7の平方根

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7の平方根

出典: フリー百科事典『ウィキペディア（Wikipedia）』 (2023/12/13 17:40 UTC 版)

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The rectangle that bounds an equialateral triangle of side 2, or a regular hexagon of side 1, has size square root of 3 by square root of 4, with a diagonal of square root of 7.

A Logarex system Darmstadt slide rule with 7 and 6 on A and B scales, and square roots of 6 and of 7 on C and D scales, which can be read as slightly less than 2.45 and somewhat more than 2.64, respectively

7の平方根（ななのへいほうこん、英: square root of 7）は、平方して7となる実数である。すなわち、${\displaystyle r^{2}=r\times r=7}$

Explanation of how to extract the square root of 7 to 7 places and more, from Hawney, 1797

The extraction of decimal-fraction approximations to square roots by various methods has used the square root of 7 as an example or exercise in textbooks, for hundreds of years. Different numbers of digits after the decimal point are shown: 5 in 1773^[4] and 1852,^[5] 3 in 1835,^[6] 6 in 1808,^[7] and 7 in 1797.^[8] An extraction by Newton's method (approximately) was illustrated in 1922, concluding that it is 2.646 "to the nearest thousandth".^[9]

For a family of good rational approximations, the square root of 7 can be expressed as the continued fraction

${\displaystyle [2;1,1,1,4,1,1,1,4,\ldots ]=2+{\cfrac {1}{1+{\cfrac {1}{1+{\cfrac {1}{1+{\cfrac {1}{4+{\cfrac {1}{1+\dots }}}}}}}}}}.}$

Root rectangles illustrate a construction of the square root of 7 (the diagonal of the root-6 rectangle).

平面幾何学において、${\displaystyle {\sqrt {7}}\,}$

Scan of US dollar bill reverse with root 7 rectangle annotation

現行のアメリカ合衆国1ドル紙幣の裏にある大きな内箱は長さと幅の比が${\displaystyle {\sqrt {7}}\,}$で、対角線の長さが6.0インチである（測定精度の範囲内で）^[15]。

関連項目

• 平方根
• 2の平方根
• 3の平方根
• 5の平方根
• 6の平方根

脚注

1. ^ Darby, John (1843). The Practical Arithmetic, with Notes and Demonstrations to the Principal Rules, .... London: Whittaker & Company. p. 172. https://books.google.com/books?id=lfteAAAAcAAJ&pg=PA172 2022年3月27日閲覧。 
2. ^ Sloane, N.J.A. (ed.). "Sequence A010465 (Decimal expansion of square root of 7)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. {{cite web}}: Cite webテンプレートでは|access-date=引数が必須です。 (説明)
3. ^ Robert Nemiroff and Jerry Bonnell (2008). The square root of 7. https://www.gutenberg.org/ebooks/631 2022年3月25日閲覧。 
4. ^ Ewing, Alexander (1773). Institutes of Arithmetic: For the Use of Schools and Academies. Edinburgh: T. Caddell. p. 104. https://books.google.com/books?id=rUvzudeLHbQC&pg=PA104 
5. ^ Ray, Joseph (1852). Ray's Algebra, Part Second: An Analytical Treatise, Designed for High Schools and Academies, Part 2. Cincinnati: Sargent, Wilson & Hinkle. p. 132. https://books.google.com/books?id=nY4AAAAAMAAJ&pg=PA132 2022年3月27日閲覧。 
6. ^ Bailey, Ebenezer (1835). First Lessons in Algebra, Being an Easy Introduction to that Science.... Russell, Shattuck & Company. pp. 212–213. https://books.google.com/books?id=e33H8RjDxocC&pg=PA212 2022年3月27日閲覧。 
7. ^ Thompson, James (1808). The American Tutor's Guide: Being a Compendium of Arithmetic. In Six Parts. Albany: E. & E. Hosford. p. 122. https://books.google.com/books?id=8R8AAAAAMAAJ&pg=PA122 2022年3月27日閲覧。 
8. ^ Hawney, William (1797). The Complete Measurer: Or, the Whole Art of Measuring. In Two Parts. Part I. Teaching Decimal Arithmetic ... Part II. Teaching to Measure All Sorts of Superficies and Solids ... Thirteenth Edition. To which is Added an Appendix. 1. Of Gaging. 2. Of Land-measuring. London. pp. 59–60. https://books.google.com/books?id=9eSLbslYbpAC&pg=PA60 2022年3月27日閲覧。 
9. ^ George Wentworth, David Eugene Smith, Herbert Druery Harper (1922). Fundamentals of Practical Mathematics. Ginn and Company. p. 113. https://books.google.com/books?id=sqMXAAAAYAAJ&pg=PA113 2022年3月27日閲覧。 
10. ^ “Pell's Equation II”. uconn.edu. 2022年3月17日閲覧。
11. ^ Jay Hambidge (1920). Dynamic Symmetry: The Greek Vase (Reprint of original Yale University Press ed.). Whitefish, MT: Kessinger Publishing. pp. 19–29. ISBN 0-7661-7679-7. https://archive.org/details/bub_gb_Qq4gAAAAMAAJ. "Dynamic Symmetry root rectangles." 
12. ^ Matila Ghyka (1977). The Geometry of Art and Life. Courier Dover Publications. pp. 126–127. ISBN 9780486235424. https://archive.org/details/geometryofartlif00mati 
13. ^ Fletcher, Rachel (2013). Infinite Measure: Learning to Design in Geometric Harmony with Art, Architecture, and Nature. George F Thompson Publishing. ISBN 978-1-938086-02-1. https://infinitemeasure.com/publications/infinite-measure/ 
14. ^ Blackwell, William (1984). Geometry in Architecture. Key Curriculum Press. p. 25. ISBN 9781559530187. https://books.google.com/books?id=AJFZAAAAYAAJ&q=%22square+root+of+seven%22 2022年3月26日閲覧。 
15. ^ McGrath, Ken (2002). The Secret Geometry of the Dollar. AuthorHouse. pp. 47–49. ISBN 9780759611702. https://books.google.com/books?id=1BgpDwAAQBAJ&pg=PA48 2022年3月26日閲覧。 

表 話 編 歴 代数的数
代数的整数 チェビシェフ分点（英語版） 作図可能数 コンウェイの定数（英語版） (λ) アイゼンシュタイン整数 ガウス整数 黄金数 (φ) クンマー環 ペロン数（英語版） ピゾ–ビジャヤラガバン数（英語版） 二次の無理数（英語版） 有理数 (${\displaystyle \mathbb {Q} }$) 1の冪根 サレム数 白銀比 (δS) √2 √3 √5 √6 √7 3√2 12√2		ℚ