The Pythagoreans and Figurate Numbers

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The PythagoreansandFigurate Numbers
Tamara Davis MTH 4960 June 1, 2006
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Pythagoreans

• Four parts of Mathematics
• Music
• Arithmetic (Arithmetica)
• Number Theory according to the Ancient Greeks
• Astronomy
• Geometry
• Known as the quadrivium

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Pythagoreans
Number Mysticism

• Natural numbers was the key to the universe.
• Everything was composed of numbers.
• The explanation of objects existence could only
  be found in numbers.

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Pythagoreans
Number Mysticism

• Numerical Attributes

Number Property/Attribute
1 monad (unity)
2 dyad (diversity, opinion)
3 triad (harmonyunitydiversity)
4 (Justice or Retribution)
5 (Marriage)
6 (Creation)
10 tetracytys, (Universe)
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Pythagoreans
Number Mysticism

• Tetracyts (10) was the holiest number.

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Pythagoreans

1
2
3
4
1
0



Represents all Dimensions
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Pythagoreans

• Do these look familiar?

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Pythagoreans
Figurate Numbers

• Are a sequence of numbers that can be
  represented by a regular geometrical arrangement
  of equally spaced points.
• If the arrangement forms a regular polygon, they
  are called Polygonal Numbers.

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Pythagoreans
Figurate Numbers
Triangular Numbers
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Pythagoreans
Figurate Numbers
Square Numbers
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Pythagoreans
Figurate Numbers
Pentagonal Numbers
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Pythagoreans
Figurate Numbers
Hexagonal Numbers
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Pythagoreans
Figurate Numbers

• You can also form other shapes, such as
  three-dimensional solids.

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Pythagoreans

• First to
• to bring mysticism to numbers numerology.
• to study and analyze number theory / figurate
  numbers.
• understand the universe through mathematics

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• The Pentagram was the mystical symbol for the
  Pythagorean order.
• They saw in the Pentagram a mathematical
  perfectionphi also known as the Golden Ratio
  (1.61803399 )

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f 1.61803399
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Pythagoreans

• Were it not for number and its nature, nothing
  that exists would be clear to anybody either in
  itself or in its relation to other
  thingsYou can observe the power of
  number exercising itselfin all acts and
  the thoughts of men, in all handicrafts
  and music.
• Pythagorean Philolaus (425 B.C.E.)

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Work Cited

• Allen, Don Pythagoras and the Pythagoreans
  Feb. 6, 1997 lthttp//www.math.tamu.edu/don.alle
  n/history/pythag/pythag.htmlgt.
• archytech.org The History of Pythagoras and his
  Theorem Jun. 9, 2003 lthttp//www.arcytech.org/
  java/pythagoras/history.htmlgt.
• Bunt, Jones, and Bedient The Historical Roots of
  Elementary Mathematics Dover Publications,
  Inc. New York 1988 pp. 71-83.
• Math Gym Pythagoras Number Mathgym.com May
  2006 lthttp//www.mathgym.com.au/history/pythagor
  as/pythnum.htmgt.
• Weisstein, Eric W. Figurate Numbers
  MathWorld-A Wolfram Web Resource 1999
  lthttp//mathworld.wolfram.com/FigurateNumber.htmlgt
  .