I was trying in Mexico to make a living, making a living and at the same time having a good time, having a good time building things. I read practically everything that had been written about shell structures. People used to say that I didn't know how to calculate but all those things have been calculated by me personally. Anyway, I read everything but, in order to be able to build the things, I had to compete with the cheapest types of construction so my main interest was the economy, in the easy way to build. I will show you some of the things I did. I tried all kinds of shapes.
But then I remember, having seen a similar figure to this in a French magazine, and this is a hyperbolic parabola. And I was really fascinated with the possibilities of this shape. You can see here when you have these three axes, these angle Omega doesn't need to be ninety degrees. This can be any angle. So you can play with that. When it is ninety degrees, this parabola going out is the same as this other parabola going down. But if you move this angle, the acute angle produces a' very flat parabola and the other a very curved one. So with this you can manipulate the thing and make a lot of combinations. This is probably my contribution to the analysis of this. The important one was to take an axis for the equations, these three axes here, instead of the usual ones which are the real axis of the surface. It is one of the second degree surfaces and has this incredible property to be a dome which has straight lines. So you can use straight pieces of wood to make the form and it becomes very economical. Also it has the simplest equations, equations of second degree. Therefore you can integrate the equations of equilibrium which you cannot do with any other surface. It is really a miracle. You have some sort of automatic beauty, a perfect thing for an architect.
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