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"|''&#981;'' =<br /> {{sfrac|&#8730;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&thinsp;393|985}} || {{sfrac|3&thinsp;363|2&thinsp;378}} || {{sfrac|8&thinsp;119|5&thinsp;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&thinsp;393|985}} || {{sfrac|3&thinsp;363|2&thinsp;378}} || {{sfrac|8&thinsp;119|5&thinsp;741}}
 +
|-
 +
|- style="font-weight:bold;"
 +
| rowspan="2"|{{sfrac|1|&#8730;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&thinsp;393}} || {{sfrac|2&thinsp;378|3&thinsp;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|&#8730;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|&#8730;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&thinsp;170|1&thinsp;351}} || {{sfrac|2&thinsp;521|2&thinsp;911}} || {{sfrac|16&thinsp;296|18&thinsp;817}} || {{sfrac|35&thinsp;113|40&thinsp;545}} || {{sfrac|226&thinsp;974|262&thinsp;087}} 
 
|-
 
|-
 
|- style="font-weight:bold;"
 
|- style="font-weight:bold;"

Revision as of 13:20, 21 August 2014

Number r 0 1 2 3 4 5 6 7 8 9 10
ϕ =
Template:Sfrac
ar 1 1 1 1 1 1 1 1 1 1 1
ra 1 2 Template:Sfrac Template:Sfrac Template:Sfrac Template:Sfrac Template:Sfrac Template:Sfrac Template:Sfrac Template:Sfrac Template:Sfrac
√2 ar 1 2 2 2 2 2 2 2 2 2 2
ra 1 Template:Sfrac Template:Sfrac Template:Sfrac Template:Sfrac Template:Sfrac Template:Sfrac Template:Sfrac Template:Sfrac Template:Sfrac Template:Sfrac
Template:Sfrac ar 0 1 2 2 2 2 2 2 2 2 2
ra 0 1 Template:Sfrac Template:Sfrac Template:Sfrac Template:Sfrac Template:Sfrac Template:Sfrac Template:Sfrac Template:Sfrac Template:Sfrac
√3 ar 2 1 2 1 2 1 2 1 2 1 2
ra 1 2 Template:Sfrac Template:Sfrac Template:Sfrac Template:Sfrac Template:Sfrac Template:Sfrac Template:Sfrac Template:Sfrac Template:Sfrac
Template:Sfrac ar 0 1 1 2 1 2 1 2 1 2 1
ra 0 1 Template:Sfrac Template:Sfrac Template:Sfrac Template:Sfrac Template:Sfrac Template:Sfrac Template:Sfrac Template:Sfrac Template:Sfrac
Template:Sfrac ar 0 1 6 2 6 2 6 2 6 2 6
ra 0 1 Template:Sfrac Template:Sfrac Template:Sfrac Template:Sfrac Template:Sfrac Template:Sfrac Template:Sfrac Template:Sfrac Template:Sfrac
e ar 2 1 2 1 1 4 1 1 6 1 1
ra 2 3 Template:Sfrac Template:Sfrac Template:Sfrac Template:Sfrac Template:Sfrac Template:Sfrac Template:Sfrac Template:Sfrac Template:Sfrac
π ar 3 7 15 1 292 1 1 1 2 1 3
ra 3 Template:Sfrac Template:Sfrac Template:Sfrac Template:Sfrac Template:Sfrac Template:Sfrac Template:Sfrac Template:Sfrac Template:Sfrac Template:Sfrac

ra: rational approximant obtained by expanding continued fraction up to ar