectory.

Sankyo the defense form may be applied as an upward spiral or a downward spiral, or both in succession. Pronation or forward twisting about the axis of the forearm is characteristic.

Sankyo is aikido in three dimensions.

Yonkyo and Beyond

I generally do not try to force yonkyo, gokyo, and the rest into this particular scheme. There may be some benefit in the exercise, however. We could, for example, suggest that yonkyo is the principle of radial motion, or kaiten. But this does not fit so nicely with our progression through one, two, and three dimensions (and to suggest that yonkyo is somehow related to the fourth dimension, time, is to really strain the model).

Mostly I present this paradigm as a deliberate artificial contrivance. I am told that when students asked O-Sensei what to call the various forms, he said "I don't care, call them what you like!" So any "deep" significance we find in the names is rightly what we bring to them.

What we can say for certain is that aikido is expressed in Matter, Energy, Space, Time, and Mind. Two or more bodies interacting in this great field of being will manifest certain forms, both transitory and eternal. It's natural that we see repeating patterns and give them names. Some believe that aikido is what happens when we do these patterns, while others believe that these forms are what arise inevitably and organically when we participate in aikido.

Either way, a deeper appreciation is available when we look at what lies behind the names, and what lies at the root of the forms so named.

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