Brunelleschi's Dome: Quinto Acuto Function in Cylindrical Coordinates

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In summary, the conversation discusses the need to write a function in cylindrical coordinates to describe the shape of Brunelleschi's Dome on the cathedral of Santa Maria del Fiore in Florence. The dome's base is an octagon and the exterior is not a surface of revolution, so the function must include both r and phi. The term "pointed fifth" refers to imaginary cones that form horizontal rings within the dome's structure. The ribs of the dome are not weight-bearing elements. One person suggests using the Pythagorean theorem to set up the function.
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xjumpman
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i need to write a function which describes the surface of brunelleschi's dome, the shape of the sides are called quinto acuto meaning pointed fifth. the function needs to be in cylindrical coordinates z=f(r), span of the base of dome is 143 feet
 
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The cupola or dome atop the cathedral of Santa Maria del Fiore in Florence?

This ought to help!:
http://www.arch.mcgill.ca/prof/sijpkes/arch374/winter2001/sfarfa/ensayo1.htm

The figures here might also be of assistance:
http://www.obscure.org/~perky/uofr/fall2002/ISYS203U/Duomo_Site/
Apparently there is a book by Ross King, Brunelleschi's Dome, which should help.

From the pictures you can see that the base of the dome is a straight sided octagon, so the shape formed by the exterior (say) of the courses of bricks is not a surface of revolution. Thus, describing the shape of the outer surface (say) would seem to require giving height z as a function of both [itex]r, \, \phi[/itex] rather than r alone. The term "pointed fifth" seems to refer to five imaginary cones with different vertices and different opening angles, positioned (in imagination) to make five "latitudes" where they form the five horizontal rings contained in the structure of the dome. The architect says that the eight ribs are not weight-bearing elements. Other than that I can't figure out what the guy at McGill is trying to say. Anyone else?
 
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i was told that r would be the distance of a point on the dome from the central axis and the radius would be .8(143)...setting up the picture i got a triangle I guess i would use the pythagorean theorem from there?
 

1. What is the Quinto Acuto Function in Cylindrical Coordinates?

The Quinto Acuto Function, also known as the Sharp Fifth Function, is a mathematical concept developed by Italian architect Filippo Brunelleschi to aid in the construction of the dome of the Florence Cathedral. It is a mathematical formula that calculates the dimensions and angles necessary to construct a dome with a pointed or "acuto" shape.

2. Why was the Quinto Acuto Function used in the construction of the dome?

The use of the Quinto Acuto Function allowed Brunelleschi to create a dome with a pointed shape, which was a popular architectural style at the time. It also allowed for a more efficient and stable construction process, as the function determined the exact measurements and angles needed for each section of the dome.

3. How did Brunelleschi come up with the Quinto Acuto Function?

Brunelleschi was a skilled mathematician and architect who studied ancient Roman and Greek architecture. He used his knowledge of geometry and mathematical principles to create the Quinto Acuto Function, which was a breakthrough in dome construction at the time.

4. Was the Quinto Acuto Function used in other architectural projects?

Yes, the Quinto Acuto Function was widely used by other architects in the Renaissance period and beyond. It was particularly popular in the construction of churches and cathedrals, as it allowed for the creation of large and impressive domes.

5. How does the Quinto Acuto Function contribute to the stability of the dome?

The Quinto Acuto Function ensures that each section of the dome is precisely measured and angled, which helps distribute the weight of the dome evenly and prevent any weak spots. This allows for a more stable and durable structure that can withstand the test of time.

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