Cannabaceae

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In arithmetic and algebra the eighth power of a number n is the result of multiplying eight instances of n together. So:

n8 = n × n × n × n × n × n × n × n.

Eighth powers are also formed by multiplying a number by its seventh power, or the fourth power of a number by itself.

The sequence of eighth powers of integers is:

0, 1, 256, 6561, 65536, 390625, 1679616, 5764801, 16777216, 43046721, 100000000, 214358881, 429981696, 815730721, 1475789056, 2562890625, 4294967296, 6975757441, 11019960576, 16983563041, 25600000000, 37822859361, 54875873536, 78310985281, 110075314176, 152587890625 ... (sequence A001016 in the OEIS)

In the archaic notation of Robert Recorde, the eighth power of a number was called the "zenzizenzizenzic".[1]

Algebra and number theory[edit]

Polynomial equations of degree 8 are octic equations. These have the form

The smallest known eighth power that can be written as a sum of eight eighth powers is[2]

The sum of the reciprocals of the nonzero eighth powers is the Riemann zeta function evaluated at 8, which can be expressed in terms of the eighth power of pi:

(OEIS: A013666)

This is an example of a more general expression for evaluating the Riemann zeta function at positive even integers, in terms of the Bernoulli numbers:

Physics[edit]

In aeroacoustics, Lighthill's eighth power law states that the power of the sound created by a turbulent motion, far from the turbulence, is proportional to the eighth power of the characteristic turbulent velocity.[3][4]

The ordered phase of the two-dimensional Ising model exhibits an inverse eighth power dependence of the order parameter upon the reduced temperature.[5]

The Casimir–Polder force between two molecules decays as the inverse eighth power of the distance between them.[6][7]

See also[edit]

References[edit]

  1. ^ Womack, David (2015). "Beyond tetration operations: their past, present and future". Mathematics in School. 44 (1): 23–26. JSTOR 24767659.
  2. ^ Quoted in Meyrignac, Jean-Charles (2001-02-14). "Computing Minimal Equal Sums Of Like Powers: Best Known Solutions". Retrieved 2019-12-18.
  3. ^ Lighthill, M. J. (1952). "On sound generated aerodynamically. I. General theory". Proc. R. Soc. Lond. A. 211 (1107): 564–587. Bibcode:1952RSPSA.211..564L. doi:10.1098/rspa.1952.0060. S2CID 124316233.
  4. ^ Lighthill, M. J. (1954). "On sound generated aerodynamically. II. Turbulence as a source of sound". Proc. R. Soc. Lond. A. 222 (1148): 1–32. Bibcode:1954RSPSA.222....1L. doi:10.1098/rspa.1954.0049. S2CID 123268161.
  5. ^ Kardar, Mehran (2007). Statistical Physics of Fields. Cambridge University Press. p. 148. ISBN 978-0-521-87341-3. OCLC 1026157552.
  6. ^ Casimir, H. B. G.; Polder, D. (1948). "The influence of retardation on the London-van der Waals forces". Physical Review. 73 (4): 360. Bibcode:1948PhRv...73..360C. doi:10.1103/PhysRev.73.360.
  7. ^ Derjaguin, Boris V. (1960). "The force between molecules". Scientific American. 203 (1): 47–53. Bibcode:1960SciAm.203a..47D. doi:10.1038/scientificamerican0760-47. JSTOR 2490543.


source: https://en.wikipedia.org/wiki/Eighth_power

One thought on “Cannabaceae”

  1. Well, that’s interesting to know that Psilotum nudum are known as whisk ferns. Psilotum nudum is the commoner species of the two. While the P. flaccidum is a rare species and is found in the tropical islands. Both the species are usually epiphytic in habit and grow upon tree ferns. These species may also be terrestrial and grow in humus or in the crevices of the rocks.
    View the detailed Guide of Psilotum nudum: Detailed Study Of Psilotum Nudum (Whisk Fern), Classification, Anatomy, Reproduction

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