This theory is the result of scientific analyze of Budo-waza (reason why a waza/technique works), directions of energy (energy has a direction and is very mcuh connected to mind), Kyusho (weak points/ dangerous vital points on meridians of a human body) and physics.
1. Kamae / Fighting Stance If your Kamae is 90 degrees to your opponent, you have a quick chance to execute an attach, but you have also wide opening and you become a easy target. If your Kamae is 180 degrees to your opponent, you have minimum chance to execute attach and can use only front arm and leg, but you have also smallest opening. It is difficult for your opponent to attack.
180 d. narrow, 45 d. medium (easy to become 180 d. or 90 d.), 90 d. wide
If your Kamae is 45 d. to your opponent, you have both right and left side attacks. You can kick and punch from both side, have possibilities to execute all kind of Kogeki waza - attacking techniques. At the same time it is very difficult for opponent to guess what kind of attack and from which side it will come. Try to find out or guess what kind of attack he can/will do!! And do not show what you want to do. If you know the attack, you know how to stop. The key is how to see the future!!!!!
2. If you move straight ahead or back, you will get the collision with your opponent, or you will be constantly pressed backward. If you move 45d. forward you can easily attack, easily change direction and so on. If you move 45d. backward, especially to the JUN.side, you can stand side by side to your opponent, then it is very easy to defense or attack. If you want to move ahead or backward, you have to move zigzag (f.expl. 45d. to left then 45d. to right)
3. Push your opponent 45d. up, then you can push him back. If you throw a baseball directly up to sky, the ball will come back to you (fall upon you). Throw 45d. up, then it can reach far way. Throw parallel to the ground, like baseball pitcher does, it will not reach as far as by 45 d. way. This is the method how you can use the Physics law in Budo. Sumo people are using all the time. If you can combine with Spiral movement, then you can see the result. I do not need to tell you. Attacking angle for human body is 45d. up. see drawing.
4. Push opponents left shoulder 45d. up and simultaneously pull right shoulder down, then you can feel that opponet is losing his balance. Then you move circle, opponet falls down. This is the energymovement called spiral. see drawing.
Push 45d. + pull 45d. + circle movement = spiral and centripetal energy. World famous Small Circle Jujitsu created by Prof. Wally Jay is based on this Push and Pull system. I thank him a lot for teaching me his uniqe theory. He is the one who gave me an inspiration of understanding of Ki-energy movement and it's effect.
5. Millions of years ago, our ancestors came out of bush / jangle and started to go and run by only two legs. Apes and monkeys are using four legs to run. This made front legs (arms) free from supporting body weight, then finally we got arms and hands. Unfortunately we have been on this planet only around 4 million years. We are still under evolution. We are Erectus, but bone-structures are not developed yet, not good enough, that is why human have to suffer from the pain at the back of hips permanently. Also the wiring of out vital nerve systems are not perfect. When we are in 4 legs position like apes and other animals, are protected from the attack or impact from falling objects such as apple and orange. Even we, standing position, are protected against impact from up to down, diagonal up to down. But we are not strong against impact from 90d.. If the impact from 45d. down to up, we are almost hopeless. We are very vulnerable. Main Kyushos (dangerous points, very effective points for Budo-ka) are naked/ not covered and easily be attacked. Try to punch the Solar Plexus up to down with 45d. angle. Almost no effect! Try with the 90d. angle, it is OK, but sometimes strong stomach mussel protects the solar plexus well. Try the 45d. down to up angle, then you know what I am talking about.
These are little examples of the theory of 45 degree in Budo.