This post will discuss one way knowledge of trigonometry could be useful to a Kung Fu man.
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Trigonometry is the name given to the study of triangles. One of the main uses of Trigonometry is in checking the alignment of things. It is very easy to check the alignment of a triangle because a triangle only has three sides. A simple visual inspection is all that is necessary to determine if a triangle is aligned or not.
Please inspect the three different triangles in the following picture.
The triangle in the middle looks “right”, while the other two triangles look “wrong”. The middle triangle looks “right” because it is vertically oriented with equal length sides,
and it’s peak is directly in the center of it’s base.
The other two triangles look “wrong” because they have uneven length sides,
and their peaks are not on the center of the base of the triangle.
The study of Engineering uses Trigonometry to analyze and explain what is going on in a system of physical forces, which is one reason Trigonometry is useful to a Kung Fu man. Punching and kicking is about applying a force from your body to the body of your opponent. The force of your hand or the force of your foot is applied to the body of your opponent in a particular way that the science of engineering can scientifically explain.
One of the principles of Engineering is that the transfer of forces is more efficient when they travel a smooth path, which is a characteristic of systems that are properly aligned. That principle of Engineering is useful to a Kung Fu man because it implies that if the Kung Fu man wants to apply the maximum force possible to his opponent, his body needs to be aligned in such a way that it presents the least resistance to those forces. A Kung Fu man who was aware of some of the basic principles of Engineering and Trigonometry could use that knowledge to maximize the force they can deliver to an opponent.
The next series of pictures presents a simple example of efficient bodily alignment and transfer of forces.
The arms of a human being form a triangle with the torso as shown below.
According to the previous discussion of triangles, the arms in the picture above are “good” arms. Both arms look equal to be of equal length,
and they both meet in the center of the body.
According to Engineering principles, an individual whose arms formed a triangle like the one above would be able to efficiently deliver the majority of his power to the peak of the triangle.
The next picture shows the left hand sticking straight out and the right hand angled over to meet it so they form a triangle that has been outlined.
The triangle in the picture above looks “wrong”. The sides are unequal lengths,
and the peak of the triangle is to the left of the center of the base of the triangle.
That triangle configuration would be inefficient at delivering forces according to the principles of Engineering and according to plain common sense. Because the right arm has to reach all the way over to the left side of the body,
it cannot deliver as much force as it could if it was only reaching to the center of the body as it does with the “right” looking triangle.
In the next picture the right arm is sticking straight out from the shoulder with the left arm reaching over to create the peak of a triangle.
This triangle looks “wrong” for the same reasons the triangle whose peak was on the left side of the body looked “wrong”, The sides are of unequal length,
and the peak of the triangle is not centered on the base of the triangle.
This triangle configuration would be inefficient for the same reasons that the left biased triangle was inefficient. Because the left arm has to reach all the way over to the right side of the body,
it cannot deliver as much force as it could if it was only reaching to the center of the body as it does with the “right” looking triangle.
Some large number of readers will be of the opinion that knowledge of Trigonometry and Engineering would be a waste of time based on what is written in this blog post. Their position might be that anyone with common sense knows that if an arm has to reach unnaturally in any direction as the right and left arms do in the off center triangle pictures, that arm would not be able to efficiently deliver maximum force.
Those readers are most likely correct. The common sense of most people will tell them that an out of position limb cannot work in the most efficient way possible.
The point in knowing that Trigonometry and Engineering can prove that an out of alignment limb is less efficient at transferring forces is that the knowledge instills confidence. It is one of the characteristics of human beings that they gain mental confidence and certainty that cannot be attained in any other way, when they are able to explain in detail how something works.
Those people can transfer that confidence and certainty to other people, which is very important when teaching Kung Fu, or any subject for that matter. Instead of a pupil who asks why a particular Kung Fu move is done in a particular way being told “That is the way it has been done for thousands of years”, the individual who understands how Trigonometry and Engineering can be applied to the practice of Kung Fu, can explain to the pupil exactly, with total confidence, why a particular move is performed the way that it is.