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The mathematical secrets of Barcelona's Sagrada Familia

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Re: The mathematical secrets of Barcelona's Sagrada Familia

#21

Post by hammock »

lo_zamoyski wrote: post #15
blitzar wrote: post #8

Earlier quoted context omitted.

It seems somewhat important to me to know if something was done because it looked pretty, was random or because there was an intent to reflect maths, science, planetary alignment etc.

Whatever one might say about method, epistemically speaking, the aesthetic is prior to the mathematical. The mathematical is found in the analysis of the beautiful.

Truth, beauty and goodness are known as the “transcendentals” for a reason. They are linked. They don’t come one after the other.

Re: The mathematical secrets of Barcelona's Sagrada Familia

#22

Post by MengerSponge »

hammock wrote: post #20
jerkstate wrote: post #6

I visited this and several other Gaudi buildings about 15 years ago in Barcelona, and many of them are truly breathtaking, or at least dramatically original and unique. I went to the Gaudi museum as well and found it fascinating that the architect himself was not a professional mathematician - he did not use hyperbolic cosine to calculate the dimensions of the catenary curves, he traced the outline of hanging chains.…

Designing in an era where calculus exists, using chains and weights strikes me as gratuitous or onanistic. The Ancient Greeks and Romans also used the same or similar empirical geometric methods to generate ellipses, parabolas, and hyperbolas in their architecture. The difference is, they were still 1000-2000 years away from having formalized calculus.

Calculus exists, but analytic solutions generally don't. Gaudi's chains and weights serve as an incredibly elegant mechanical computer that were only surpassed in the last few decades by CAD. Designers used mechanical splines until the advent of CAD in the 70's/80's.

Re: The mathematical secrets of Barcelona's Sagrada Familia

#23

Post by RetroTechie »

Wow that first photo almost looks like a sci-fi contraption!

(insert suggestions here)

And wonderful such a building that embodies in stone all kinds of mathematical relations, religious references etc. Let's hope it'll stand at least as long as it took to build. :)

Re: The mathematical secrets of Barcelona's Sagrada Familia

#24

Post by RetroTechie »

jerkstate wrote: post #6

I visited this and several other Gaudi buildings about 15 years ago in Barcelona, and many of them are truly breathtaking, or at least dramatically original and unique. I went to the Gaudi museum as well and found it fascinating that the architect himself was not a professional mathematician - he did not use hyperbolic cosine to calculate the dimensions of the catenary curves, he traced the outline of hanging chains.…

> he did not use hyperbolic cosine to calculate the dimensions of the catenary curves, he traced the outline of hanging chains.

In a way that's like doing the math, but using real-world physics as your 'calculator'. No doubt Gaudi was a smart dude.

Re: The mathematical secrets of Barcelona's Sagrada Familia

#26

Post by embedding-shape »

RetroTechie wrote: post #24
jerkstate wrote: post #6

I visited this and several other Gaudi buildings about 15 years ago in Barcelona, and many of them are truly breathtaking, or at least dramatically original and unique. I went to the Gaudi museum as well and found it fascinating that the architect himself was not a professional mathematician - he did not use hyperbolic cosine to calculate the dimensions of the catenary curves, he traced the outline of hanging chains.…

> he did not use hyperbolic cosine to calculate the dimensions of the catenary curves, he traced the outline of hanging chains. In a way that's like doing the math, but using real-world physics as your 'calculator'. No doubt Gaudi was a smart dude.

> No doubt Gaudi was a smart dude.

He also died crossing the tram track, presumable not looking both ways before crossing. To be clear, I've also nearly been hit by the Barcelona tram too, so I don't blame him, but "smart" is always relative.

Re: The mathematical secrets of Barcelona's Sagrada Familia

#27

Post by srean »

hammock wrote: post #20
jerkstate wrote: post #6

I visited this and several other Gaudi buildings about 15 years ago in Barcelona, and many of them are truly breathtaking, or at least dramatically original and unique. I went to the Gaudi museum as well and found it fascinating that the architect himself was not a professional mathematician - he did not use hyperbolic cosine to calculate the dimensions of the catenary curves, he traced the outline of hanging chains.…

Designing in an era where calculus exists, using chains and weights strikes me as gratuitous or onanistic. The Ancient Greeks and Romans also used the same or similar empirical geometric methods to generate ellipses, parabolas, and hyperbolas in their architecture. The difference is, they were still 1000-2000 years away from having formalized calculus.

He is solving differential equations but with an analogue computer.

Doing it faster and with less doubts over fidelity and existence of a solution too.

Solving partial differential equations numerically and vetting the solution so obtained is not a trivial matters. Many things can go wrong in non obvious ways.

Analogue computers are a worthy alternative when applicable.

Re: The mathematical secrets of Barcelona's Sagrada Familia

#28

Post by gopher_space »

RetroTechie wrote: post #23

Wow that first photo almost looks like a sci-fi contraption! (insert suggestions here) And wonderful such a building that embodies in stone all kinds of mathematical relations, religious references etc. Let's hope it'll stand at least as long as it took to build. :)

Reminds me of diatom pictures. The soft edges in nature comfort me.

Re: The mathematical secrets of Barcelona's Sagrada Familia

#29

Post by imp0cat »

embedding-shape wrote: post #26
RetroTechie wrote: post #24

Earlier quoted context omitted.

> he did not use hyperbolic cosine to calculate the dimensions of the catenary curves, he traced the outline of hanging chains. In a way that's like doing the math, but using real-world physics as your 'calculator'. No doubt Gaudi was a smart dude.

> No doubt Gaudi was a smart dude. He also died crossing the tram track, presumable not looking both ways before crossing. To be clear, I've also nearly been hit by the Barcelona tram too, so I don't blame him, but "smart" is always relative.

He was smart, but not street smart.

Also, I do belive the story was that he had the appearance of a homeless man and thus received sub-standard care. When someone finally recognized him, it was already too late.

Re: The mathematical secrets of Barcelona's Sagrada Familia

#30

Post by anthk »

hammock wrote: post #20
jerkstate wrote: post #6

I visited this and several other Gaudi buildings about 15 years ago in Barcelona, and many of them are truly breathtaking, or at least dramatically original and unique. I went to the Gaudi museum as well and found it fascinating that the architect himself was not a professional mathematician - he did not use hyperbolic cosine to calculate the dimensions of the catenary curves, he traced the outline of hanging chains.…

Designing in an era where calculus exists, using chains and weights strikes me as gratuitous or onanistic. The Ancient Greeks and Romans also used the same or similar empirical geometric methods to generate ellipses, parabolas, and hyperbolas in their architecture. The difference is, they were still 1000-2000 years away from having formalized calculus.

Ahem https://en.wikipedia.org/wiki/Archimedes_Palimpsest
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