From Wikipedia, the free encyclopedia
Natural number
48 (forty-eight ) is the
natural number following
47 and preceding
49 . It is four
dozens or one third of a
gross .
In mathematics
Forty-eight is the
double factorial of
6 ,
[1]
[2] a
highly composite number .
[3] Like all other multiples of 6, it is a
semiperfect number .
[4] 48 is the second 17-
gonal number .
[5]
48 is the smallest number with exactly ten divisors,
[6] and the first multiple of 12 not to be a sum of
twin primes .
There are 11 solutions to the equation
φ (x ) = 48, namely 65, 104, 105, 112, 130, 140, 144, 156, 168, 180 and 210. This is more than any integer below 48, making 48 a
highly totient number .
[7]
Since the greatest prime factor of 482 + 1 = 2305 is 461, which is clearly more than twice 48, 48 is a
Størmer number .
[8]
48 is a
Harshad number in decimal,
[9] as it is divisible by 4+8 = 12.
Riemann hypothesis
48 is the
floor and
nearest-integer value of the ninth
imaginary part of non-trivial
zeroes in the
Riemann zeta function (see,
Riemann hypothesis ).
[10]
[11]
Among the nine first such floor and
ceiling values, this is the
closest to an integer , differing from 48 by a value of around
+
0.0051508811671597279
…
{\displaystyle +{\text{ }}0.0051508811671597279\dots }
[12]
In science
Astronomy
In religion
The prophecies of 48 Jewish
prophets and 7 prophetesses
[13] were recorded in the
Tanakh for posterity.
According to the
Mishnah ,
Torah wisdom is acquired via 48 ways (
Pirkei Avoth 6:6).
In
Buddhism ,
Amitabha Buddha had made 48 great vows and promises to provide ultimate salvation to countless beings through countless eons, with benefits said to be available merely by thinking about his name with
Nianfo practice. He is thus hailed as "King of Buddhas" through such skillful compassion and became a popular and formal refuge figure in
Pureland Buddhism .
In music
Johann Sebastian Bach's
Well-Tempered Clavier is informally known as The Forty-Eight because it consists of a prelude and a fugue in each major and minor key, for a total of forty-eight pieces.
"48" is a song by
Sunny Day Real Estate .
"48" is a song by
Tyler, The Creator .
"Forty eight" is a song by
Truckfighters on their 2007 album, Phi.
"48 Hour Parole" is a song by the
Hollies .
"
48 Crash " is a song by Suzi Quatro.
Familiar 48 is an alternative pop/rock band formerly known as
Bonehead .
On Tool's album Ænima , there is a song named "
Forty-Six & 2 ", the sum of which is 48.
AKB48 Group is a Japanese female idol group.
In sports
48 is the total number of minutes in a full
NBA game.
In other fields
Forty-eight may also refer to:
See also
References
^
Sloane, N. J. A. (ed.).
"Sequence A006882 (Double factorials n!!: a(n) = n*a(n-2) for n > 1, a(0) = a(1) = 1)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^
Sloane, N. J. A. (ed.).
"Sequence A000165 (Double factorial of even numbers: (2n)!! = 2^n*n!)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^
Sloane, N. J. A. (ed.).
"Sequence A002182 (Highly composite numbers)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^
Sloane, N. J. A. (ed.).
"Sequence A005835 (Pseudoperfect (or semiperfect) numbers)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^
Sloane, N. J. A. (ed.).
"Sequence A051869 (17-gonal numbers)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^
Sloane, N. J. A. (ed.).
"Sequence A005179 (Smallest number with exactly n divisors)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^
Sloane, N. J. A. (ed.).
"Sequence A097942 (Highly totient numbers)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^
Sloane, N. J. A. (ed.).
"Sequence A005528 (Størmer numbers)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^
Sloane, N. J. A. (ed.).
"Sequence A005349 (Niven (or Harshad) numbers)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^
Sloane, N. J. A. (ed.).
"Sequence A013629 (Floor of imaginary parts of nontrivial zeros of Riemann zeta function)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^
Sloane, N. J. A. (ed.).
"Sequence A002410 (Nearest integer to imaginary part of n-th zero of Riemann zeta function)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^
Odlyzko, Andrew .
"The first 100 (non trivial) zeros of the Riemann Zeta function [AT&T Labs]" . Andrew Odlyzko: Home Page .
UMN CSE . Retrieved 2024-01-16 .
^
"How many prophets were there and who were they? - philosophy prophecy history prophets torah the bible the prophets" . Archived from
the original on 2007-08-10. Retrieved 2006-07-17 .
^
"Chinese Numerology: Lucky and Unlucky Numbers Meaning" . My Today's Horoscope . 2019-11-09. Retrieved 2021-09-20 .
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