In Mathematics
666 is the sum of the first 36 natural numbers (i.e. ), and thus it is a triangular number.
Since 36 is both square and triangular, 666 is the sixth number of the form (sequence A037270 in OEIS) and the eighth number of the form (doubly triangular numbers) (sequence A002817 in OEIS).
The number of prime numbers up to 666 is 121, which is the square of 11, which is the number of prime numbers up to 36.
666 is an abundant number.
The harmonic mean of the decimal digits of 666 is (trivially — all repdigit natural numbers have this property) an integer: 3/(1/6 + 1/6 + 1/6) = 6, making 666 the 54th number with this property.
In base 10, 666 is a repdigit (and therefore a palindromic number) and a Smith number. A prime reciprocal magic square based on 1/149 in base 10 has a magic total of 666.
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The Roman numeral for 666, DCLXVI, has exactly one occurrence of all symbols whose value is less than 1000 (D=500, C=100, L=50, X=10, V=5, I=1).
(60 and 360 were used as bases in Babylonian mathematics, as in the degrees of a circle; 360=10x36 and 666 is the sum of the numbers from 1 to 36.)
666 is 1010011010 in the binary numeral system which is the same as its one's complement in reverse digit order.
666 is a member of the indices of prime Padovan numbers: 3, 4, 5, 7, 8, 14, 19, 30, 37, 84, 128, 469, 666, 1262, 1573, 2003, 2210, ... (sequence A112882 in OEIS).
The sine of the angle 666° multiplied by -2 is equal to the golden ratio:
Read more about this topic: 666 (number)
Famous quotes containing the word mathematics:
“It is a monstrous thing to force a child to learn Latin or Greek or mathematics on the ground that they are an indispensable gymnastic for the mental powers. It would be monstrous even if it were true.”
—George Bernard Shaw (1856–1950)
“Mathematics alone make us feel the limits of our intelligence. For we can always suppose in the case of an experiment that it is inexplicable because we don’t happen to have all the data. In mathematics we have all the data ... and yet we don’t understand. We always come back to the contemplation of our human wretchedness. What force is in relation to our will, the impenetrable opacity of mathematics is in relation to our intelligence.”
—Simone Weil (1909–1943)