7の平方根

ウィキペディア

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)

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、 $r^{2}=r\times r=7$

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 and 1852, 3 in 1835, 6 in 1808, and 7 in 1797. An extraction by Newton's method (approximately) was illustrated in 1922, concluding that it is 2.646 "to the nearest thousandth".

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

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

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、 ${\sqrt {7}}\,$

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 ${\sqrt {7}}\,$ カテゴリ