While I must say I am very wary of any 'New Age' associations with 'sacred geometry' I am fascinated with the medieval, and ultimately platonic, ideas regarding the subject.
I think that anyone who wants to give the idea of 'sacred geometry' a serious consideration needs to look at it in a historical perspective. We need to not look at a lot of the modern ideas, which all to often fall into the category of pseudo science, among other complaints I might have to make against them. Instead, we need to study the sources of the great philosophers who shaped the western world.
Instead of getting your knowledge from youtube, I would highly recommend a serious study of the works of Plato, Augustine of Hippo, Johannes Kepler, and others from before the so called 'enlightenment' (one of the worst things to ever happen to western society, in my opinion)
http://www.skyscript.co.uk/kepler.html Now, all of this is actually quite unnecessary when we are actually designing buildings, that is unless you actually ascribe to the medieval notions of geometry, which I myself tend towards to some small degree.
My view is not that geometry brings any sort of heavenly blessing as the medieval man might have thought. Rather, it is that geometry gives you something that is very real and tangible, and that cannot be achieved through any other means. Geometric relations exist in harmony, which means they are naturally strong. Geometry divides a frame along lines that follow the patterns of the natural world.
On this topic, I have been developing what could be termed a 'simplified geometry' It is a system intended to be used by those who wish to design houses and other such, rather than Gothic Cathedrals. It is also designed with the intention of being performed at full scale, rather than on paper (although you might use paper to draft the design) because full scale is so much more accurate.
To this end, this system is much more line oriented rather than circle oriented. Although circles must be used to create any sort of geometry. The idea of this is that it is considerably harder to scribe giant circles than to connect points over a long distance. This system is designed so that it can be performed with merely a rope, stakes, and string.
