Monday, October 13, 2008

The Rule of Threes

(Content borrowed from the useful, if not always entirely accurate Wikipedia)

The rule of three is a principle in English writing that suggests that things that come in threes are inherently funnier, (Should be!!) more satisfying, (definitely!) or more effective than other numbers of things...There were three musketeers, three little pigs, three billy goats Gruff, Goldilocks and the three bears, and Three Stooges.

A series of three is often used to create a progression in which the tension (I see a lot of that!) is created, then built up, and finally released.

Should be an awesome family vacation next summer as our family grows and grows and grows!

  • Three is the first odd prime number and the second smallest prime.
  • Three is both the first Fermat prime (22n + 1) and the first Mersenne prime (22 − 1), as well as the first lucky prime.
  • Three is the second Sophie Germain prime, the second Mersenne prime exponent, the second factorial prime (2! + 1), the second Lucas prime, the second Stern prime.
  • Three is the first unique prime due to the properties of its reciprocal.
  • Three is the aliquot sum of one number, the square number 4 and is the base of the 3-aliquot tree.
  • Three is the third Heegner number.
  • Three is the second triangular number and it is the only prime triangular number.
  • Three is the only prime which is one less than a perfect square. Any other number which is n2 − 1 for some integer n is not prime, since it is (n − 1)(n + 1). This is true for 3 as well, but in its case one of the factors is 1.
  • Three non-collinear points determine a plane and a circle.
  • Three is the fourth Fibonacci number and the third that is unique.
  • In the Perrin sequence, 3 is both the zeroth and third Perrin numbers.
  • Three is the fourth open meandric number.
  • Vulgar fractions with 3 in the denominator have a single digit repeating sequences in their decimal expansions, (.000..., .333..., .666...)
  • A natural number is divisible by three if the sum of its digits in base 10 is divisible by 3. For example, the number 21 is divisible by three (3 times 7) and the sum of its digits is 2 + 1 = 3. Because of this, the reverse of any number that is divisible by three (or indeed, any permutation of its digits) is also divisible by three. For instance, 1368 and its reverse 8631 are both divisible by three (and so are 1386, 3168, 3186, 3618, etc..).
  • A triangle is the most durable shape possible, the only "perfect" figure which if all endpoints have hinges will never change its shape unless the sides themselves are bent.
  • 3 is the only integer between e and π.
  • Three of the five regular polyhedra have triangular faces — the tetrahedron, the octahedron, and the icosahedron.
  • Three of the five regular polyhedra have vertices where three faces meet — the tetrahedron, the hexahedron (cube), and the dodecahedron.
  • Three different types of polygons comprise the faces of the five regular polyhedra — the triangle, the quadrilateral, and the pentagon.
  • There are only three distinct 4×4 panmagic squares.
  • Only three tetrahedral numbers are also perfect squares.


Meghan Wier
Author Writer Web Consultant

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