Difference between revisions of "Template:Continued fraction examples"
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imported>Cedar101 m (''ra'') |
imported>Colonies Chris m (minor fixes) |
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| (2 intermediate revisions by one other user not shown) | |||
| Line 35: | Line 35: | ||
|- | |- | ||
|- style="font-weight:bold;" | |- style="font-weight:bold;" | ||
| − | | rowspan="2"|''ϕ'' =<br /> {{sfrac|{{ | + | | rowspan="2"|''ϕ'' =<br /> {{sfrac|{{radic|5}} + 1|2}} |
! ''a<sub>r</sub>'' | ! ''a<sub>r</sub>'' | ||
| 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 | | 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 | ||
| Line 43: | Line 43: | ||
|- | |- | ||
|- style="font-weight:bold;" | |- style="font-weight:bold;" | ||
| − | | rowspan="2"|−''ϕ'' =<br /> −{{sfrac|{{ | + | | rowspan="2"|−''ϕ'' =<br /> −{{sfrac|{{radic|5}} + 1|2}} |
! ''a<sub>r</sub>'' | ! ''a<sub>r</sub>'' | ||
| −2 || 2 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 | | −2 || 2 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 | ||
| Line 51: | Line 51: | ||
|- | |- | ||
|- style="font-weight:bold;" | |- style="font-weight:bold;" | ||
| − | | rowspan="2"|{{ | + | | rowspan="2"|{{radic|2}} |
! ''a<sub>r</sub>'' | ! ''a<sub>r</sub>'' | ||
| 1 || 2 || 2 || 2 || 2 || 2 || 2 || 2 || 2 || 2 || 2 | | 1 || 2 || 2 || 2 || 2 || 2 || 2 || 2 || 2 || 2 || 2 | ||
| Line 59: | Line 59: | ||
|- | |- | ||
|- style="font-weight:bold;" | |- style="font-weight:bold;" | ||
| − | | rowspan="2"|{{frac|1|{{ | + | | rowspan="2"|{{frac|1|{{radic|2}}}} |
! ''a<sub>r</sub>'' | ! ''a<sub>r</sub>'' | ||
| 0 || 1 || 2 || 2 || 2 || 2 || 2 || 2 || 2 || 2 || 2 | | 0 || 1 || 2 || 2 || 2 || 2 || 2 || 2 || 2 || 2 || 2 | ||
| Line 67: | Line 67: | ||
|- | |- | ||
|- style="font-weight:bold;" | |- style="font-weight:bold;" | ||
| − | | rowspan="2"|{{ | + | | rowspan="2"|{{radic|3}} |
! ''a<sub>r</sub>'' | ! ''a<sub>r</sub>'' | ||
| 1 || 1 || 2 || 1 || 2 || 1 || 2 || 1 || 2 || 1 || 2 | | 1 || 1 || 2 || 1 || 2 || 1 || 2 || 1 || 2 || 1 || 2 | ||
| Line 75: | Line 75: | ||
|- | |- | ||
|- style="font-weight:bold;" | |- style="font-weight:bold;" | ||
| − | | rowspan="2"|{{frac|1|{{ | + | | rowspan="2"|{{frac|1|{{radic|3}}}} |
! ''a<sub>r</sub>'' | ! ''a<sub>r</sub>'' | ||
| 0 || 1 || 1 || 2 || 1 || 2 || 1 || 2 || 1 || 2 || 1 | | 0 || 1 || 1 || 2 || 1 || 2 || 1 || 2 || 1 || 2 || 1 | ||
| Line 83: | Line 83: | ||
|- | |- | ||
|- style="font-weight:bold;" | |- style="font-weight:bold;" | ||
| − | | rowspan="2"|{{frac|{{ | + | | rowspan="2"|{{frac|{{radic|3}}|2}} |
! ''a<sub>r</sub>'' | ! ''a<sub>r</sub>'' | ||
| 0 || 1 || 6 || 2 || 6 || 2 || 6 || 2 || 6 || 2 || 6 | | 0 || 1 || 6 || 2 || 6 || 2 || 6 || 2 || 6 || 2 || 6 | ||
| Line 91: | Line 91: | ||
|- | |- | ||
|- style="font-weight:bold;" | |- style="font-weight:bold;" | ||
| − | | rowspan="2"| | + | | rowspan="2"|{{radic|2|3}} |
! ''a<sub>r</sub>'' | ! ''a<sub>r</sub>'' | ||
| 1 || 3 || 1 || 5 || 1 || 1 || 4 || 1 || 1 || 8 || 1 | | 1 || 3 || 1 || 5 || 1 || 1 || 4 || 1 || 1 || 8 || 1 | ||
| Line 107: | Line 107: | ||
|- | |- | ||
|- style="font-weight:bold;" | |- style="font-weight:bold;" | ||
| − | | rowspan="2"|''& | + | | rowspan="2"|''π'' |
! ''a<sub>r</sub>'' | ! ''a<sub>r</sub>'' | ||
| 3 || 7 || 15 || 1 || 292 || 1 || 1 || 1 || 2 || 1 || 3 | | 3 || 7 || 15 || 1 || 292 || 1 || 1 || 1 || 2 || 1 || 3 | ||
| Line 113: | Line 113: | ||
! ''ra'' | ! ''ra'' | ||
| 3 || {{sfrac|22|7}} || {{sfrac|333|106}} || {{sfrac|355|113}} || {{sfrac|103 993|33 102}} || {{sfrac|104 348|33 215}} || {{sfrac|208 341|66 317}} || {{sfrac|312 689|99 532}} || {{sfrac|833 719|265 381}} || {{sfrac|1 146 408|364 913}} || {{sfrac|4 272 943|1 360 120}} | | 3 || {{sfrac|22|7}} || {{sfrac|333|106}} || {{sfrac|355|113}} || {{sfrac|103 993|33 102}} || {{sfrac|104 348|33 215}} || {{sfrac|208 341|66 317}} || {{sfrac|312 689|99 532}} || {{sfrac|833 719|265 381}} || {{sfrac|1 146 408|364 913}} || {{sfrac|4 272 943|1 360 120}} | ||
| + | |+ | ||
| + | ! Number !! ''r'' !! 0 !! 1 !! 2 !! 3 !! 4 !! 5 !! 6 !! 7 !! 8 !! 9 !! 10 | ||
|} | |} | ||
'''ra''': rational approximant obtained by expanding continued fraction up to ''a<sub>r</sub>'' | '''ra''': rational approximant obtained by expanding continued fraction up to ''a<sub>r</sub>'' | ||
Latest revision as of 15:09, 31 August 2020
ra: rational approximant obtained by expanding continued fraction up to ar