Learning Geometry in the Dance Studio MAA Special Session: - - PowerPoint PPT Presentation

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Learning Geometry in the Dance Studio MAA Special Session: - - PowerPoint PPT Presentation

Nov 19, 2022 160 likes •522 views

Learning Geometry in the Dance Studio MAA Special Session: Connecting Math to the Liberal Arts 29 March 2008 Charleston, SC Jason Parsley (Math Dept.) Christina Soriano (Theatre/Dance Dept.) Wake Forest University Who we are

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Learning Geometry in the Dance Studio

MAA Special Session: Connecting Math to the Liberal Arts 29 March 2008 Charleston, SC

Jason Parsley

(Math Dept.)

Christina Soriano

(Theatre/Dance Dept.)

Wake Forest University

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  • J. Parsley & C. Soriano, Learning Geometry in

the Dance Studio 2

Who we are

Christina Soriano: modern dance

choreographer/performer & professor, minimal math background

me: researching 3-dim. geometry & topology,

no dance background

at new faculty dinner, she said “I’m thinking of

choreographing a geometric piece this fall”

Collaboration led to cross-disciplinary

teaching past 2 semesters

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  • J. Parsley & C. Soriano, Learning Geometry in

the Dance Studio 3

Cross-disciplinary Teaching

Brought together liberal arts math class &

  • intro. to modern dance

class (fall) dance composition class (spring) They formed Platonic solids both in the math classroom & dance studio They studied reflection properties of ellipses

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  • J. Parsley & C. Soriano, Learning Geometry in

the Dance Studio 4

Today’s Outline

  • 1. Goals
  • 2. Fall 2006 `Trace of a Moving Point’ dance
  • 3. Some historical dance context

(Laban & Schlemmer)

  • 4. Our interdisciplinary pedagogical exercise
  • 5. Evaluating impacts
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  • J. Parsley & C. Soriano, Learning Geometry in

the Dance Studio 5

  • 1. Our Goals

For us

  • Chart pedagogical exercise
  • applicable to numerous courses/settings
  • Motivate others to think spatially
  • Geometry influencing creative process
  • Demonstrate interconnectedness of math &
  • f motion
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  • J. Parsley & C. Soriano, Learning Geometry in

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  • 1. Our Goals

For students

  • Experiential learning
  • Increase spatial reasoning & memory
  • Interconnectedness of math & arts
  • Understand duality, in the large
  • Producing math & producing dance are journeys
  • [math students] greater appreciation of regularity
  • [dance students] introduce geometric ideas into

future choreography

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  • J. Parsley & C. Soriano, Learning Geometry in

the Dance Studio 7

  • 2. Soriano’s geometry piece

‘Trace of a Moving Point’ (fall 2006)

  • Seeks to represent human form as point

moving along line & later on circle

  • Geometric input
  • brainstorming sessions

Pascal’s triangle, triangular numbers, fractals, Cantor set, Flatland, positive/negative curvature & triangles

  • Arranging 14 dancers
  • Rehearsal visits
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  • J. Parsley & C. Soriano, Learning Geometry in

the Dance Studio 8

  • 3. Dance history

Rudolph von Laban

(1879-1958) introduced vector notation for dance motions

  • energy, time, space

Strongly connected Euclidean geometry & Platonic solids with canon of dance

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  • J. Parsley & C. Soriano, Learning Geometry in

the Dance Studio 9

Laban & Platonic Solids

Laban introduced idea of the kinesphere, allowable motions

primary – up/down secondary – left/right tertiary – forward/backward

Within kinesphere, Laban was fascinated by

Platonic solids, particularly cube, tetrahedron, & icosahedron, for detailing motion space

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  • J. Parsley & C. Soriano, Learning Geometry in

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Laban wasn’t the first

Da Vinci considered similar

ideas with body motions & rational proportions Vitruvian Man (c.1492)

Golden rectangle & human

form (c.f., Pacioli, De Divina

Proportione, 1509)

recall: 3 orthogonal golden

rectangles produce an icosahedron

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  • J. Parsley & C. Soriano, Learning Geometry in

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Icosahedron & Golden Rectangles

3 orthogonal golden

rectangles produce an icosahedron

All 12 vertices are

given by the vertices

  • f the 3 rectangles
  • http://www.hypatia-lovers.com/geometry/

Divine_Proportions_of_Icosahedron.gif

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The 5 Platonic Solids

Tetrahedron Cube Octahedron Dodecahedron Icosahedron + Duality

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  • J. Parsley & C. Soriano, Learning Geometry in

the Dance Studio 13

  • 4. Cross-disciplinary Teaching

Brought together liberal arts math class &

  • intro. to modern dance

class (fall) dance composition class (spring) Step 1: dance class visits the math class & we build Platonic solids

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  • J. Parsley & C. Soriano, Learning Geometry in

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  • 4. Cross-disciplinary

Teaching

Step 2: math class visits the dance studio & we build Platonic solids In order, they form cube

  • ctahedron

dodecahedron dual octahedron within cube icosahedron

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  • J. Parsley & C. Soriano, Learning Geometry in

the Dance Studio 16

Cube

  • 36 students, split into 5 groups

4 groups of 7 students 1 group of 8 students

  • All 5 groups formed cube differently
  • Group of 8 students did it in obvious way:

each student formed a trivalent vertex, 4 standing, 4 on floor

  • Bodies used as edges, etc.
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  • J. Parsley & C. Soriano, Learning Geometry in

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Cube, II

  • groups of 7 students faced tougher task
  • - forcing more creative, physical motion
  • for all groups, floor was natural choice of

bottom face

  • each group showed their static configuration
  • then we asked them to rotate their cube, to

make it stand on a vertex

  • recurrent concern: how do you represent a

regular shape with non-regular bodies?

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  • J. Parsley & C. Soriano, Learning Geometry in

the Dance Studio 18

Octahedron

  • 4 groups of 9-11 students
  • more challenging than cube
  • some groups used bodies as faces,

some as edges

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  • J. Parsley & C. Soriano, Learning Geometry in

the Dance Studio 19

Octahedron, group 1

  • center axis

student

  • 4 seated

students lean against 4 standing students

  • using fellow

students to support some body weight

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  • J. Parsley & C. Soriano, Learning Geometry in

the Dance Studio 20

Octahedron, group 2

  • 1 central figure,

who clapped to begin their presentation

  • 4 inner students

clearly demonstrated the square

  • uter students

went clockwise; inner ones ccw

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  • J. Parsley & C. Soriano, Learning Geometry in

the Dance Studio 21

Octahedron, group 3

  • 4 central figures
  • 4 outer students,

bent at the waist. They form 2 faces each

  • Hands interlock

for support

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  • J. Parsley & C. Soriano, Learning Geometry in

the Dance Studio 22

Octahedron, group 4

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  • J. Parsley & C. Soriano, Learning Geometry in

the Dance Studio 23

Dodecahedron, group 1

5 central students, standing form top pentagon 5 outer students, leaning in 5 seated students, legs form bottom pentagon

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  • J. Parsley & C. Soriano, Learning Geometry in

the Dance Studio 24

Dodecahedron, group 2

3 central students, standing form top pentagon 5 outer students, leaning in, arms bent 5 seated students arms can be 1 or 2 (or 1.5) edges

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Dual Octahedron in Cube

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Icosahedron was a Struggle

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Icosahedron was a Struggle

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Icosahedron was a Struggle

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  • J. Parsley & C. Soriano, Learning Geometry in

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  • 5. Evaluating Impacts

Spatial reasoning. 21 of 22 survey takers:

their visualization abilities had increased

“The 3-d image we created with bodies is now

something that will come to mind anytime I think of a Platonic solid. Attempting to move through space in these shapes was an interesting inspiration for possible spatial patterns to be used in dance choreography.”

  • “I really got a feel for how 3D these figures are. Dealing

with bodies and gravity while trying to construct these figures really showed all of their dimensions and how they can be rotated in space.”

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  • J. Parsley & C. Soriano, Learning Geometry in

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Evaluating Impacts II

Body sizes & regularity “I learned how important it is for the angles and sides of the regular polygon to be the

  • same. Our shapes were

distorted because not all our bodies were the same.”

  • anonymous response

(right:) Cyhl Quarles, WFU football

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  • J. Parsley & C. Soriano, Learning Geometry in

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Evaluating Impacts III

Weight & balance

  • many students were

shocked by the necessity/utility to lean on & support each other

“My favorite part was seeing how to use other bodies and gravity to make different shapes, to support, and to stretch.”

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Evaluating Impacts IV

  • Duality. dancers especially enjoyed the idea
  • f an infinite pattern of solids within solids,

getting smaller [or larger]

“I could visualize the cube, the octahedron

and the duality of the octahedron in the cube better after I experienced them in space.”

“Easier to remember what different shapes are

after this class. Duality is much more understandable once I was physically able to see it.”

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  • J. Parsley & C. Soriano, Learning Geometry in

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Evaluating Impacts V

  • Fun. The students loved it!

“I thought this was a really fun activity,

especially the more complicated solids.”

“Do it again! It’s fun to apply math in

different ways.”

“I loved this activity!”

“I loved how beautiful our creation was, and

the importance of each individual to make it happen.”

“I had a great time doing this and loved

getting to think about math in a different way.”

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  • J. Parsley & C. Soriano, Learning Geometry in

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Broader Impacts: students

1 dancer from spring decided, because of this

activity, to take Math 107 in the fall … even though she had already met the requirement

more students with dance background

enrolled in fall class

several dancers are planning to incorporate

geometric ideas into their spring concert choreography

  • vercome math phobia; math 107 is ‘fun’
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  • J. Parsley & C. Soriano, Learning Geometry in

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Broader Impacts: faculty

influence of geometry on Soriano’s recent &

future works

as of yet, no research connections for me affects my ideas on how students can best

learn spatial reasoning & symmetry

we’re presenting at (1) math conferences

(2) dance panels (3) on-campus teaching/learning fair

paper forthcoming

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Thanks for coming!!!