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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

#41
post #40

TFA does not quite explain the logic of this and somewhat suggests it as unique when it was the norm. If you are building a church, what better metric is there than the church you are building? There is no reason to measure, you can just subdivide with very basic tools. We want the entrance to be in the center, that is 1/2 church instead of 8.385 meters and that door is 1/6 church wide and 3/4 church tall. We want wi…

A lot of words but I agree with you with all my heart. Proportions best relate to the whole, not some “2 inches from the edge” or whatever arbitrary standard. What I would add also is the human scale . Along with the dimensions of the space you are filling, the scale of the humans using the cabinet are important as well. Height, eye level, arm length, waist height, etc.

The human scale is often the source of the square, the 1. The height of common chair seats such as most dining chairs is ~elbow to finger tip of the average adult male, effortless to measure on the workbench and it will get your chairs into the range people expect from such chairs. This height would often be the source of the square the chair would be designed around because it forms the most substantial part of a chair, the base.

Standard table height is stand up straight, let your arm hang straight down, make a fist, your knuckles are at table height. Works perfectly with chairs measured by elbow to finger tip and perfect for working at while standing when doing things like kneading bread or pushing a hand plane, puts the surface low enough that you can put your upper body into it and not just your arms.

A great many of things we interact with on a daily basis developed the standards we have today centuries before we had standards for measurement, back when calibrated measurement was academic and legal, impractical and abstract.

Re: The mathematical secrets of Barcelona's Sagrada Familia

#42
post #39
post #27

Earlier quoted context omitted.

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.

No doubt. I call them empirical geometric methods, you call it an analog computer, same thing. He didn’t invent anything though. The method of hanging a chain and adding custom weights to find the ideal shape for a complex masonry structure was invented by Giovanni Poleni in 1743 to fix the dome of St. Peter’s basilica. Poleni himself was extending Robert Hooke's 1675 inverted chain concept for optimal arches. The te…

I did not know of Poleni, thanks for that story. I always thought that the notable insight was by Robert Hooked.

Oh wait I misread, it was Robert Hooke as you said, but Poleni used and developed it.

I find the study of funicular shapes very gratifying.

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