????? ??????? ??? ??? ? ?????? ?????????? ?? ??? ??? . ????? ????? ?? ??? ??????? ????????? , ?????? ????? ???? ???? ????, ?? ?????? ? ??? ?-19 ?????-????? ??????? ???? ????? .

????? ???: "???? ???? ?????? ??? ?? ?????? ????? ??????? ???? ?????? ?" ?????, ?????? ????? ?? ??????, ???? ???? ????? ?? ?????? ?? ??????? ?????? ???? ?????. ???? ??? ????? ?????? ????? ${\displaystyle {\sqrt[{3}]{2}}}$.

???????? [ ????? ??? ???? | ????? ]

????? ?????? ?? ????? ???? ? ????? ???? ???? . ????? ??????? ???? ???? ????? ????, ???? ? ????? ?????? ?????? ?? ??? ? ???? ?? ????? , ?????? ????? ??????. ??????? ???? ????? ??? ?? ??? ????? ???? ??????, ?? ????? ?? ??? ???? ???? ?????? ??? ????? ?? ??? ??????? ?? 8. ????? ????, ?? ??????? ?? ?????? ?? ${\displaystyle a}$, ?? ??? ??????? ??? ?? ${\displaystyle a^{3}}$. ??? ??? ?????? ?? ???? ?? ?????? ?? ?????? ?? ???? ?? ${\displaystyle {\sqrt[{3}]{2}}}$. ???? ?????? ?? ?????, ?? ???? ????? ??? ????? ?????? ????? ?????, ?? ??? ?????.

??????? ????? ?????? ?????? ?????? ???? ??? ???????? ????? ????? ??????: ???? ???, ?? ????? ??? ????? ?? ??????? ????? ??????? ?? ???? ????? ??? ????, ????? ???? ????? ??????? ?? ?????? ??? ??? ???? ????? ?????. ?????, ?? ???? ??? ????? a, ?? ????? r ?-s ?? ?: ${\displaystyle a:r=r:s=s:2a\ }$. ?? ????? ?- ${\displaystyle {s \over r}={\sqrt[{3}]{2}}}$. ??? ? ?????? ???? ?? ????? ????? ???? ??? ?? ??? ????? ????? ?? ?????? ? ???????? ?? ??? ?????????.

???? 1837 ????? ???? ????? ?- ${\displaystyle \ {\sqrt[{3}]{2}}}$ ????? ???? ? ??? ??????? ??????? ?????? , ?????? ????? ????? ?????.

????? [ ????? ??? ???? | ????? ]

???? ?????? ??? ??????? ??????? ?????? ?????? ? ??? ?????? ????? ? ??? ${\displaystyle 2^{n}}$ (???? n ??? ???? ???? ?????) ?? ??? ??????? ?????????? , ????? ?????? ?? ??? ????? ????? ?? ????? ????? ????, ????? ????? ?? ??? ?? ???? ?? ??? ?????? ???? ????? ???????. ???? ?????? ?- ${\displaystyle {\sqrt[{3}]{2}}}$ ???? ?????? ????? ??????, ?? ??? ???? ????? ???? ???? ????? (???? ???? ?-F). ??? ?? ???? ????? ?? ???? ${\displaystyle \mathbb {Q} ({\sqrt[{3}]{2}})}$, ???? ????? ??? 3 ?? ??? ??????? ??????????. ??? ??????:

${\displaystyle [F:\mathbb {Q} ]=[F:\mathbb {Q} ({\sqrt[{3}]{2}})][\mathbb {Q} ({\sqrt[{3}]{2}}):\mathbb {Q} ]}$

${\displaystyle 2^{n}=[F:\mathbb {Q} ({\sqrt[{3}]{2}})]\cdot 3}$

?? ???? ?????, ?? 3 ????? ???? ?? ${\displaystyle 2^{n}}$. ?????.

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