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A Playful Geometry Workshop: Creating 3D Polyhedral Structures.
Polyhedral structures play a significant role in our lives, of which we are typically unaware. We live in Platonic cubes, we are awestruck as we look at the Egyptian pyramids, and the viruseswe catch are, in fact, living icosahedrons. Physical atoms from which are world is comprised are drawn to polyhedral structures. Polyhedral structures bring together varied fields of knowledge, such as art, architecture, molecular biology, and mathematics. They were a source of fascination to polymath artists such as Leonardo Da Vinci (1452-1519) and Albrecht Dürer (1471-1528), architects such as Buckminster Fuller, and researchers such as Nobel prize laureate Dan Shechtman who had studied these structures. Yet, have we have learned about polyhedral structures in school? Have we ever built them with our hands? Held them? Sensed them? Have we ever built a geodesic dome? Heard about the rhombohedron or the decahedron? Had we ever experience the spiritual beauty of the stella octangulla or the aesthetics simplicity of the octahedron?
To date, any such attempt would have required complex mathematical calculations. Lacking the availability of simple pedagogical tools, it was impossible to investigate, simply and joyfully, this rich world of polyhedral structures that comprise our world, and our own beings. Most of us had never had the opportunity to hold an icosahedron in our hands and were deprived of the spectacularly aesthetic world of significant multidimensional structures. Workshop participants will fold polyhedral structures, simply and quickly, to form an extensive series of paper polyhedral structures. The game and workshop are developed on the basis of a single paper folding unit comprising eight equilateral triangles
This octahedral paper folding unit conjoins with other such units or segments thereof, creating an infinite range of two-dimensional nets that may be folded in a series of varied polyhedral structures. This paper folding game thus demonstrates the power of one specific form of octahedral net comprising eight equilateral triangles, one of 11 known nets of the octahedron, in explaining a specific series of polyhedra
This workshop allows participants to get acquainted with the world of two-dimensional nets and the historic evolution of this field from the 16th century, the time of Da Vinci and Dürer, until our time. Participants will experience first hand the folding of two-dimensional nets into complex structures using a simple new technique. This technique overcomes the need of mathematical formulae or angle computation. It even forsakes the need for glue or scissors. No previous knowledge is required of the folded polyhedral structures, which reveal themselves through the folding process. This simple pedagogical tool may serve math teachers of in their endeavors of teaching spatial geometry . Moreover, the model presented herein unifies most polyhedral structures by unfolding them into a single net of a single cut.
workshop is suitable for both small and large groups of children and adults, starting at he age of 7. This experiential workshop is not only educational and fun but also serves to develop participants sense of achievement.
Albrecht Durer, (1471-1528),a German painter, made an important contribution to polyhedral literature in his 1525 book, A Painter's Manual. This was one of the first books to teach methods of perspective, and was highly regarded throughout the 16th century. Durer was considered the founder of the net theory, the theory governing the manner by which two dimensional nets fold into three dimensional structures.