Friday, 24 August 2007

A special pentagonal figure, after David Woods in GENESET - consider this Part One

This is the penta-shape discovered by David Woods in the Rennes Le Chateau area, with a controlling circle of 15 divisions, of 24 degrees each, or 4 clock-face-minutes(cfms). I only have GENESET of his works, and this figure is presented there but with subtle alterations which do not concern us here. This is a symmetrical firgure with all angles equal to 36 degrees.
This little session is vital for the next stage, describing it in the landscape of Lothian and its implications for the development of the geometry in total. It was described first by W.S.Buehler, and I did some follow up work on it with interesting developments. A special point of intersection was found which allowed a tightening up of the original pent system as it was found that it and this interlinked.

The hexagon in the circle.

The penta and the hexagon, with common horizontal chord.

The perfect pentagon is found by extending the short chord, and drawing a horizontal at 42degrees, or 7 minutes on a clock-face. I believe this to be correct but shouldn't get upset if it was slightly off. My geometry ain't fool-proof, and I am the living proof!

The centre of the pentagon is found by drawing in of axes.

An interesting construct on the pentagon gives a golden ratio rhombus, using a half penta side as unit. The golden ratio rhombus is a figure I first heard about from the postings of W.S.Buehler, who I have mentioned previously, and shall be covering common geometric topics.
It has axes of phi(FC&CG), and phi-squared(HC&CI), with the half penta-side as unit, equal to BC&CO.
This post explains the geometry that is based on Bill's centering this figure on Borthwick church. To follow.

Next, I will describe this system as it is in the landscape of Lothian and the Borders. It gets very complex, and this and the original penta system need to be understood seperately to keep track!

No comments: