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ROTATIONAL GEOMETRY AS A TEACHING TOOL :
APPLYING THE WORK OF GIORGIO SCARPA
PINO TROGU – SAN FRANCISCO STATE UNIVERSITY
SIXTH INTERNATIONAL CONFERENCE ON DESIGN PRINCIPLES AND PRACTICES
LOS ANGELES, JANUARY 21, 2012
1
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ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA P INO TROGU – SAN FRANCISCO STATE UNIVERSITY 2
3ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA P INO TROGU – SAN FRANCISCO STATE UNIVERSITY
4ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA P INO TROGU – SAN FRANCISCO STATE UNIVERSITY
5ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA P INO TROGU – SAN FRANCISCO STATE UNIVERSITY
6ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA P INO TROGU – SAN FRANCISCO STATE UNIVERSITY
7ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA P INO TROGU – SAN FRANCISCO STATE UNIVERSITY
8ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA P INO TROGU – SAN FRANCISCO STATE UNIVERSITY
9ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA P INO TROGU – SAN FRANCISCO STATE UNIVERSITY
10ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA P INO TROGU – SAN FRANCISCO STATE UNIVERSITY
11ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA P INO TROGU – SAN FRANCISCO STATE UNIVERSITY
12ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA P INO TROGU – SAN FRANCISCO STATE UNIVERSITY
B A B
E
D
C C
D
E1 2 3 4 5
TWIN SECTION
Fig. 1
13ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA P INO TROGU – SAN FRANCISCO STATE UNIVERSITY
Fig. 2
C
B
B D
14ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA P INO TROGU – SAN FRANCISCO STATE UNIVERSITY
Fig. 3
C C
C C
15ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA P INO TROGU – SAN FRANCISCO STATE UNIVERSITY
Fig. 4
B
B
Z
16ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA P INO TROGU – SAN FRANCISCO STATE UNIVERSITY
Fig. 5
A B C
CDE
B
B
BB B
Z
A
D
D
C
C
E
2 3 4 51
17ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA P INO TROGU – SAN FRANCISCO STATE UNIVERSITY
Fig. 6
B
ZB
BD
B
B
DB B
D
B B
18ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA P INO TROGU – SAN FRANCISCO STATE UNIVERSITY
Fig. 7
19ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA P INO TROGU – SAN FRANCISCO STATE UNIVERSITY
Fig. 8-11
8 9
10 11A 11B
20ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA P INO TROGU – SAN FRANCISCO STATE UNIVERSITY
Fig. 12-13
13
1
2
C
B
B
C
D
12
13
1
2
C
B
B
C
D
12
13
1
2
C
B
B
C
D
12
TRIPLET SECTION
21ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA P INO TROGU – SAN FRANCISCO STATE UNIVERSITY
Fig. 14
C
22ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA P INO TROGU – SAN FRANCISCO STATE UNIVERSITY
Fig. 15
23ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA P INO TROGU – SAN FRANCISCO STATE UNIVERSITY
Fig. 16
24ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA P INO TROGU – SAN FRANCISCO STATE UNIVERSITY
Fig. 17
25ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA P INO TROGU – SAN FRANCISCO STATE UNIVERSITY
Fig. 18
26ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA P INO TROGU – SAN FRANCISCO STATE UNIVERSITY
Fig. 19
27ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA P INO TROGU – SAN FRANCISCO STATE UNIVERSITY
Fig. 20
A B C
CDE
B B
B
B
B
B
BD E
D
B
BBB
Z
ED
CB
Z
Z
2 3 41
28ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA P INO TROGU – SAN FRANCISCO STATE UNIVERSITY
Fig. 21
29ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA P INO TROGU – SAN FRANCISCO STATE UNIVERSITY
Fig. 22
30ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA P INO TROGU – SAN FRANCISCO STATE UNIVERSITY
Fig. 23
ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA P INO TROGU – SAN FRANCISCO STATE UNIVERSITY 31
Fig. 24
HINGES AND ROTATIONS
ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA P INO TROGU – SAN FRANCISCO STATE UNIVERSITY 32
Fig. 25
ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA P INO TROGU – SAN FRANCISCO STATE UNIVERSITY 33
Fig. 26
ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA P INO TROGU – SAN FRANCISCO STATE UNIVERSITY 34
Fig. 27
ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA P INO TROGU – SAN FRANCISCO STATE UNIVERSITY 35
Fig. 28
ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA P INO TROGU – SAN FRANCISCO STATE UNIVERSITY 36
Fig. 29
ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA P INO TROGU – SAN FRANCISCO STATE UNIVERSITY 37
ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA P INO TROGU – SAN FRANCISCO STATE UNIVERSITY 38
ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA P INO TROGU – SAN FRANCISCO STATE UNIVERSITY 39
ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA P INO TROGU – SAN FRANCISCO STATE UNIVERSITY 40
Fig. 30
ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA P INO TROGU – SAN FRANCISCO STATE UNIVERSITY 41
ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA P INO TROGU – SAN FRANCISCO STATE UNIVERSITY 42
ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA P INO TROGU – SAN FRANCISCO STATE UNIVERSITY 43
ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA P INO TROGU – SAN FRANCISCO STATE UNIVERSITY 44
ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA P INO TROGU – SAN FRANCISCO STATE UNIVERSITY 45
ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA P INO TROGU – SAN FRANCISCO STATE UNIVERSITY 46
ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA P INO TROGU – SAN FRANCISCO STATE UNIVERSITY 47
ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA P INO TROGU – SAN FRANCISCO STATE UNIVERSITY 48
ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA P INO TROGU – SAN FRANCISCO STATE UNIVERSITY 49
ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA P INO TROGU – SAN FRANCISCO STATE UNIVERSITY 50
ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA P INO TROGU – SAN FRANCISCO STATE UNIVERSITY 51
ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA P INO TROGU – SAN FRANCISCO STATE UNIVERSITY 52
ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA P INO TROGU – SAN FRANCISCO STATE UNIVERSITY 53
ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA P INO TROGU – SAN FRANCISCO STATE UNIVERSITY 54
ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA P INO TROGU – SAN FRANCISCO STATE UNIVERSITY 55
ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA P INO TROGU – SAN FRANCISCO STATE UNIVERSITY 56
ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA P INO TROGU – SAN FRANCISCO STATE UNIVERSITY 57
ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA P INO TROGU – SAN FRANCISCO STATE UNIVERSITY 58
ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA P INO TROGU – SAN FRANCISCO STATE UNIVERSITY 59
60ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA P INO TROGU – SAN FRANCISCO STATE UNIVERSITY
REFERENCES & LINKS
Jürg Spiller, ed., Paul Klee: The Thinking Eye, trans. Ralph Manheim. Wittenborn, 1961.
Giorgio Scarpa, Modelli di geometria rotatoria [Models of rotational geometry]
Zanichelli, 1978.
Erik D. Demaine and Joseph O’Rourke, Geometric Folding Algorithms. Linkages, Origami,
Polyhedra. Cambridge University Press, 1997.
Cube Section trogu.com/projects/getProject/20051225082001/project_html
Giorgio Scarpa userwww.sfsu.edu/~trogu/scarpa
PDF of slides and handouts
trogu.com/Documents/conference/design-principles-and-practices
Contact
[email protected] design.sfsu.edu trogu.com go to first slide
Music: il nuotatore, Giovanni Allevi