Difference between revisions of "Template:Continued fraction examples"
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imported>Cmglee (Create template) |
imported>Cmglee (Add trigonometric function values for common numbers) |
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|- style="font-weight:bold;" | |- style="font-weight:bold;" | ||
| − | | rowspan="2"|''ϕ'' = {{sfrac|√5 + 1|2}} | + | | rowspan="2"|''ϕ'' =<br /> {{sfrac|√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 17: | Line 17: | ||
! ra | ! ra | ||
| 1 || {{sfrac|3|2}} || {{sfrac|7|5}} || {{sfrac|17|12}} || {{sfrac|41|29}} || {{sfrac|99|70}} || {{sfrac|239|169}} || {{sfrac|577|408}} || {{sfrac|1 393|985}} || {{sfrac|3 363|2 378}} || {{sfrac|8 119|5 741}} | | 1 || {{sfrac|3|2}} || {{sfrac|7|5}} || {{sfrac|17|12}} || {{sfrac|41|29}} || {{sfrac|99|70}} || {{sfrac|239|169}} || {{sfrac|577|408}} || {{sfrac|1 393|985}} || {{sfrac|3 363|2 378}} || {{sfrac|8 119|5 741}} | ||
| + | |- | ||
| + | |- style="font-weight:bold;" | ||
| + | | rowspan="2"|{{sfrac|1|√2}} | ||
| + | ! ''a<sub>r</sub>'' | ||
| + | | 0 || 1 || 2 || 2 || 2 || 2 || 2 || 2 || 2 || 2 || 2 | ||
| + | |- | ||
| + | ! ra | ||
| + | | 0 || 1 || {{sfrac|2|3}} || {{sfrac|5|7}} || {{sfrac|12|17}} || {{sfrac|29|41}} || {{sfrac|70|99}} || {{sfrac|169|239}} || {{sfrac|408|577}} || {{sfrac|985|1 393}} || {{sfrac|2 378|3 363}} | ||
|- | |- | ||
|- style="font-weight:bold;" | |- style="font-weight:bold;" | ||
| Line 25: | Line 33: | ||
! ra | ! ra | ||
| 1 || 2 || {{sfrac|5|3}} || {{sfrac|7|4}} || {{sfrac|19|11}} || {{sfrac|26|15}} || {{sfrac|71|41}} || {{sfrac|97|56}} || {{sfrac|265|153}} || {{sfrac|362|209}} || {{sfrac|989|571}} | | 1 || 2 || {{sfrac|5|3}} || {{sfrac|7|4}} || {{sfrac|19|11}} || {{sfrac|26|15}} || {{sfrac|71|41}} || {{sfrac|97|56}} || {{sfrac|265|153}} || {{sfrac|362|209}} || {{sfrac|989|571}} | ||
| + | |- | ||
| + | |- style="font-weight:bold;" | ||
| + | | rowspan="2"|{{sfrac|1|√3}} | ||
| + | ! ''a<sub>r</sub>'' | ||
| + | | 0 || 1 || 1 || 2 || 1 || 2 || 1 || 2 || 1 || 2 || 1 | ||
| + | |- | ||
| + | ! ra | ||
| + | | 0 || 1 || {{sfrac|1|2}} || {{sfrac|3|5}} || {{sfrac|4|7}} || {{sfrac|11|19}} || {{sfrac|15|26}} || {{sfrac|41|71}} || {{sfrac|56|97}} || {{sfrac|153|265}} || {{sfrac|209|362}} | ||
| + | |- | ||
| + | |- style="font-weight:bold;" | ||
| + | | rowspan="2"|{{sfrac|√3|2}} | ||
| + | ! ''a<sub>r</sub>'' | ||
| + | | 0 || 1 || 6 || 2 || 6 || 2 || 6 || 2 || 6 || 2 || 6 | ||
| + | |- | ||
| + | ! ra | ||
| + | | 0 || 1 || {{sfrac|6|7}} || {{sfrac|13|15}} || {{sfrac|84|97}} || {{sfrac|181|209}} || {{sfrac|1 170|1 351}} || {{sfrac|2 521|2 911}} || {{sfrac|16 296|18 817}} || {{sfrac|35 113|40 545}} || {{sfrac|226 974|262 087}} | ||
|- | |- | ||
|- style="font-weight:bold;" | |- style="font-weight:bold;" | ||
Revision as of 13:20, 21 August 2014
ra: rational approximant obtained by expanding continued fraction up to ar