# Brunelleschi's dome

1. Nov 28, 2007

### xjumpman

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

2. Nov 29, 2007

### Chris Hillman

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 $r, \, \phi$ 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?

Last edited: Nov 29, 2007
3. Nov 30, 2007

### xjumpman

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?