Niven's theorem
Removed degree symbol from the radians inequality
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In [[radian]]s, one would require that {{Math|0 |
In [[radian]]s, one would require that {{Math|0 ≤ ''x'' ≤ ''π''/2}}, that {{Math|''x''/''π''}} be rational, and that {{Math|sin(''x'')}} be rational. The conclusion is then that the only such values are {{Math|1=sin(0) = 0}}, {{Math|1=sin(''π''/6) = 1/2}}, and {{Math|1=sin(''π''/2) = 1}}. |
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The theorem appears as Corollary 3.12 in Niven's book on [[irrational number]]s.{{cite book |last=Niven |first=Ivan |author-link=Ivan Niven |year=1956 |title=Irrational Numbers |url=https://archive.org/details/irrationalnumber00nive |url-access=registration |series=The [[Carus Mathematical Monographs]] |number=11 |publisher=[[The Mathematical Association of America]] |mr=0080123 |page=[https://archive.org/details/irrationalnumber00nive/page/41 41]}} |
The theorem appears as Corollary 3.12 in Niven's book on [[irrational number]]s.{{cite book |last=Niven |first=Ivan |author-link=Ivan Niven |year=1956 |title=Irrational Numbers |url=https://archive.org/details/irrationalnumber00nive |url-access=registration |series=The [[Carus Mathematical Monographs]] |number=11 |publisher=[[The Mathematical Association of America]] |mr=0080123 |page=[https://archive.org/details/irrationalnumber00nive/page/41 41]}} |
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