**ORIGINAL QUERY:****Date: Monday, 13 January 2003 11:27:42 +0100****From:
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I have noticed, possibly largely from those more mathematically inclined, the tendency to limit one's inquiry to the question of "how". What Professor Peter Schneider of University of Colorado meant by distinguishing "reasoning" from "problem-solving" during the Nexus 2002 round-table, the point Dr. Alberto Perez-Gomez has made in years in his work in theory, and what Dr. Robert Tavernor pointed out by "quality" as distinguished from "quantity" all point to yet another kind of inquiry, that is, the question of "why". **"Why is mathematics used in architecture?"** or "Why is this particular mathematics appear in this piece of architecture?", as opposed to "How mathematics is used in architecture?", provides another important aspect of the subject. Expanding on the questions regarding of "why" will, I think, allow us to go beyond the surface of form and structure making, and toward the understanding of the ideas and the ideals that have supported architecture.

## Comments

This reminds me of a question that came up at one of my conferences here. I was talking about form and space and someone asked me what is space? I said space is space. Then I said that if you asked me "why is space?", that is a good question. For me, sculpture is form, space, and light. Space is where the light goes! That was my answer to this why question.

But if you consider the rest of mathematics, why is it used in architecture? Let us try to give two examples of possible answers: 1) because there is a

"Generative Theory of Shape"(see the book with that title by Michael Leyton www.amazon.com/.../thenexusnetworkj), developed using the most abstract concept of symmetry groups, which is used as an intelligent means of describing the entire complex structure of a building; 2) because if you consider the fascination that numbers have in architectonic design, we may conclude that we have an innate proportion science that obliges us to measure dimensions comparing one with another.The fascination starts with the integer numbers as indicated by the egiptian "sacred triangle", a right-angled triangle with the two cathetus and the hypotenuse in the proportion 3, 4 and 5. But quickly goes from magic triangles and perfect squares to the square root of 2 rectangle and to the golden rectangle, where the numbers considered are irrationals and demand rational approximations to be applied in the real construction (seeby Vera W. de Spinadel). Among these two examples there is a myriad of applications of mathematical subjects, going from number theory to fractals and frontiers of chaos, to architecture.From the Golden Mean to ChaosIts the way structures are

not wobbly neither bad

its geometry , shapes ,

sizes , lines , curves ,

That takes over our mind.

2