Draft:Square root of 10
Submission declined on 13 August 2022 by KylieTastic (talk).
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This draft has not been edited in over six months and qualifies to be deleted per CSD G13. Declined by KylieTastic 2 years ago. Last edited by Tali64^2 2 years ago. Reviewer: Inform author.
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Comment: I see no reason this is notable - also see previous discussion Wikipedia:Articles for deletion/Square root of 10 KylieTastic (talk) 15:57, 13 August 2022 (UTC)
- Comment: The term 'Square root of 10' redirs to 'Square root', and it's not immediately obvious to me why a new standalone article should be created to replace that redir. Is the intention to have articles on other non-perfect-squares as well, or is there something noteworthy about 10, which would justify this especially? DoubleGrazing (talk) 13:00, 13 August 2022 (UTC)
In mathematics, the square root of 10 is the positive real number that when multiplied by itself, gives the number 10. The approximation 117/37 (≈ 3.1621) can be used for the square root of 10. Despite having a denominator of only 37, it differs from the correct value by about 1/9000 (approx. 1.1×10−4).
It is an irrational algebraic number. The first sixty significant digits of its decimal expansion are:
As of December 2013, it numerical value in decimal has been computed to at least ten billion digits.[1]
Because of its closeness to the mathematical constant π, it was used as an approximation for it in some ancient texts.[2]
Continued fraction
√10 can be expressed as the continued fraction
![{\displaystyle [3;6,6,6,6,6,\ldots ]=3+{\cfrac {1}{6+{\cfrac {1}{6+{\cfrac {1}{6+{\cfrac {1}{6+\dots }}}}}}.}}}](/media/api/rest_v1/media/math/render/svg/ae279a7ca8b87674916ecdabd71ffe79f03353ae)
Uses
- In ancient times, √10 has been used as an approximation for π, especially in India and China.[2] According to William Alexander Myers, some Arab mathematicians calculated the circumference of a unit circle to be √10.[3]
- √10 has been used as a folding scale for slide rules, mainly because scale settings folded with the number can be changed without changing the result.[4]
- In 2018, mathematician David Fuller discovered that several physical relationships appeared to use √10 or an approximation of it instead of π.[5]
- Joseph Oswald Mauborgne demonstrated in his 1913 book Practical Uses of the Wave Meter in Wireless Telegraphy that as the capacity and inductance increase by factors of 10, the corresponding wavelength increases by factors of √10.[6]
- The equilibrium potential (in volts) of plasma with a Maxwellian velocity distribution is approximately its mean energy multiplied by √10.[7]
References
- ^ "Computations | Łukasz Komsta".
- ^ a b Arndt & Haenel 2006, p. 169.
- ^ Myers 1873, p. 11.
- ^ "Square Root of 10 Folded Scales" (PDF). www.osgalleries.org. Retrieved 14 August 2022.
- ^ }Giordano, Warren R. "Is the Universe Cheating at Math By Using the Square Root of 10 Instead of Pi (Revised Sept 11, 2018)" – via www.academia.edu.
{{cite journal}}: Cite journal requires|journal=(help) - ^ Mauborgne 1913, p. 66.
- ^ Krasovski, V. I. "CONCERNING SOME PROPERTIES OF DUST IN SPACE" – via apps.dtic.mil.
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