2012 = 22 x 503.
2012, 2013, 2014, and 2015 are each the product of three prime numbers.
2012! has a square number of digits (5776 = 762).
20122 = 4048144 and 4418404 = 21022.
2012 and its square (4048144) use only the digits 0, 1, 2, 4, and 8.
2012 is a year in which there are five Wednesdays in the month of February.
2012 is a blue moon year.
The end of the "longest period" (Long Count) Mayan calendar known to exist is said to be December 21, 2012.
2012 is the 100th anniversary of the sinking of the RMS Titanic. It is also the centennial of the birth of Alan Turing.
Algunas propiedades analíticas del número 2012:
ReplyDeleteEcuación Pell: 12150478072 - 2012•270881522 = 1
Ver http://math.fau.edu/richman/pell-m.htm
Formas cuadráticas complejas: Polinomio mínimo: z^2-Sz+P= 0
N(a+b(-D)^(1/2) = x^2+Dy^2=41^2+331*1^2
P=(41+1(-331)^(1/2)(41-1(-331)^(1/2)=2012
S=(41+1(-331)^(1/2)+(41-1(-331)^(1/2)=82
PM: z^2-82z+2012=0 => z=41+-(331)^(1/2)
Logaritmo discreto:
47^37= 43(mód.2012)
ver http://www.alpertron.com.ar/DILOG.HTM
Otras propiedades muy variadas las podrán encontrar en
http://hojamat.es/parra/prop2012.pdf
Thanks for their attention. I wish you a Merry Christmas and a Happy New Year
Rafael Parra Machío