Difference between revisions of "Template:Continued fraction examples"
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imported>Cedar101 m ({{sqrt}}) |
imported>Cedar101 m (''ra'') |
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| Line 7: | Line 7: | ||
| 123 | | 123 | ||
|- | |- | ||
| − | ! ra | + | ! ''ra'' |
| 123 | | 123 | ||
|- | |- | ||
| Line 15: | Line 15: | ||
| 12 || 3 || 3 | | 12 || 3 || 3 | ||
|- | |- | ||
| − | ! ra | + | ! ''ra'' |
| 12 || {{sfrac|37|3}} || {{sfrac|123|10}} | | 12 || {{sfrac|37|3}} || {{sfrac|123|10}} | ||
|- | |- | ||
| Line 23: | Line 23: | ||
| 1 || 4 || 2 || 1 || 7 | | 1 || 4 || 2 || 1 || 7 | ||
|- | |- | ||
| − | ! ra | + | ! ''ra'' |
| 1 || {{sfrac|5|4}} || {{sfrac|11|9}} || {{sfrac|16|13}} || {{sfrac|123|100}} | | 1 || {{sfrac|5|4}} || {{sfrac|11|9}} || {{sfrac|16|13}} || {{sfrac|123|100}} | ||
|- | |- | ||
| Line 31: | Line 31: | ||
| 0 || 8 || 7 || 1 || 2 || 5 | | 0 || 8 || 7 || 1 || 2 || 5 | ||
|- | |- | ||
| − | ! ra | + | ! ''ra'' |
| 0 || {{sfrac|1|8}} || {{sfrac|7|57}} || {{sfrac|8|65}} || {{sfrac|23|187}} || {{sfrac|123|1 000}} | | 0 || {{sfrac|1|8}} || {{sfrac|7|57}} || {{sfrac|8|65}} || {{sfrac|23|187}} || {{sfrac|123|1 000}} | ||
|- | |- | ||
| Line 39: | Line 39: | ||
| 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 | | 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 | ||
|- | |- | ||
| − | ! 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}} | ||
|- | |- | ||
| Line 47: | Line 47: | ||
| −2 || 2 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 | | −2 || 2 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 | ||
|- | |- | ||
| − | ! ra | + | ! ''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}} | | −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}} | ||
|- | |- | ||
| Line 55: | Line 55: | ||
| 1 || 2 || 2 || 2 || 2 || 2 || 2 || 2 || 2 || 2 || 2 | | 1 || 2 || 2 || 2 || 2 || 2 || 2 || 2 || 2 || 2 || 2 | ||
|- | |- | ||
| − | ! 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}} | ||
|- | |- | ||
| Line 63: | Line 63: | ||
| 0 || 1 || 2 || 2 || 2 || 2 || 2 || 2 || 2 || 2 || 2 | | 0 || 1 || 2 || 2 || 2 || 2 || 2 || 2 || 2 || 2 || 2 | ||
|- | |- | ||
| − | ! ra | + | ! ''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}} | | 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}} | ||
|- | |- | ||
| Line 71: | Line 71: | ||
| 1 || 1 || 2 || 1 || 2 || 1 || 2 || 1 || 2 || 1 || 2 | | 1 || 1 || 2 || 1 || 2 || 1 || 2 || 1 || 2 || 1 || 2 | ||
|- | |- | ||
| − | ! 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}} | ||
|- | |- | ||
| Line 79: | Line 79: | ||
| 0 || 1 || 1 || 2 || 1 || 2 || 1 || 2 || 1 || 2 || 1 | | 0 || 1 || 1 || 2 || 1 || 2 || 1 || 2 || 1 || 2 || 1 | ||
|- | |- | ||
| − | ! ra | + | ! ''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}} | | 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}} | ||
|- | |- | ||
| Line 87: | Line 87: | ||
| 0 || 1 || 6 || 2 || 6 || 2 || 6 || 2 || 6 || 2 || 6 | | 0 || 1 || 6 || 2 || 6 || 2 || 6 || 2 || 6 || 2 || 6 | ||
|- | |- | ||
| − | ! 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}} | ||
|- | |- | ||
| Line 95: | Line 95: | ||
| 1 || 3 || 1 || 5 || 1 || 1 || 4 || 1 || 1 || 8 || 1 | | 1 || 3 || 1 || 5 || 1 || 1 || 4 || 1 || 1 || 8 || 1 | ||
|- | |- | ||
| − | ! ra | + | ! ''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}} | | 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}} | ||
|- | |- | ||
| Line 103: | Line 103: | ||
| 2 || 1 || 2 || 1 || 1 || 4 || 1 || 1 || 6 || 1 || 1 | | 2 || 1 || 2 || 1 || 1 || 4 || 1 || 1 || 6 || 1 || 1 | ||
|- | |- | ||
| − | ! ra | + | ! ''ra'' |
| 2 || 3 || {{sfrac|8|3}} || {{sfrac|11|4}} || {{sfrac|19|7}} || {{sfrac|87|32}} || {{sfrac|106|39}} || {{sfrac|193|71}} || {{sfrac|1 264|465}} || {{sfrac|1 457|536}} || {{sfrac|2 721|1 001}} | | 2 || 3 || {{sfrac|8|3}} || {{sfrac|11|4}} || {{sfrac|19|7}} || {{sfrac|87|32}} || {{sfrac|106|39}} || {{sfrac|193|71}} || {{sfrac|1 264|465}} || {{sfrac|1 457|536}} || {{sfrac|2 721|1 001}} | ||
|- | |- | ||
| Line 111: | Line 111: | ||
| 3 || 7 || 15 || 1 || 292 || 1 || 1 || 1 || 2 || 1 || 3 | | 3 || 7 || 15 || 1 || 292 || 1 || 1 || 1 || 2 || 1 || 3 | ||
|- | |- | ||
| − | ! 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}} | ||
|} | |} | ||
'''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>'' | ||
Revision as of 05:36, 8 November 2018
ra: rational approximant obtained by expanding continued fraction up to ar