# Geometry

### Forces and geometry in structure

All structures experience forces at all times. We can’t see a force, but we can deduce its existence by observing its effect. Sometimes the effects of those forces are not apparent until time has passed. That is why it is crucial to design a structure carefully, build it skillfully, maintain it periodically, and monitor it diligently throughout its useful life.

Understanding the relationship of the forces, geometry and structure helps us to maintain a better body posture for different actions, correct some parts which may hurt your body posture, and take more centripetal force. We all know body structure involves health in normal life: like standing and bending posture; and body structure is crucial for all sports: weight lifting, baseball pitching, tennis serve……

For golf swing, to set up powerful body posture is the foundation of the whole swing, because the golf swing consists of the coherent actions of the whole symmetrical body structure which is built by skeletons and muscles.

### Internal and External Forces

Structures should be designed to withstand all kinds of forces that can act on them. Some of those forces come from outside the structure — these are external forces. An external force acts on an object from outside the object. Gravity is an external force that acts on all structures all the time. Gravity is the natural force of attraction between two objects. Gravity constantly pulls objects or structures toward Earth’s centre. As well, your body weight always acts on the earth if you are standing on the ground. For example, a bridge has to support the cars and trucks, as well as the force of wind.

Other forces are caused by one part of the structure acting on other parts of the structure. This type of force is called an internal force. Internal forces are classified as compression, tension, shear, or torsion. For example: If our body’s weight is on the feet, the weight of the upper body is on hips — this is compression force; another one: the torsion force is in stretched spring.

### Solid Geometry

Geometry is one branch of mathematics. It is concerned with properties of space that are related with distance, shape, size, and relative position of figures. There are many concepts we used in our normal life like line, plane, angle, curve, surface and  dimension. For example in golf swing, we alway talk about the swing plane — that means our club’s moving trajectory is in one plane during the whole swing, but in fact nobody’s swing is in one flat plane.

In geometry, the Pythagorean theorem is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides. This theorem can be written as an equation relating the lengths of the sides a, b and c, often called the “Pythagorean equation”: where c represents the length of the hypotenuse and a and b the lengths of the triangle’s other two sides. The theorem, whose history is the subject of much debate, is named for the ancient Greek thinker Pythagoras. The theorem has been given numerous proofs – possibly the most for any mathematical theorem.

The Pythagorean theorem is applied in many scientific areas, like mechanics & civil engineering. For example, for designing a crane machine, we have to calculate the forces in the pulling ropes and truss if hanging up  5000lbs of weight. It is the same for golf swing: we can get the pulling force along the arms & club direction if we know the vertical force and the horizontal force.  Then we can calculate the club head speed according to Newton’s second law.

Geometry has many applications in architecture. In fact, it has been said that geometry lies at the core of structural design.  Even though our body structure is not exactly the shape of lines and angles like the building and the bridge, the geometry concepts of the symmetry, similarity and the topology are still applied on the research of the body posture and functions.

### Forces and Geometry in body Structure

When we’re looking at how things work or move, we try to identify the force that’s responsible. So when a flying ball falls to the ground, we say “Aha! That’s the force of gravity.” But it’s very rare to find only one force acting on something. Most of the time, there are several different forces working at once, all pulling or pushing with different strength, often in completely different directions. The effects of all these forces add together or subtract from one another to produce a resultant force.

How to calculate the resultant force? The simple way is to  utilize the basic principles of geometry.

Sometimes all the forces are exactly in balance—their effects cancel one another out. If you look at a giant suspension bridge, it’s not going anywhere or changing its shape, so you might think there are no forces acting on it. Wrong! There’s the weight of all the cars driving across it pulling downward, plus its own weight. So why doesn’t the bridge tumble into the river? The force of gravity pulling down on the bridge is exactly balanced by tension (pulling forces) in the suspension cables tugging it back up again. Because all the forces on a bridge are equal, the bridge itself goes nowhere—so it’s safe for the cars to drive across.

The bridge design will consider the worst condition — the heaviest trucks at the center of the bridge.That means all parts of the bridge work together to take most forces without any damage — this is like the moment of impact zone for golf swing.  This is the project of spaghetti bridge competition.

The other example is the load force hanging on the top of the crane machine: we can figure out the force applied on the boom if we know the weight of the load by geometry.

Athletes’ bodies experience these forces in many ways. The forces experienced by playing different actions on different sports, because of their own movements or because of different equipment they use.

During golf swing, there are many internal forces created: the torsion force is created on the torso during backswing; the compression force is created on the knees and hips as the lower body straightens up during the impact zone.

For golf swing it is more complicated because the centripetal force at the impact is not vertical with ground like the load force on the crane machine.  So it needs solid geometry to figure out the three forces along three directions ( show in two 2-D graphs).

1. The vertical pulling force: the lower body’s jump and erection at hips just like the action of deadlift , we can see these actions from the swing of Tiger Woods and Rory Mcilroy.
2. The horizontal pulling force:  the square feet position and controlling heels down & behind can make the body at the best position to pull arms horizontally; we can see these positions from the swing of Sergio Garcia and Kenny Perry.
3. The lateral pulling force: The lateral movement of the pelvic is a basic action of creating lateral pulling force. Besides, if the torso’s turning is leading the shoulder and  the arms just following, the lag position along the lateral direction will happen naturally at the impact .

### Creating bigger forces with actions of body structure

Human body is a perfect structure and human movement is actually very complex. Movement is a change in place, position, or posture in relation to the environment. Movement happens only when different body systems, such as the skeletal system, cardiovascular system, neuromuscular system, and the muscular system, work together to create the force. (By physics, any item can not move without a force acting on it. )

Thanks to human ingenuity. With clever tools help, we can make our arms and legs move much bigger and heavier weights. Simple tools include levers, such as wrenches. They work by allowing your body to produce more force than it can make alone.

So if you use a wrench to turn a rusty nut, you’re using the power of a lever to magnify a force: the longer the lever, the more the force at the center is magnified and applying less force at the edge. By the same way we can create more force ( and high speed) at the club head by body’s action working together with the club.

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