Difference between revisions of "Template:Continued fraction examples"

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imported>Cedar101
m ({{radic}}, {{pi}})
imported>Cedar101
m (footer)
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! ''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}}
 +
|+
 +
! Number !! ''r'' !! 0 !! 1 !! 2 !! 3 !! 4 !! 5 !! 6 !! 7 !! 8 !! 9 !! 10
 
|}
 
|}
 
'''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 06:07, 8 November 2018

Number r 0 1 2 3 4 5 6 7 8 9 10
123 ar 123
ra 123
12.3 ar 12 3 3
ra 12 Template:Sfrac Template:Sfrac
1.23 ar 1 4 2 1 7
ra 1 Template:Sfrac Template:Sfrac Template:Sfrac Template:Sfrac
0.123 ar 0 8 7 1 2 5
ra 0 Template:Sfrac Template:Sfrac Template:Sfrac Template:Sfrac Template:Sfrac
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
ϕ =
Template:Sfrac
ar −2 2 1 1 1 1 1 1 1 1 1
ra −2 Template:Sfrac Template:Sfrac Template:Sfrac Template:Sfrac Template:Sfrac Template:Sfrac Template:Sfrac Template:Sfrac Template:Sfrac Template:Sfrac
Template:Sqrt 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
1Template:Sqrt 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
Template:Sqrt ar 1 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
1Template:Sqrt 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:Sqrt2 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
Template:Radic ar 1 3 1 5 1 1 4 1 1 8 1
ra 1 Template:Sfrac 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
Number r 0 1 2 3 4 5 6 7 8 9 10

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