Golden Mean  Sheres

 Tetra Blocks


By Mary Moon

B.C. (approximate dates to 976 B.C.)

  • -50,000 counting
  • -25,000 Geometric design                             Paleolithic
  •   -3,000 Hieroglyphic numerals                     Egypt
  •   -2,800 Great Pyramid                                 1/2 octahedron form
  •   -2,400 Positional                                         Mesopotamia
  •      -600 Babylonian Art                                 Star Pentagon
  •      -500 Discovery near Padua of an Etruscan Dodecahedron stone
 Dawn of Greek Classical Geometry     (Mathematics)

 -585  Thales of Miletus deductive geometry; logic traveled to Egypt introduced "rope pulling" to the Greeks; Egyptian practice of measuring the land after annual Nile floods.
Thales elevated measurements from practical to philosophical logic
"not what we know, but how we know it" (scientific method).   
Mathematics defined "that which is learned".

 -540  Pythagorean arithmetic and geometry  (Italian coast) Harmonics/Music.
Pythagoreans were secretive and cultish.
Motto:  "All is number".
Discovered theory of proportions and constructed the "cosmic figures" or Regular Polyhedra.
They were partially interested in the pentagon and pentagram or the star pentagon which describes the "golden mean". They knew of the cube and octahedron (seen in minerals and crystals) and pentagonal dodecahedron. Did not know of the tetrahedron or icosahedron.
 -427  Birth of Plato.
Plato was not a mathematician but had the Academy in Athens and encouraged mathematics discoveries. Elevated math to "pure intelligence" and discouraged practical applications.  Academy motto "Let no one ignorant of geometry enter here".  Restricted geometric construction to the use of a straight edge and compass; the Academy originated the basic "liberal" education: arithmetic, music, geometry, astronomy  (quadravium).
-414  Theltetus, friend of Plato and student of the Academy who developed the theorems of the Five Platonic Solids. Proved there are only five possible.
The theorems appear in Euclid's Elements
-388  Plato visited the Pythagoreans and returned to Athens where the five regular polygons were developed and associated with natural elements: Tetrahedron=Fire, Octahedron=Air, Cuboctahedron=Earth, Icosahedron=Water, Dodecahedron=Universe.
 "God used it for the Whole" Written down in the Timeaus Platonic Dialogue.
-370  Aristotle: Greatest scholar of all time and started the Lyceum School.  He was astudent of Plato and tutor of Alexander the Great.
-332  Euclid of Alexandrea in 300 B.C. produced the greatest math book of all times called The Elements. Thirteen Books in all. The last book contains the "Cosmic Figures" (Platonic Solids) and describes how they can be constructed within spheres.  This would later inspire Kepler's cosmology.
-306  Ptolemy: Started the School of Alexandria also called The Museum or The Library located in Alexandria Egypt (Part of Greece at the time).  The seat of Greek learning for the next nine hundred years.
-287  Archimedes: Considered the greatest mathematician of Antiquity.  Killed by Roman soldier 212B.C. He was called on to invent defensive weapons  against Rome.  He preferred pure mathematics to practical invention. Discovered the 13(?) semi-regular polyhedra: convex polyhedron whose
faces are all regular polygons but not the same.  Finite set.  Many of Archimedes' works are lost. The Method, which included the theorems for the Archimedes Solids are lost from approx. 11th Century to 1906 when it was discovered in Constantinopal.
-44  Death of Julius Ceaser.

If you are interested in this topic, see the full version of our timeline (200 A.D. to present day) in the members area of this site.

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