Recycle your outdated business cards into a three dimensional math-art work with VIKTOR GENEL!
American standard business cards have a length/width ratio 3.5/2. It is a perfect proportion to allow all sorts of symmetry related manipulations. I’ve been asked if this relates to the golden ratio. The answer is – no. Close, but not quite…
The Golden Ratio: phi = (1+sqrt(5)/2 = 1.6180339887… For the proposed operations, the ratio must be Sqrt(3) = 1.732050807568877… It is the ratio between a side and a median of an equilateral triangle. American and Canadian business card ratio are 1.75 – the best! Being folded three times the cards can be used to model many of well-known polyhedrons, such as Plato’s solids, Archimedean solids and Johnson solids… Folding the cards once (along their diagonals) allows for the creation of “Jumbified” versions of the same solids. One of the most striking consequences of this is an ability of business cards to create a structurally sound model of such a remarkable polyhedron as a truncated octahedron or Mecon (Richard Buckminster Fuller has coined the term).
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