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）』 (2024/09/16 15:23 UTC 版)

この項目「7の平方根」は途中まで翻訳されたものです。（原文：en:Square root of 7 (08:56, 15 January 2023 (UTC))） 翻訳作業に協力して下さる方を求めています。ノートページや履歴、翻訳のガイドラインも参照してください。要約欄への翻訳情報の記入をお忘れなく。（2023年1月）

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${\displaystyle {\sqrt {7}}\,}$ カテゴリ