From the blog Just Thomism :I know it's kind of obvious, but wasp cells sure look like an attempted approximation of a Euclidean ideal. And bird nests sure look structurally circular to me. For those who deny nature acts for an end, I can see the argument being made, but for a Thomist to make it, or at the very least to not even see it when it's plain as day?
. . . even those animals in nature that make things do not seem to care much for trying to approximate Euclidean ideals.
The Curves of Life covers the subject from the angle of the pentagon whose ratio is the golden mean and logarithmic proportion. A naturally unstable proportion on which all material life is grounded.
But leaving insects and birds aside, we're also "animals in nature that make things", and human motion and space is Euclidean motion and space.
I have never designed any structure which wasn't pure attempted approximation of Euclidean space. And I design that way because that space is what is most comfortable for people to live in.
We're most comfortable walking on flat surfaces inside parallel planes. Stairs are a multiplicity of planes. And when ceiling planes are even a few inches off parallel to the floor plane the disconcerting effect can be enough to cause us to stumble or grab for a support.
Our basilica form churches are a multiplicity of euclidean planes and lines moving our bodied and eyes. They move us similarly to how sacraments move us by visible signs to see what is not visible. For instance, the aedicule, i.e. the tabernacle on the back alter, in the sanctuary is first seen and experienced as a function of parallel lines of sight from a one point perspective focus where columns, window, pews, tiles, wall and roof lines all converge.
Francis Ching's standard to the art book Architecture : Form Space Order is nothing but manipulation of Euclidean space in the service of human life.
It's not only that our living in euclidean spance forms our cultural memory, but that we naturally form euclidean space because it is natural to us.
We order our homes in gradients of intimacy and arrange our furniture in euclidean patterns. We set our dishes, arrange our desks, fold our clothes etc. similarly. It is how we live.
Our books and bookshelves they sit upon, pans, plates, pottery, paintings, knitted or woven cloth, and virtually all aspects of our lives are Euclidean.
In fact Euclidean space is so much a part of our lives that we have difficulty scaling that which is not Euclidean. A man even with experience cannot typically judge the height of a gradual slope in a field. And even less so objects found in the wilderness unless he is close enough to judge it by his own scale.
When rough nature is used as a motif such as leaves and branches, they are typically abstracted into a Euclidean pattern. Art Nouveau, which far more literal than typical, attempts to seamlessly join Euclidean space to the wild exigencies of flora. The attempt is not wild nature, but tamed nature at human euclidean scale.
Even when the plasticity of nature is morphed seamlessly as the D.L. James house is, the transition is into Euclidean space.
A very clear example of seamless morphing from nature to Euclidean space is the transition from the existing sandstone walls to the man made sandstone walls at Fallingwater. Fallingwater exemplifies Euclidean space while wonderfully transitioning out the existing natural formations.
Fallingwater's horizontal concrete planes structurally held in place by sandstone walls transitioned seamlessly out of the earth signify its intended design of letting us commune with nature, but on our own Euclidean terms. Fallingwater's clear purpose lets us in turn see how we both fit in with the plasticity of wild nature and how we in turn abstract nature to fit our Euclidean scale.
We are part of nature, but separate from it. Our appetites naturally seek Euclidean space. Euclidean space is human scale both physically and immaterially. It's the form which shapes our physical world, and its the form we consider most perfect as platonically abstracted from nature. Human Scale is Euclidean.