Let's not forget that the answer to the “ultimate question of life, the universe, and everything, is the number 42!"
Although made famous in 1979 by author Douglas Adams in his popular science-fiction novel The Hitchhiker’s Guide to the Galaxy....... A subsequent article in the magazine Scientific American (
www.scientificamerican.com/article/for-math-fans-a-hitchhikers-guide-to-the-number-42) also notes that:
In ancient Egyptian mythology, during the judgment of souls, the dead had to declare
before 42 judges that they had not committed any of 42 sins.
The marathon distance of just over 42 kilometers corresponds to the legend of how far the ancient Greek messenger Pheidippides traveled between Marathon and Athens to announce victory over the Persians in 490 B.C. The fact that the kilometer had not yet been defined at that time only makes the connection all the more astonishing.
Ancient Tibet had
42 rulers. Nyatri Tsenpo, who reigned around 127 B.C., was the first. And Langdarma, who ruled from 836 to 842 A.D. (i.e., the 42nd year of the ninth century), was the last.
The Gutenberg Bible, the first book printed in Europe, has 42 lines of text per column and is also called the “Forty-Two-Line Bible.”
In the binary system, or base 2, 42 is written as 101010, which is pretty simple and, incidentally, prompted a few fans to hold parties on October 10, 2010 (10/10/10).
42 is also the answer to the question “What do you get if you multiply six by nine?” That idea seems absurd because 6 x 9 = 54. But in base 13, the number expressed as “42” is equal to (4 x 13) + 2 = 54. Not so absurd after all.
The number is the sum of the first three odd powers of two—that is, 2^1 + 2^3 + 2^5 = 42. It is an element in the sequence a(n), which is the sum of n odd powers of 2 for n > 0. The sequence corresponds to entry A020988 in The On-Line Encyclopedia of Integer Sequences (OEIS), created by mathematician Neil Sloane.
In base 2, the nth element may be specified by repeating 10 n times (1010 ... 10). The formula for this sequence is a(n) = (2/3)(4n – 1). As n increases, the density of numbers tends toward zero, which means that the numbers belonging to this list, including 42, are exceptionally rare.
The number 42 is the sum of the first two nonzero integer powers of six—that is, 61 + 62 = 42.
The sequence b(n), which is the sum of the powers of six, corresponds to entry A105281 in OEIS. It is defined by the formulas b(0) = 0, b(n) = 6b(n – 1) + 6. The density of these numbers also tends toward zero at infinity - therefore also exceedingly rare!
Forty-two is a Catalan number. These numbers are extremely rare, much more so than prime numbers: only 14 of the former are lower than one billion. Catalan numbers were first mentioned, under another name, by Swiss mathematician Leonhard Euler, who wanted to know how many different ways an
n-sided convex polygon could be cut into triangles by connecting vertices with line segments. The beginning of the sequence (
A000108 in OEIS) is 1, 1, 2, 5, 14, 42, 132.... The
nth element of the sequence is given by the formula
c(
n) = (2
n)! / (
n!(
n + 1)!). And like the two preceding sequences, the density of numbers is null at infinity.
The article goes further, so feel free to explore the wonders of 42.
