Difference between revisions of "Template:Continued fraction examples"
Jump to navigation
Jump to search
imported>Cmglee (Add trigonometric function values for common numbers) |
imported>Cmglee (Add rational numbers) |
||
| Line 1: | Line 1: | ||
{| class="wikitable" style="text-align:center;" | {| class="wikitable" style="text-align:center;" | ||
! Number !! ''r'' !! 0 !! 1 !! 2 !! 3 !! 4 !! 5 !! 6 !! 7 !! 8 !! 9 !! 10 | ! Number !! ''r'' !! 0 !! 1 !! 2 !! 3 !! 4 !! 5 !! 6 !! 7 !! 8 !! 9 !! 10 | ||
| + | |- | ||
| + | |- style="font-weight:bold;" | ||
| + | | rowspan="2"|123 | ||
| + | ! ''a<sub>r</sub>'' | ||
| + | | 123 | ||
| + | |- | ||
| + | ! ra | ||
| + | | 123 | ||
| + | |- | ||
| + | |- style="font-weight:bold;" | ||
| + | | rowspan="2"|12.3 | ||
| + | ! ''a<sub>r</sub>'' | ||
| + | | 12 || 3 || 3 | ||
| + | |- | ||
| + | ! ra | ||
| + | | 12 || {{sfrac|37|3}} || {{sfrac|123|10}} | ||
| + | |- | ||
| + | |- style="font-weight:bold;" | ||
| + | | rowspan="2"|1.23 | ||
| + | ! ''a<sub>r</sub>'' | ||
| + | | 1 || 4 || 2 || 1 || 7 | ||
| + | |- | ||
| + | ! ra | ||
| + | | 1 || {{sfrac|5|4}} || {{sfrac|11|9}} || {{sfrac|16|13}} || {{sfrac|123|100}} | ||
| + | |- | ||
| + | |- style="font-weight:bold;" | ||
| + | | rowspan="2"|0.123 | ||
| + | ! ''a<sub>r</sub>'' | ||
| + | | 0 || 8 || 7 || 1 || 2 || 5 | ||
| + | |- | ||
| + | ! ra | ||
| + | | 0 || {{sfrac|1|8}} || {{sfrac|7|57}} || {{sfrac|8|65}} || {{sfrac|23|187}} || {{sfrac|123|1 000}} | ||
|- | |- | ||
|- style="font-weight:bold;" | |- style="font-weight:bold;" | ||
| Line 9: | Line 41: | ||
! ra | ! ra | ||
| 1 || 2 || {{sfrac|3|2}} || {{sfrac|5|3}} || {{sfrac|8|5}} || {{sfrac|13|8}} || {{sfrac|21|13}} || {{sfrac|34|21}} || {{sfrac|55|34}} || {{sfrac|89|55}} || {{sfrac|144|89}} | | 1 || 2 || {{sfrac|3|2}} || {{sfrac|5|3}} || {{sfrac|8|5}} || {{sfrac|13|8}} || {{sfrac|21|13}} || {{sfrac|34|21}} || {{sfrac|55|34}} || {{sfrac|89|55}} || {{sfrac|144|89}} | ||
| + | |- | ||
| + | |- style="font-weight:bold;" | ||
| + | | rowspan="2"|−''ϕ'' =<br /> −{{sfrac|√5 + 1|2}} | ||
| + | ! ''a<sub>r</sub>'' | ||
| + | | −2 || 2 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 | ||
| + | |- | ||
| + | ! ra | ||
| + | | −2 || −{{sfrac|3|2}} || −{{sfrac|5|3}} || −{{sfrac|8|5}} || −{{sfrac|13|8}} || −{{sfrac|21|13}} || −{{sfrac|34|21}} || −{{sfrac|55|34}} || −{{sfrac|89|55}} || −{{sfrac|144|89}} || −{{sfrac|233|144}} | ||
|- | |- | ||
|- style="font-weight:bold;" | |- style="font-weight:bold;" | ||
| Line 49: | Line 89: | ||
! ra | ! 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}} | | 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;" | ||
| + | | rowspan="2"|<sup>³</sup>√2 | ||
| + | ! ''a<sub>r</sub>'' | ||
| + | | 1 || 3 || 1 || 5 || 1 || 1 || 4 || 1 || 1 || 8 || 1 | ||
| + | |- | ||
| + | ! ra | ||
| + | | 1 || {{sfrac|4|3}} || {{sfrac|5|4}} || {{sfrac|29|23}} || {{sfrac|34|27}} || {{sfrac|63|50}} || {{sfrac|286|227}} || {{sfrac|349|277}} || {{sfrac|635|504}} || {{sfrac|5 429|4 309}} || {{sfrac|6 064|4 813}} | ||
|- | |- | ||
|- style="font-weight:bold;" | |- style="font-weight:bold;" | ||
Revision as of 13:57, 21 August 2014
ra: rational approximant obtained by expanding continued fraction up to ar