1. Elementary Mathematics and Architecture
MAA Minicourse, Boston, January 4-
8, 2012
Alexander Hahn
University of Notre Dame
Part IIb: The Sydney Opera House (continued)

4. B
C
B
C
A
A
O O
A1 A2
B B C
C
A
A
O
O
A3 A4

6. 0 100 200 300 feet

7. C
C
B B
A
(a) O A
(b)

8. rib number 12
ridge beam segment
top cut-off segment
standard rib segment
standard rib segment
standard rib segment
246
foo
t ra
d iu
s
standard rib segment
standard rib segment
pedestal
tie beam
column (a) (b)
standard rib segment number 7
(c)

11. Curvature and Combinatorics
of Surfaces

15. M
x
S

16. Gauss map
unit normals
U(q) U(q)
U(p)
U(p)
A
q
p
S
on the surface the unit sphere

17. M
x
S
The Gaussian curvature of the surface at x is
Area A
K(x) = l i m
S 0 Area S
(Consider a flat piece of surface on M)

22. h
r
R

24. c(T) = V - E + F = 1
C
g
T
a
A
b
B

26. a
T
b g
M
A geodesic triangle T on M has area
R 2 (a + b + g - p)