Posts Tagged ‘Regular Solids’

There can be an infinite number of polygons, but only five regular solids.  Four of the solids were associated with earth, fire, air and water.  The cube for example represented earth.  These four elements, they thought, make up terrestrial matter.  So the fifth solid they mystically associated with the Cosmos.  Perhaps it was the substance of the heavens.  This fifth solid was called the dodecahedron.  Its faces are pentagons, twelve of them.  Knowledge of the dodecahedron was considered too dangerous for the public.  Ordinary people were to be kept ignorant of the dodecahedron.  In love with whole numbers, the Pythagoreans believed that all things could be derived from them.  Certainly all other numbers.
So a crisis in doctrine occurred when they discovered that the square root of two was irrational.  That is: the square root of two could not be represented as the ratio of two whole numbers, no matter how big they were.  “Irrational” originally meant only that.  That you can’t express a number as a ratio.  But for the Pythagoreans it came to mean something else, something threatening, a hint that their world view might not make sense, the other meaning of “irrational”.
   —    Carl Sagan
On This Day In:
2020 The Butterflies Are In Trouble
2019 The Deep Center
2018 Oh, Heaven (Too)
2017 Now Pausing Makes Sense
2016 Just Spicy
Only One Part
2015 Positive Acts Of Creation
2014 One Thing Is Clear
2013 Corrections
See Greatness
2012 Gemutlichkeit
2011 Back On The Asphalt

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