User:Lilyuserin/SVG/tbl

Tabelle • Tabellenseite bearbeiten

Zahlenwert	ungefähr	Kettenbruch	sin	cos	Näherung
${\frac {1}{2}}(1+{\sqrt {5}})=\Phi$	$\approx 1.61803398875$	$[1;{\overline {1}}]$	$1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,\ldots$ ${\frac {8}{5}}\diamond {\frac {13}{8}}\diamond {\frac {21}{13}}\diamond {\frac {34}{21}}\diamond \ldots$
${\frac {1}{2}}({\sqrt {5}}-1)=\Phi -1$ $={\frac {1}{\Phi }}$	$\approx 0.61803398875$	$[0;{\overline {1}}]$	${\frac {5}{8}}\diamond {\frac {8}{13}}\diamond {\frac {13}{21}}\diamond {\frac {21}{34}}\diamond \ldots$
${\frac {1}{4}}({\sqrt {5}}-1)={\frac {\Phi -1}{2}}$ $={\frac {1}{2\Phi }}$	$\approx 0.3090169947$	$[0;3,{\overline {4}}]$	$18^{o}={\frac {\pi }{10}}$	$72^{o}={\frac {2\pi }{5}}$	${\frac {4}{13}}\diamond {\frac {17}{55}}\diamond {\frac {72}{233}}$
${\frac {\sqrt {2}}{4}}{\sqrt {5-{\sqrt {5}}}}$ $={\sqrt {{\frac {5}{8}}-{\frac {\sqrt {5}}{8}}}}$ $={\frac {1}{2}}{\sqrt {{\frac {1}{2}}(5-{\sqrt {5}})}}$	$\approx 0.58778525229$	$[0;1,1,2,2,1,6,1,56,\ldots ]$	$36^{o}={\frac {\pi }{5}}$	$54^{o}={\frac {3\pi }{10}}$	${\frac {4379}{7450}}\diamond {\frac {77}{131}}$
${\frac {1}{4}}(1+{\sqrt {5}})={\frac {\Phi }{2}}$	$\approx 0.8090169943749474$	$[0;1,{\overline {4}}]$	$54^{o}={\frac {3\pi }{10}}$	$36^{o}={\frac {\pi }{5}}$	${\frac {305}{377}}\diamond {\frac {72}{89}}\diamond {\frac {17}{21}}$
${\frac {\sqrt {2}}{4}}{\sqrt {5+{\sqrt {5}}}}$ $={\sqrt {{\frac {5}{8}}+{\frac {\sqrt {5}}{8}}}}$ $={\frac {1}{2}}{\sqrt {{\frac {1}{2}}(5+{\sqrt {5}})}}$	$\approx 0.9510565162951536$	$[0;1,19,2,3,6,5,1,1,1,\ldots ]$	$72^{o}={\frac {2\pi }{5}}$	$18^{o}={\frac {\pi }{10}}$	${\frac {855}{899}}\diamond {\frac {136}{143}}\diamond {\frac {39}{41}}$
			$108^{o}={\frac {3\pi }{5}}$	$-162^{o}=-{\frac {9\pi }{10}}$
${\frac {{\sqrt {6}}-{\sqrt {2}}}{4}}$ $={\frac {{\sqrt {3}}-1}{2{\sqrt {2}}}}$	$\approx 0.2588190$	$[0;3,1,6,2,1,30,5,2,9,3,1,\ldots ]$	$15^{o}={\frac {\pi }{12}}$	$75^{o}={\frac {5\pi }{12}}$	${\frac {22}{85}}\diamond {\frac {675}{2608}}$
${\frac {{\sqrt {6}}+{\sqrt {2}}}{4}}$ $={\frac {{\sqrt {3}}+1}{2{\sqrt {2}}}}$	$\approx 0.96592582$	$[0;1,28,2,1,7,21,1,8,1,\ldots ]$	$75^{o}={\frac {5\pi }{12}}$	$15^{o}={\frac {\pi }{12}}$	${\frac {652}{675}}\diamond {\frac {85}{88}}$
${\frac {\sqrt {2}}{2}}$	$\approx 0.7071067811865475$	$[0;1,{\overline {2}}]$	$45^{o}={\frac {\pi }{4}}$		${\frac {5}{7}}\diamond {\frac {12}{17}}\diamond {\frac {29}{41}}\diamond {\frac {70}{99}}\diamond {\frac {169}{239}}\diamond {\frac {408}{577}}$
${\frac {1}{2}}$			$30^{o}={\frac {\pi }{6}}$	$60^{o}={\frac {\pi }{3}}$
${\frac {\sqrt {3}}{2}}$	$\approx 0.8660254037844386$	$[0;1,{\overline {6,2}}]$	$60^{o}={\frac {\pi }{3}}$	$30^{o}={\frac {\pi }{6}}$	${\frac {84}{97}}\diamond {\frac {181}{209}}\diamond {\frac {1170}{1351}}$
${\sqrt {2}}$	$\approx 1.414213562373095$	$[1;{\overline {2}}]$	${\frac {99}{70}}\diamond {\frac {239}{169}}\diamond {\frac {577}{408}}$
${\sqrt {3}}$	$\approx 1.732050807568877$	$[1;{\overline {1,2}}]$	${\frac {99}{70}}\diamond {\frac {265}{153}}\diamond {\frac {362}{209}}\diamond {\frac {1351}{780}}$
${\sqrt {5}}$	$\approx 2.23606797749979$	$[2;{\overline {4}}]$	${\frac {95}{56}}\diamond {\frac {521}{233}}\diamond {\frac {682}{305}}$
$4{\frac {({\sqrt {2}}-1)}{3}}=\varkappa$	$\approx 0.5522847498307933$	$[0;{\overline {1,1,4,3}}]$	${\frac {5}{9}}\diamond {\frac {16}{29}}\diamond {\frac {21}{38}}\diamond {\frac {37}{67}}\diamond {\frac {169}{306}}\diamond {\frac {544}{985}}$