Appreciating Mathematical Beauty Volume II
Matthew, super intruiging article you are a Grand Canyon of knowledge and interests. I do cad and drafting, (talk to me) and I want to live in that little space. If my house was closer to paid off, I would love to tear it down and make 2 of these on my lot, so the rest of it could be food. Living in these 100 year old hard to heat and cool houses is not easy and makes little sense when we need to grow our own food. Best
"Tiny homes", a.k.a. kennels. When Charles Schwab, Emmanuel Macron, Justin Trudeau, Barak Obama, Bill Gates, and Al Gore all move into one, I may start thinking about it.
Looks inspired by the huts built by people everywhere for the last 30 000 years, give or take a couple of milennia depending on location. Yurt, straw and mud hut, igloo, you name it. Dome means home.
As they say, if our ancestors had been studid, we wouldn't be at all.
Looks like a great off the grid away from intruding governments option.
Have you read about rohtak domes? Built by skilled craftsman without any steel or formwork. What I find fascinating is that these rohtak dome builders probably don't think in terms of math geometry, but yet they can still build such beautiful dome like roof structures. It's like they understand geometry but not in terms of math but more in terms of intuition and feel. https://www.youtube.com/watch?v=z7K99RUlfVk
As something of a master builder, I find the math a bit mystifying, but with the proper specs I could probably build such a thing. It would certainly be more elegant and possibly long lasting than modern buildings, which are basically energy sinks. It is hard to imagine raising a family in such a thing, insofar as to scale it for that it would be considerably more expensive and challenging to build. Not to mention American expectations. But for a reduced energy per capita future? Perhaps.
These are cool! I can see them used on a family compound or just a small footprint! Love how they mimic nature!
Love the construction concept for many reasons. Clearly some advantages. The shell and vault are naturally elegant solutions. This concept offers some real promise. However like so many other home concepts, the completion of an actual civilized home is vastly over simplified and its expense understated wildly. As for the price? Is a 600 sq ft structure for $10K really an advantage? The interior walls are part of the air crete fabric? I'll be paying attention to this. Realizing the powers that be don't want us developing equity the tiny home movement suits their 2030 goals perfectly. 3D printing homes are not ready for prime time yet either.
In the first video he mentions "air-crete" which is cement with foam instead of sand/gravel aggregate. It is another very interesting concept but like he says it's a lot more work. The results are still impressive and much better on safety, thermal & acoustic properties than wood frame architecture.
The hemp building folks have a month long class happening just down the road from me. I stopped by the other day and am really wishing I had signed up for the course.
The last image made me think of this book of Gaudi, the Guell Pavillions horse stables, huge arches. http://www.portalgaudi.cat/en/buildings/els-pavellons-de-la-finca-guell/
The math is WAY beyond me but it's intriguing to know some people actually use numbers to solve physical problems.
I own a copy of Richard P. Stanley's book on Catalan numbers. He lists 214 combinatorial interpretations of Catalan numbers (inviting readers to become experts by finding all the 214 * 213 = 45582 bijections)...
At some point (in 2004, my God) I was interested in the generalization from squares to rectangles (learning from Richard K. Guy's papers): http://www.meyer-idstein.de/article_walks.pdf
I've been looking at the idea of tiny homes for a while. There's definitely got to be something worthwhile about them.
I was at the same event in January, so I had the pleasure of being astounded by Grant and Gustavo's engineering and company. I didn't think I could be more amazed by the beauty and genius of this project until I got the link to this blog! Bookmarked it so I can read it many times again.
I think calling vaults, arches, and domes, triangles is an oversimplification from a structural engineering or architecture perspective.
You might try looking into catenary curves. This is the curve formed by a hanging cord or string under uniform gravity load. The loads are almost purely tensile along the length of the cord.
Arches are the inversion of this. A perfectly inverted catenary curve results in (mostly) compressive forces along the curve.
History shows us many different forms of compression arches (mostly not strictly catenary curves) and not purely efficient in terms of all compressive forces, but the principle is the same. This accounts for the final placement of the ‘keystone’ at the pinnacle of arches, which closes the circuit on the loads.