48 (number)

← 47 48 49 →
← 40 41 42 43 44 45 46 47 48 49 → List of numbers Integers ← 0 10 20 30 40 50 60 70 80 90 →
Cardinal	forty-eight
Ordinal	48th (forty-eighth)
Factorization	24 × 3
Divisors	1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Greek numeral	ΜΗ´
Roman numeral	XLVIII, xlviii
Binary	1100002
Ternary	12103
Senary	1206
Octal	608
Duodecimal	4012
Hexadecimal	3016

48 (forty-eight) is the natural number following 47 and preceding 49. It is one third of a gross, or four dozens.

In mathematics

48 is a highly composite number, and a Størmer number. ^[1]

By a classical result of Honsberger, the number of incongruent integer-sided triangles of perimeter ${\displaystyle m}$ is given by the equations ${\displaystyle {\tfrac {m^{2}}{48}}}$ for even ${\displaystyle m}$, and ${\displaystyle {\tfrac {(m+3)^{2}}{48}}}$ for odd ${\displaystyle m}$. ^[2]

48 is the order of full octahedral symmetry, which describes three-dimensional mirror symmetries associated with the regular octahedron and cube.

There are 48 symmetries of a cube.

In other fields

Forty-eight may also refer to:

• In Chinese numerology, 48 is an auspicious number meaning 'determined to prosper', or simply 'prosperity', which is good for business. ^[3]
• '48 is a slang term in Palestinian Arabic for parts of Israel or Palestine not under the control of the State of Palestine. Arab people from those parts are colloquially known as 48-Arabs (Arabic: عرب ٤٨, romanized: ‘Arab Thamāniya wa-Arba‘īn).

References

1. Sloane, N. J. A. (ed.). "SequenceA002182(Highly composite numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
2. East, James; Niles, Ron (2019). "Integer polygons of given perimeter". Bulletin of the Australian Mathematical Society . 100 (1). Canberra: Australian Mathematical Society: 131–147. arXiv: 1710.11245 . doi:10.1017/S0004972718001612. MR   3977311. S2CID   119729735. Zbl   1420.52014.
3. "Chinese Numerology: Lucky and Unlucky Numbers Meaning". My Today's Horoscope. 2019-11-09. Retrieved 2021-09-20.