Difference between revisions of "Template:Continued fraction examples"

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imported>Anita5192
(Corrected a0 term in sqrt(3))
imported>Cedar101
m ({{sqrt}})
Line 35: Line 35:
 
|-
 
|-
 
|- style="font-weight:bold;"
 
|- style="font-weight:bold;"
| rowspan="2"|''&#981;'' =<br /> {{sfrac|&#8730;5 + 1|2}}
+
| rowspan="2"|''&#981;'' =<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"|&#8722;''&#981;'' =<br /> &#8722;{{sfrac|&#8730;5 + 1|2}}
+
| rowspan="2"|&#8722;''&#981;'' =<br /> &#8722;{{sfrac|{{sqrt|5}} + 1|2}}
 
! ''a<sub>r</sub>''
 
! ''a<sub>r</sub>''
 
| &#8722;2 || 2 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1
 
| &#8722;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"|&#8730;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"|{{sfrac|1|&#8730;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"|&#8730;3
+
| 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"|{{sfrac|1|&#8730;3}}
+
| 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"|{{sfrac|&#8730;3|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>&#179;</sup>&#8730;2
+
| rowspan="2"|<sup>&#179;</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

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
³Template:Sqrt 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

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