April 28, 2011

• String, Straightedge, and Shadow

   

  

  Storytelling is the most powerful way to put ideas into the world today.

  —Robert McKee

  Facts and theorems can be difficult to swallow.  They often get gunked up in the throat, remain lodged in the esophagus, useless for nourishment or growth.  But stories!  Stories get gulped down with eagerness and along with them much useful knowledge is digested.  Julia E. Diggins tells the compelling story of geometry in String, Straight-Edge, and Shadow.  Written for children, it would be beneficial to anyone interested in learning geometry. 

  They used the string to trace a circle, to lay off a right angle, to stretch a straight line.
  They used as a straightedge anything else with which they could draw a straight line.
  They came to realize that shadows are the sun’s handwriting upon the earth to tell the
  secrets of order in the universe.

  Diggin’s story would be a great stand-alone read; individual chapters, however, could supplement studies of Mesopotamia, Egypt, Babylon, or Greece.  The solutions that geometry offers are told in the context of the problems people faced.  In the question of ancient property rights and surveying farmer’s fields, boundaries could not be casually (by freehand) drawn.  They needed to know how to trace an accurate right-angle corner.  The answer is in roper-stretchers, knotted rope, stakes…and the 3-4-5 right triangle.  Corydon Bell’s illustrations make geometry easier to understand.  What a pleasant introduction to Thales, Pythagorus, Eudoxus, Archimedes and Eratosthenes. 

   

  You can read sections of the book here,  here and here.  I leave with you the opening quote of this book, from Plato.
  
  

  But by beauty of shape
  I want you to understand
  not what the multitude generally
  means by this expression,
  like the beauty of living beings
  or of paintings representing them,
  but
  something alternatively rectilinear and circular,
  and the surfaces and solids
  which one can produce
  from the rectilinear and circular
  with compass, set square, and rule.
  For these things are not like the others,
  conditionally beautiful,
  but are beautiful in themselves.

  ~ Plato

  • 1:55 pm
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