Giant Triangles

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Publications by Eva Knoll pertaining to Giant Triangles.


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Now showing 1 - 5 of 6
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    Polyhedra, Learning by Building: Design and Use of a Math-Ed. Tool.
    (Bridges: Mathematical Connections in Art, Music, and Science, 2000) Knoll, Eva
    This is a preliminary report on design features of large, light-weight, modular equilateral triangles and classroom activities developed for using them. They facilitate the fast teaching of three dimensional geometry together with basic math skills, and create a lasting motivational impact on low achievers and their subsequent performance in math and science. In directed discovery activities, lasting from 20 to 90 minutes, large models of basic polyhedra are made, enabling their properties to be explored. Faces, edges and vertices can all be counted and tabulated, providing opportunities to see number patterns and inter-relationships, to plot graphs, to extract algebraic relationships and to look for proofs of those relationships. These building activities can be kept central, under the teacher’s control for large classes with limited time, or building can be split out into groups of children where co-operative problem solving skills are also developed. In interviews, children have stressed the effectiveness of learning by building the shapes themselves. In classroom activities, it is clear to see that these triangles make children excited. Learning by building gives a concrete, active, authentic and personal experience of mathematics to children and teachers enabling them to feel the full excitement of the subject.
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    Barn-Raising an Endo-Pentakis-Icosi-Dodecahedron
    (Bridges: Mathematical Connections in Art, Music, and Science, 1999) Knoll, Eva; Morgan, Simon
    The workshop is planned as the raising of an endo-pentakis-icosi-dodecahedron with a 1 meter edge length. This collective experience will give the participants new insights about polyhedra in general, and deltahedra in particular. The specific method of construction applied here, using kite technology and the snowflake layout allows for a perspective entirely different from that found in the construction of hand-held models or the observation of computer animations. In the present case, the participants will be able to pace the area of the flat shape and physically enter the space defined by the polyhedron.
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    Decomposing Deltahedra
    (International Society of the Arts, Mathematics, and Architecture, 2000) Knoll, Eva
    Deltahedra are polyhedra with all equilateral triangular faces of the same size. We consider a class of we will call ‘regular’ deltahedra which possess the icosahedral rotational symmetry group and have either six or five triangles meeting at each vertex. Some, but not all of this class can be generated using operations of subdivision, stellation and truncation on the platonic solids. We develop a method of generating and classifying all deltahedra in this class using the idea of a generating vector on a triangular grid that is made into the net of the deltahedron. We observed and proved a geometric property of the length of these generating vectors and the surface area of the corresponding deltahedra. A consequence of this is that all deltahedra in our class have an integer multiple of 20 faces, starting with the icosahedron which has the minimum of 20 faces.
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    From the circle to the icosahedron
    (Bridges: Mathematical Connections in Art, Music, and Science, 2000) Knoll, Eva
    The following exercise is based on experiments conducted in circular Origami. This type of paper folding allows for a completely different geometry than the square type since it lends itself very easily to the creation of shapes based on 30-60-90 degree angles. This allows for experimentation with shapes made up of equilateral triangles such as deltahedra. The results of this research were used in Annenberg sponsored activities conducted in a progressive middle school in Houston TX, as well as a workshop presented at the 1999 Bridges Conference in Winfield, KS. Not including preparatory and follow up work by the teacher, the activities in Houston were composed of two main parts, the collaborative construction of a three-yard-across, eighty-faced regular deltahedron (the Endo- Pentakis Icosi-dodecahedron) and the following exercise. The barn-raising was presented last year in Winfield, and the paper folding is the topic of this paper.
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    Circular Origami: a Survey of Recent Results
    (A.K Peters, 2001) Knoll, Eva