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45 (number)

From Wikipedia, the free encyclopedia
Natural number
← 4445 46 →
Cardinalforty-five
Ordinal45th
(forty-fifth)
Factorization32 × 5
Divisors1, 3, 5, 9, 15, 45
Greek numeralΜΕ´
Roman numeralXLV,xlv
Binary1011012
Ternary12003
Senary1136
Octal558
Duodecimal3912
Hexadecimal2D16

45 (forty-five) is thenatural number following44 and preceding46.

In mathematics

[edit]
45 as the difference of two nonzero squares (in orange)

45 is acomposite number and aStørmer number.

Forty-five is conjectured fromRamsey numberR(5,5){\displaystyle R(5,5)}.[1][2]

ϕ(45)=ϕ(σ(45)){\displaystyle \phi (45)=\phi (\sigma (45))}[3]

Forty-five degrees is half of a right angle (90°).

In music

[edit]
45rpmgramophone record

In other fields

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  • Guns or ammunition of.45 caliber. In the United States, "45" is often a reference to one of two specific .45 caliber cartridges—the.45 Colt or the.45 ACP.
  • In years of marriage, thesapphirewedding anniversary.
  • Issue 45 ofThe North Briton was thought to be seditious but its publisher,John Wilkes, was celebrated as a champion of liberty. The number 45 was used as a symbol of support for him. Banquets were held with a theme of 45 while many items were produced showing the number or featuring it in some way. For example, a wig was produced with 45 curls.[4]

References

[edit]
  1. ^Sloane, N. J. A. (ed.)."Sequence A120414 (Conjectured Ramsey number R(n,n).)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2023-02-17.
  2. ^Sloane, N. J. A. (ed.)."Sequence A212954 (Triangle read by rows: two color Ramsey numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2022-11-25.
  3. ^Sloane, N. J. A. (ed.)."Sequence A006872".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  4. ^Arthur Hill Cash (2007),John Wilkes: The Scandalous Father of Civil Liberty, Yale University Press, p. 219,ISBN 978-0-300-12363-0
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