Thank you Chris.
The article was most enlightening.
The Kosho Ryu Kenpo monks appear to make use of geometry and numbers as well. Much of their "folding" techniques and throwing techniques are derived from their use.
Have you compared these two experiences at all? I suspect it would be an interesting endeavor.
Since you mention geometry in relationship to Kosho Ryu Kenpo; there were older martial arts that used geometry: Probably the most famous martial artist of his time was Gerardus Thibault. He was a true master of the art of fencing in the 17th century and could not be beaten by anyone. He was wellknown in Europe and visited the important courts to show his art. He became fencingmaster of the city of Amsterdam (later also in other cities) and taught according to his "mathematical method based on the mystical circle". He wrote a book about his art, that was published after his death in 1628. To this day it is the largest book on martial arts ever published. Beautiful prints made by several wellknown artists, printed by Elzevier. One of the prints is clearly inspired by the vitruvian man by Leonardo da Vinci. It shows the relationship between man, sword and the geometric figures of circle, square and triangle. The more technical prints show methods of avoiding the sword of the other, while at the same moment being able to hit the other. There is a lot in the book that reminds of Aikido. The basic stance looks like hanmi. Some of the moves are similar.
Interesting detail; he speaks of the "sentiment d'espee", the feeling of the sword - meaning that the sword sort of has a will of its own, it wants to move without interruption towards and in the opponent.
According to some historians Shakespeare refers to Thibaut in his Romeo and Juliet (act III, scene 1) when Mercutio speaks about Thybalt; "a villain, that fights by the book of arithmetic".
To get back to the start of your thread, Thibault was famous in his time. It was a time of war and fencing was not a sport. His method really worked and he had a large number of students. Despite this and despite the publication and world-wide spread of his book his teachings were lost over time. The paradigm shifted as well. While Thibault used a circle to engage any opponent, in modern fencing as a sport we prefer a line. Many of the things Thibault taught as essential to his method are no longer even allowed in modern fencing.
And in fact, the modern fencer does no longer even have the ability to understand Thibault's method, his knowledge has been lost, his name almost forgotten, his grave unknown.
(which by the way reminds me of some of the statements made by Dan Harden on other threads).