Write an essay by researching and answering the questions. Be careful to attribute material from the references, and use quote marks appropriately in your paper. Illustrate each section appropriately, being careful to attribute the source with the illustration. Each question has the letters of books that may be helpful. See the book list below. The minimum writing for the paper is six pages, double-spaced, excluding (small) illustrations. The paper must have a cover sheet with your name, date, and title. Use either Times New Roman or Cambria font, 12 point, with 1 inch or 1.25 inch margins. Number the pages (header or footer). In your bibliography list all sources that you have used. NOTES: (1) You must have at least one print reference for each section. (2) The number of print references must be at least twice the number of electronic references. (3) For web pages, list URL and date accessed. Take your final draft to a writing tutor in the AAC; attach a signed form to your essay as verification. I. Penrose tiles What is an aperiodic tiling? (H, S) What are Penrose tiles? Who are they named for? (Name, date born, where lives, field of work). (H, S, others) Describe and diagram one set of the tiles, kites and darts, and give some fun facts (how made, angles of the polygons, lengths or ratios of their sides). Show some patterns that can be made with these Penrose tiles. (H, S) Where is the Golden Ratio found in Penrose tiles? (H, S) II. Platonic and Archimedean solids and their symmetries Choose one Platonic and one Archimedean solid and make a table to answer the question: What are the rotation and reflection symmetries of these solids? (S, others) Which of the Platonic and Archimedean solids fill space, singly or in pairs? (W, K, C, S) Where is the Golden Ratio found in Platonic solids? (H, S, L) Bonus: Where are the Platonic solids and Archimedean solids and their duals found in Renaissance painting, prints, and sculpture? (W, K, F, P, PC, L) III. Perspective as the connection between art and math in the Renaissance. How did perspective develop during the Renaissance? (P, F, K, PC) Who were the prominent artists, architects, and mathematicians in each stage of the development, and what was their contribution? Choose a minimum of two people to discuss. (P, F, PC) Examples: Brunelleschi, Alberti, Piero, Leonardo, Stevin, Desargues, (Note the term Renaissance Man) Where is the Golden Ratio or Golden Rectangle found in Renaissance painting and architecture? (K, F, H, PC, L) Bonus: What is Desargues Theorem? Book List. You may find other books that are helpful, but these have the answers to the questions. Note: All books other than your text are on reserve in the library. W = Hermann Weyl, Symmetry K = Jay Kappraff, Connections: the Geometric Bridge Between Art and Science F = J. V. Field, The Invention of Infinity P = A. Perez-Gomez & L. Pelletier, Architectural Representation and the Perspective Hinge C = Peter Cromwell, Polyhedra H = E. Burger & M. Starbird, Heart of Mathematics S = L.C. Kinsey & T.E. Moore, Symmetry, Shape, and Space L = Mario Livio, The Golden Ratio PC = Paul Calter, Squaring the Circle: Geometry in Art and Architecture
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