Tessellations

For my blog, I decide to look some stuff up about tessellations - even though they may seem like a very elementary concept, I enjoy their artistic aspects. Thus, here's an answer to your question of "Why are there only three regular polygons that tessellate?" So, a regular tessellation is periodic (repeated translations of polygons) and uniform (same type of polygons at each vertex), composed of congruent regular polygons. Apparently only three regular tessellations exist (triangle, square, and hexagon) and that's because these polygons are the only ones that have interior angles that divide evenly into 360 degrees. To find an interior angle of a regular polygon, you use the formula: a = 180 - 360/n. Also, "of the regular polygons, only triangles, squares, hexagons, octagons, and dodecagons can be used for tiling around a common vertex because of the angel value." (http://www.beva.org/math323/asgn5/tess/regpoly.htm)

Speaking of the artsy side, I think it's pretty beautiful how we can apply math to things such as architectural design, not just architectural structure.   I enjoyed reading this quite a bit! http://www.ysjournal.com/article.asp?issn=0974-6102;year=2009;volume=2;issue=7;spage=35;epage=46;aulast=Khaira Apparently people are really into tessellations and origami, too. Image sources: http://origamiblog.com/origami-tessellations-islamic-design/2009/06/08 http://vi.sualize.us/i_w_a_m_o_o_r_c_h_i_t_e_c_t_u_r_e_voussoir_wooden_art_tessellations_clouds_installation_picture_6rgT.html