Difference between revisions of "Template:Continued fraction examples"
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imported>Anita5192 (Corrected a0 term in sqrt(3)) |
imported>Cedar101 m ({{sqrt}}) |
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| Line 35: | Line 35: | ||
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|- style="font-weight:bold;" | |- style="font-weight:bold;" | ||
| − | | rowspan="2"|''ϕ'' =<br /> {{sfrac| | + | | rowspan="2"|''ϕ'' =<br /> {{sfrac|{{sqrt|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|{{sqrt|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"|{{sqrt|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"|{{ | + | | rowspan="2"|{{frac|1|{{sqrt|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"|{{sqrt|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"|{{ | + | | rowspan="2"|{{frac|1|{{sqrt|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"|{{ | + | | rowspan="2"|{{frac|{{sqrt|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"|<sup>³</sup> | + | | rowspan="2"|<sup>³</sup>{{sqrt|2}} |
! ''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 | ||
Revision as of 05:35, 8 November 2018
ra: rational approximant obtained by expanding continued fraction up to ar