In teaching Tai Chi to older adults it is best to combine teaching the internal principles along with the form, which means you are basically reteaching people how to walk and move. After warm-ups, I have everyone pick a linoleum tile and place the feet heel to heel in a right angle on a corner on a tile. We stand like that for a moment and I have them take a step forward with their right foot, and about 4" over with their left foot, leaving their right on the square but turned at a 45 degree angle. As you are reading this you might be trying to visualize a bunch of older adults assembled in rows standing on a grid-like pattern.
I have been teaching Tai Chi to older adults since 2001 and it took me awhile to catch on how to difficult it is for older adults to get into a bow stance and especially when turning 180 degrees with clear aligned movement. After so many students having difficulty I started using the tiles on the floor along with a cardinal directional sign on each of the four walls. As I started to create these methods of teaching people to do Tai Chi I realized that there was a geometric logic to how we align ourselves to the earth. When looking at the illustration (above) you can see one possible way sacred geometry developed. If you stay in one place facing north and turn around in a complete circle it will be 360 degrees. Then going back to basic geometry you can divide that up an infinite amount of ways but typically we divide it up first in quarters and then in eighths, hence the origin of the bagua (Pictured below).
That inspired me to seek out geometric relationships in Tai Chi, moreover, when I was exploring Tai Chi I became aware of Feng Shui and their usage of the bagua. I also knew that the original 13 postures of Tai Chi are patterned off of the very same bagua symbol; eight main postures and five secondary ones (pictured below). These connections made me appreciate Tai Chi even more because the whole Taoist system worked in concordance with one another. There was not too many contradictions, although there are smaller discrepancies with certain assignments of what fits into which area, for instance, an animal and an emotion and actually everything in existence is prescribed to each cardinal direction. 
As the caption states in the 13 postures of Tai Chi, there are 8 energies and directions, which are also added to the elemental directions of the 5 elements, north, south, east, west, and center.
The early Chinese people created a compass (pictured below) that linked up the waxing and the waning of the moon with the 8 directions and this was used to predict floods and then more was added on to it. The I Ching or Book of Transformation was also created from there. The early Chinese people figured that significant events occur during the seasonal changes, i.e. floods, winter, harvest season etc. The idea is that by understanding the natural forces one could prepare ahead of time and avoid more acute emergencies. 
Other cultures have discovered many of the same ideas; stonehenge follows the same circular formations as does the Kabbalah with its numerical structure. The phases of the moon are based in reality but the socially constructed aspect of attributing certain emotions, elements, animals to each phase is where there is not cross cultural corroboration. This doesn’t mean it is not worth studying. I view it more as an art form that deserves respect and consideration. An interesting fact is how deeply our psychology and physiology is tied to night and day. Circadian rhythms and seasonal patterns are strong determinants of hormonal secretions and
they play a major role in our psychological functioning as well of the well being of our vital organs.
As you can see there are many connections with codified symbols found in Taoism that connect the heavens to man and to the earth. Another example of this intense connection is the 64 hexagrams, 32 yin and 32 yang found in the I Ching, and their exact match with the 64 codons found in DNA.
“ —We defragged three I Ching representations of the genetic code while emphasizing Nirenberg's historical finding. The synthetic genetic code chromosomes obtained reflect the protective strategy of enzymes with a similar function, having both humans and mammals a biased G-C dominance of three H-bonds in the third nucleotide of their most used codons per amino acid, as seen in one chromosome of the i, M and M' genetic codes, while a two H-bond A-T dominance was found in their complementary chromosome, as seen in invertebrates and plants. The reverse engineering of chromosome I' into 2D rotating circles and squares was undertaken, yielding a 100% symmetrical 3D geometry which was coupled to a previously obtained genetic code tetrahedron in order to differentiate the start methionine from the methionine that is acting as a codifying non-start codon”
The depth of early Chinese people is astounding, even today this at least 4000 year old symbol still influences and explains phenomena in our lives. I think the reason why is that these early Taoist masters discovered a spiral network of energy vectors that determine all growth on this planet. They called these energy vectors “Chi” or “Qi.” Admittedly, the word Qi did not arrive until later years after the I Ching was created, nonetheless is it currently used in this manner to describe these energetic vectors and hence the 8 energies of the Tai Chi movement. So from a simple joint lock, to the structure of DNA to the Milky way solar system we are constrained by a spiral force that connects all life and all inanimate objects to the earth rotation and its evolution around the sun. Just to be clear, I am not a proponent of divination. I know this kind of thinking has led to over use to put it mildly. I am speaking from a physical science perspective. That said, this movement has an affect on us and it is hard to figure out just how much because there is no counterfactual ideal. We do not have another galaxy to measure its effect on the beings there. You may think I am starting to go off the deep end. There are people who I have run into who love sacred geometry but end up tying the origin of it to aliens. Believe me it gets even weirder with when the illuminati conspiracies start piling up.
As with many of the phenomena I write about, I am able to parse out the wheat from the chaff and where there is unknown I simply leave it at that. I don’t need to believe in aliens or a personal god either to substantiate the physical reality of certain things. I also don’t need to deny it all and be an atheist either.
Another thing that happened when I was teaching the 180 degree turns was I saw how the foot positions fit within a box grid and if you draw diagonal lines and add circles it can become a flower of life. The flower of life (pictured above)is something in many cultures together, even Leonardo Da Vinci drew this in his Codex. Of course explaining the relationship between Davinci, stonehenge, the Kabbalah, and the I Ching could be an endless exploration that is not suited to the purpose of this blog post. If you are interested there are hundreds of videos and books on this topic but be forewarned that you will be hearing some crazy theories.
Anyway back to Tai Chi
I have always wondered why all the Tai Chi forms don't sync up with the bagua (8 directions), wu xing (5 elements) (pictured below) and ultimately the I Ching. Fortunately, I found Tai Chi According to the I Ching by Stuart Alve Olson who brilliantly tackled my dilemma. Per usual for Olson, he breaks everything down and backs it up with the ancient texts to support his reasoning. I have been searching for a truly symmetrical form for years and thanks to Mr. Olson I finally have that..
Conclusion
One of the reason why I love Tai Chi is because there is this internal logic that starts really small like with a step and then expands outwards to encompass the whole universe, the Chinese call it the microcosm and the macrocosm. Is it scientifically sound? I am not sure but I think it is worth investigating. Moreover, humans love symmetry we seek it out whenever we can and I find discovering the underlying symmetry in Tai Chi increases my love of it and enhances my personal practice.
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