PINO TROGU – SAN FRANCISCO STATE UNIVERSITY

ROTATIONAL GEOMETRY AS A TEACHING TOOL :APPLYING THE WORK OF GIORGIO SCARPA

DRS // CUMULUS – OSLO, NORWAYTHE 2ND INTERNATIONAL CONFERENCE FOR DESIGN EDUCATION RESEARCHERS

15 MAY 2013

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ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA PINO TROGU – SAN FRANCISCO STATE UNIVERSITY 2

ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA PINO TROGU – SAN FRANCISCO STATE UNIVERSITY3

ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA PINO TROGU – SAN FRANCISCO STATE UNIVERSITY4

ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA PINO TROGU – SAN FRANCISCO STATE UNIVERSITY5

ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA PINO TROGU – SAN FRANCISCO STATE UNIVERSITY6

ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA PINO TROGU – SAN FRANCISCO STATE UNIVERSITY7

ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA PINO TROGU – SAN FRANCISCO STATE UNIVERSITY8

9 9ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA PINO TROGU – SAN FRANCISCO STATE UNIVERSITY

10 10ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA PINO TROGU – SAN FRANCISCO STATE UNIVERSITY

ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA PINO TROGU – SAN FRANCISCO STATE UNIVERSITY1111

ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA PINO TROGU – SAN FRANCISCO STATE UNIVERSITY

TWIN SECTION

Fig. 1

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ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA PINO TROGU – SAN FRANCISCO STATE UNIVERSITY

Fig. 2

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ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA PINO TROGU – SAN FRANCISCO STATE UNIVERSITY

Fig. 2b

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ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA PINO TROGU – SAN FRANCISCO STATE UNIVERSITY

Fig. 3

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ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA PINO TROGU – SAN FRANCISCO STATE UNIVERSITY

Fig. 4

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ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA PINO TROGU – SAN FRANCISCO STATE UNIVERSITY

Fig. 5

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ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA PINO TROGU – SAN FRANCISCO STATE UNIVERSITY

Fig. 6

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ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA PINO TROGU – SAN FRANCISCO STATE UNIVERSITY

Fig. 7

7 7a

7b 7c 7d

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ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA PINO TROGU – SAN FRANCISCO STATE UNIVERSITY

Fig. 8-9

TRIPLET SECTION

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ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA PINO TROGU – SAN FRANCISCO STATE UNIVERSITY

Fig. 9b

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ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA PINO TROGU – SAN FRANCISCO STATE UNIVERSITY

Fig. 9c

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ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA PINO TROGU – SAN FRANCISCO STATE UNIVERSITY

Fig. 10

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ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA PINO TROGU – SAN FRANCISCO STATE UNIVERSITY

Fig. 11

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ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA PINO TROGU – SAN FRANCISCO STATE UNIVERSITY

Fig. 12

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ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA PINO TROGU – SAN FRANCISCO STATE UNIVERSITY

Fig. 12b

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ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA PINO TROGU – SAN FRANCISCO STATE UNIVERSITY

Fig. 13

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ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA PINO TROGU – SAN FRANCISCO STATE UNIVERSITY

Fig. 14

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ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA PINO TROGU – SAN FRANCISCO STATE UNIVERSITY

Fig. 15

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30 30ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA PINO TROGU – SAN FRANCISCO STATE UNIVERSITY

Fig. 15b

ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA PINO TROGU – SAN FRANCISCO STATE UNIVERSITY

Fig. 16

HINGES AND ROTATIONS

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ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA PINO TROGU – SAN FRANCISCO STATE UNIVERSITY

Fig. 16b

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ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA PINO TROGU – SAN FRANCISCO STATE UNIVERSITY

Fig. 17

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ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA PINO TROGU – SAN FRANCISCO STATE UNIVERSITY

Fig. 17b

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ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA PINO TROGU – SAN FRANCISCO STATE UNIVERSITY

Fig. 18

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Fig. 19 Models by Florence Yuen, San Francisco State University.

37ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA PINO TROGU – SAN FRANCISCO STATE UNIVERSITY

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38ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA PINO TROGU – SAN FRANCISCO STATE UNIVERSITY

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39ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA PINO TROGU – SAN FRANCISCO STATE UNIVERSITY

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40ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA PINO TROGU – SAN FRANCISCO STATE UNIVERSITY

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Fig. 20

41ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA PINO TROGU – SAN FRANCISCO STATE UNIVERSITY

42ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA PINO TROGU – SAN FRANCISCO STATE UNIVERSITY

43ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA PINO TROGU – SAN FRANCISCO STATE UNIVERSITY

44ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA PINO TROGU – SAN FRANCISCO STATE UNIVERSITY

45ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA PINO TROGU – SAN FRANCISCO STATE UNIVERSITY

46ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA PINO TROGU – SAN FRANCISCO STATE UNIVERSITY

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ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA PINO TROGU – SAN FRANCISCO STATE UNIVERSITY47

ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA PINO TROGU – SAN FRANCISCO STATE UNIVERSITY48

ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA PINO TROGU – SAN FRANCISCO STATE UNIVERSITY

Circular grid by Slate Werner, San Francisco State University

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ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA PINO TROGU – SAN FRANCISCO STATE UNIVERSITY52

53ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA PINO TROGU – SAN FRANCISCO STATE UNIVERSITY

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ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA PINO TROGU – SAN FRANCISCO STATE UNIVERSITY54

ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA PINO TROGU – SAN FRANCISCO STATE UNIVERSITY55

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57ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA PINO TROGU – SAN FRANCISCO STATE UNIVERSITY

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58ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA PINO TROGU – SAN FRANCISCO STATE UNIVERSITY

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ROTATIONAL GEOMETRY AS A TEACHING TOOL: APPLYING THE WORK OF GIORGIO SCARPA PINO 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.

Giorgio Scarpa online.sfsu.edu/trogu/scarpa

Cube Section online.sfsu.edu/trogu/scarpa/cube

PDF of slides and handouttrogu.com/Documents/conference/2013_drs_cumulus_oslo

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

Music: Discovery At Night by Ludovico Einaudi 60