ROTATIONAL GEOMETRY AS A TEACHING TOOL :...

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

trogu@sfsu.edu design.sfsu.edu trogu.com go to first slide

Music: il nuotatore, Giovanni Allevi