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Geometric Unity Constructions

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2013 ASEE Annual Conference & Exposition


Atlanta, Georgia

Publication Date

June 23, 2013

Start Date

June 23, 2013

End Date

June 26, 2013



Conference Session

Visualization tools and uses in graphics

Tagged Division

Engineering Design Graphics

Page Count


Page Numbers

23.637.1 - 23.637.8



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Paper Authors


James A Wronecki East Tennessee State University

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Assistant Professor James Wronecki works in the Department of Engineering Technology, Surveying, and Digital Media at East Tennessee State University. He has a master's degree in Industrial Design from the University of the Arts in Philadelphia, Pa.

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Euclidian Geometric ConstructionsPresent computationally based illustration and aided design (CAD) programs afford easyways to create basic elementary shapes and forms. The three basic 2D shapes: circle,triangle, and square, and their 3D counterparts: sphere, tetrahedron, and cube may becreated in a variety of ways. Holding various keys while dragging a mouse creates andscales shapes from their center out or via diagonal selection marques.Most CAD techniques are proprietary, software specific, algorithmically scripted toolbuttons that emphasize ease-of-use for rapid creation and placement of shape and form.As a result, very little critical thinking or creative activity may be required to create basicshape and form. While CAD technique workflows provide efficient ways and effectivemeans in geometric construction, fundamental understandings about these shapes andforms may not be fully present to a student’s knowledge base. Students may therefore,neither know how to construct them in the real world, nor truly understand their physicalproperties, proportional relationships, or underlying mathematical attributes.A quote by Orson Wells “The enemy of art is the absence of constraint” challenges theauthor to educate future artisans and technicians by providing them with guidinglimitations to promote deeper critical thinking and higher levels of creative activity.Towards these ends, this paper provides an overview of ancient Euclidean geometricconstructions to provide constraint based methods for the creation of the aforementionedshapes and forms. The approach applies the geometers tools, straight-edge and compass,via their modern CAD tools, straight-line and circle created from the center-out. Thisconstrained challenge to construct shape and form with limited ways and technicallyscripted means enables beginning students to know and be able to: practically use basicCAD tools, critically think through problems with geometric constructions, as well asreview applied understandings of relevant axioms, equations, and theorems.

Wronecki, J. A. (2013, June), Geometric Unity Constructions Paper presented at 2013 ASEE Annual Conference & Exposition, Atlanta, Georgia. 10.18260/1-2--19651

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