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Matematicum 2012 Geometric Analysis Hands-on v./ Steen Markvorsen

Geometric Analysis Hands-on

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Geometric Analysis Hands-on. v./ Steen Markvorsen. Geometric Analysis. Synopsis. Idea Recruitment, education, research Case : Parametric Modelling, digital fabrication and casting Case : Minimal surfaces Case : Autarkic mini wind turbines, wing sections, and boomerangs - PowerPoint PPT Presentation

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Page 1: Geometric Analysis Hands-on

Matematicum 2012

Geometric AnalysisHands-on

v./ Steen Markvorsen

Page 2: Geometric Analysis Hands-on

Matematicum 2012

Geometric AnalysisSynopsis

• Idea

• Recruitment, education, research

• Case : Parametric Modelling, digital fabrication and casting

• Case : Minimal surfaces

• Case : Autarkic mini wind turbines, wing sections, and boomerangs

• Case : Moineau pump geometry

• End

Page 3: Geometric Analysis Hands-on

Matematicum 2012

Geometric Analysis3D PRINTER ZP450

Page 4: Geometric Analysis Hands-on

Matematicum 2012

Geometric AnalysisFume cupboard

Page 5: Geometric Analysis Hands-on

Matematicum 2012

Geometric Analysis

MatematicumThe Mathematical Inspiratorium at DTU

Recruitment, education, and research

http://www.matematicum.dtu.dk/

Page 6: Geometric Analysis Hands-on

Matematicum 2012

Geometric Analysis

Geometric OperationsCourse 01999

Recruitment, education, and research

Notes

Tetrahedral deformation

Page 7: Geometric Analysis Hands-on

Matematicum 2012

Geometric Analysis

Differential GeometryCourse 01234

Recruitment, education, and research

Hyperbolic curvature 1

Hyperbolic curvature 2

Page 8: Geometric Analysis Hands-on

Matematicum 2012

Geometric Analysis

EvolverOptimizer

Recruitment, education, and research

Maple2Evolver2Maple

Mound, s, q, r, G 4, g 50

Mound, s, q, r, G -4, g 50

Page 9: Geometric Analysis Hands-on

Matematicum 2012

Geometric AnalysisMatematicum

Page 10: Geometric Analysis Hands-on

Matematicum 2012

Geometric AnalysisMatematicum

Page 11: Geometric Analysis Hands-on

Matematicum 2012

Geometric AnalysisMatematicum

Page 12: Geometric Analysis Hands-on

Matematicum 2012

Geometric AnalysisMatematicum

Page 13: Geometric Analysis Hands-on

Matematicum 2012

Geometric AnalysisMatematicum

Page 14: Geometric Analysis Hands-on

Matematicum 2012

Geometric AnalysisMatematicum

Page 15: Geometric Analysis Hands-on

Matematicum 2012

Geometric Analysis

Digital fabrication and casting

Parametric modelling

Jacob Drachmann and Rasmus Holst

Page 16: Geometric Analysis Hands-on

Matematicum 2012

Geometric Analysis

Conformal Minimal Surfaces

Minimal surfaces

Page 17: Geometric Analysis Hands-on

Matematicum 2012

Geometric AnalysisMinimal surfaces

Locally of smallest area, soap film models

Page 18: Geometric Analysis Hands-on

Matematicum 2012

Geometric AnalysisMinimal surfaces

Locally of smallest area, soap film models

Parametric representations

Page 19: Geometric Analysis Hands-on

Matematicum 2012

Geometric AnalysisMinimal surfaces, isometric family of deformations

Page 20: Geometric Analysis Hands-on

Matematicum 2012

Geometric AnalysisFrom Maple to 3D PRINTER, hands-on

Page 21: Geometric Analysis Hands-on

Matematicum 2012

Geometric AnalysisFrom Maple to 3D PRINTER, hands-on

Page 22: Geometric Analysis Hands-on

Matematicum 2012

Geometric AnalysisFrom Maple to 3D PRINTER, hands-on

Page 23: Geometric Analysis Hands-on

Matematicum 2012

Geometric AnalysisMinimal surfaces, Costa’s minimal surface

Page 24: Geometric Analysis Hands-on

Matematicum 2012

Geometric AnalysisMinimal surfaces, Costa in snow and in LEGO

Page 25: Geometric Analysis Hands-on

Matematicum 2012

Geometric AnalysisMinimal surfaces, Costa in soap

Page 26: Geometric Analysis Hands-on

Matematicum 2012

Geometric AnalysisMinimal surfaces, Costa in plaster of Paris (dk: gips)

Page 27: Geometric Analysis Hands-on

Matematicum 2012

Geometric AnalysisMinimal surfaces, Costa, ready to print, hands-on

Page 28: Geometric Analysis Hands-on

Matematicum 2012

Geometric AnalysisMinimal surfaces, Costa, hands-on

Page 29: Geometric Analysis Hands-on

Matematicum 2012

Geometric Analysis

Mini wind turbineProject by Ph.D. student Christina Beller, Risø DTU -:-

Wind turbines

Page 30: Geometric Analysis Hands-on

Matematicum 2012

Geometric AnalysisAutarkic mini wind turbines

Page 31: Geometric Analysis Hands-on

Matematicum 2012

Geometric AnalysisAutarkic mini wind turbines

The word "autarky" is from the Greek: αὐτάρκεια, which means "self-sufficiency"

Page 32: Geometric Analysis Hands-on

Matematicum 2012

Geometric AnalysisMini wind turbine

Page 33: Geometric Analysis Hands-on

Matematicum 2012

Geometric AnalysisMini wind turbine

Page 34: Geometric Analysis Hands-on

Matematicum 2012

Geometric AnalysisMini wind turbine, hands-on

Page 35: Geometric Analysis Hands-on

Matematicum 2012

Geometric Analysis

Wing sections and boomerangs

Flying and rotating

Page 36: Geometric Analysis Hands-on

Matematicum 2012

Geometric Analysis

MOINEAU PUMPSAn ESGI project from Grundfos A/S

Moineau pumps

Page 37: Geometric Analysis Hands-on

Matematicum 2012

MatematicumMoineau Pump Principle

Page 38: Geometric Analysis Hands-on

Matematicum 2012

MatematicumMoineau Pump Principle

Page 39: Geometric Analysis Hands-on

Matematicum 2012

Geometric AnalysisMoineau Pump Principle, hands-on

J. Gravesen: Spherical Curves for the design of conical Moineau pumps -:-

Page 40: Geometric Analysis Hands-on

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Geometric AnalysisEnd

Thank you for your attention!