Wednesday, July 7, 2010

12

12 = 22 x 3.

12 is the sum of the first three even integers and the sum of thee consecutive odd integers: 12 = 2 + 4 + 6 = 3 + 4 + 5.

A regular dodecahedron has a regular pentagon on each of its 12 faces.


12 has a unique representation as a sum of three squares: 12 = 22 + 22 + 22.

12 is the number of integer partitions of 11 into distinct parts.

12 is 22 in base 5.

There are 12 ways to arrange eight queens on a chessboard so that no queen can capture any other queen (not counting rotations and reflections as being different). Can you find one of these chessboard arrangements?

12 is a dozen. There are 12 months in a year and 12 inches in a foot; 12 o'clock is midday or midnight. There are 12 signs of the Zodiac, 12 apostles, and typically 12 people in a jury.

Source: Phillips, R. 1994. Numbers: Facts, Figures and Fiction. Cambridge University Press.

2 comments:

Anonymous said...

12: Otras representaciones
12: 5^2+12^2=13^2
12: 12^2+16^2=20^2
12: 12^2+35^2=37^2
12=2^4-2^2=3^1+3^2=4^2-4^1
12=7^3+10^3-11^3
12^2=10^3-8^3-7^3-1^3
12^3=9^3+10^3-1^3
12^5=4^5+5^5+6^5+7^5+9^5+11^5
12*12=144 y 22*21=441
2^12+2^12+3^12 es primo seg├║n
http://primes.utm.edu/curios
12*2^12-12-1 es primo segun
http://isthe.com/tech/math/primes
12+-1 es primo ya que 11 y 13 son primos.
12 es el numero atomico del magnesio
12 tiene como norma (7+2*(12)^(1/2)*(7-2*(12)^(1/2)=1 cuya representaci├│n es 7^2-12*2^2=1
12=Q^5+1/Q+1/Q^3+1/Q^6 donde Q=Phi la Divina Proporcion que tiene como valor Q=(1/2*(1+(5)^(1/2)= 1,6180339887...
Rafael Parra de Barcelona

Anonymous said...

Otras propiedades del numero 12:
12^2-4^2=2^7
12^3-4^3=13*2^7
12^4-4^4=5*2^12
12^5-4^5=11^2*2^11
12^6-4^6=7*13*2^15
12^7-4^7=1093*2^15
12^8-4^8=5*41*2^21
12^9-4^9=13*757*2^19
La expresion 5^n-12 genera una importante cantidad de primos
-7,-2,3,13,23,43,53,73,83,103,113, 163,173,193,223,233,263,283,293, 313,353,373,383,433,443,463,503, 523,563,593,613,643,653,673,683, 733, entre otros
Rafael Parra de Barcelona