??? ?? ???? ?????? ??? ??? ?????. ?? ???????? ??????? ????, ??? ????? (?????????) .

????? (?????????; ???????, ? ?????? : ??????????? ) ??? ????? ??? ??? ????? . ???? ???????? ???????? ?? ????? ??? 540 ????? , ??? ?? 5 ???????? .

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

????? ?????? ??? ????? ??? ??????? ???? ?? ??? ??? ??????? ???? ?? ???. ???? ?? ??? ???????? ??? 108°. ???? ?? ???? ???? ?? 360, ???? ?? ???? ???? ?? ?????? ???????? ????????.

??? ????? ?????? ????? ???? a ????? ?? ?? ? ????? : ${\displaystyle A={\frac {5a^{2}}{4}}\cot {\frac {\pi }{5}}={\frac {a^{2}}{4}}{\sqrt {25+10{\sqrt {5}}}}\simeq 1.72048a^{2}}$

?? ??????? ?????? ????? ?????? ?? ???, ??? ??? ????? ???? ???? ??? ?? ???? ?????? ?????. ?????? ?? ??? ????? ?????? ????? ??? ??? ( ????? ????-?????? ????? ??? ????? ???? ??? ??? ???? ), ????? ??? ???????? ?? ??? ?????? ????? ??? ?? (????? ??? ??? ????? ??? ??? ????). ?? ????????? ?????? ?????? .

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

???? ????? ????? ?????? ?? ??? ????? ?????? ?????? ???? , ?? ??? ?????? ?????. ??? ?? ????? ?? ??? ??????? ????? ?????? (??? ?????, ???? 11) ???? ??????? ????? ???? ???. ????? ?????? ?? ?? ?- ${\displaystyle \ \cos \left({\frac {2\pi }{5}}\right)={\frac {{\sqrt {5}}-1}{4}}}$ ?- ${\displaystyle \ \sin \left({\frac {2\pi }{5}}\right)={\frac {\sqrt {10+2{\sqrt {5}}}}{4}}}$.

??? ?????? ??? ???:

1. ??????? ???? , ????? ???? O (????? ????? ??????? ?????). ???? ??????? ?? ???? ?? - ????? ???.
2. ?????? ?? ????? ?????, A, ?????? ??? ???????? ??????. ??????? ??? ?-A ??? ?????, O.
3. ????? ??? ????? AO, ??? ???? ?????, ??????? ?? ??? ???????? ??? ?? ????? ?-B.
4. ?????? ?? ?????? C ????? ???? OB. (????? ${\displaystyle \ |AC|={\sqrt {5}}/2}$).
5. ??????? ???? ?????? ?????? C ??? ?????? A, ?????? ?? ????? ?????? ??? ????? ??? OB ?-D. (????? ${\displaystyle \ |AD|={\sqrt {10-2{\sqrt {5}}}}/2}$, ???? ???? ??? ?????? ????? ????? ??????).
6. ??????? ???? ?????? A ??? ?????? D; ?????? ?? ??????? ?? ????? ?????? (?????) ??????? E ?-F.
7. ??????? ?????? ?????? E ?-F ??? ?????? A, ?????? ?? ???????? ?? ????? ?????? ?-G ?-H ??????.
8. ??????? AEFGH ????? ?? ??????? ?????? ???????.

??? ???? ?????? ???????? ??????.

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

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

?? ????? ???? ??? ???? ????? ???? ????. ????? ?????? ????? ?? ???? ????? ?????? (Poncelet).

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

???? ????????? ?? ????? ?????? ???? ??????, ??????? ?? ????? ?????. Clebsch ????? (?-1871) ??????? ?????? ???? ?????????? ?????? ??????. ?-2007 ???? Schwartz ?????? ?? ????? ??? ????? ?????? ??? ???? ??-???? ?? ????????.

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

?????? ?? ????? ???????, ???? ????? ???? ?? ???? ??? ??????????? (??? ????? ?? ???? ????????), ??? ?? ?? ??? "????? ??????" ?????? ?????? ?? ??????? ?????????. ????????? ????? ??? ??????? ???? ??? ?? ????? ^[1] ????? ??, ???? ????? ????? ?? ???? ?? ????? ??????? ?? ??????? ????????? (????? ??????? ??? ????? ????????? ?? ????? ???????? ?????? ?? ??????): ?? ???? ?- ${\displaystyle (i)}$ ?? ??? ?????? ????????? ?? ${\displaystyle (i-1,i,i+1)}$ ?? ??? ?????? ${\displaystyle A}$ ????? ?? ? ?????? ???????? ${\displaystyle A^{2}-c_{1}A+c_{2}=0}$, ???? ${\displaystyle c_{1}}$ ?- ${\displaystyle c_{2}}$ ?? ? ???????? ????????? ???????? ????? ?????? ?????? ??????? ${\displaystyle (0),(1),(2),(3),(4)}$: ${\displaystyle c_{1}=(0)+(1)+(2)+(3)+(4)}$ ${\displaystyle c_{2}=(0)(1)+(1)(2)+(2)(3)+(3)(4)+(4)(0)}$.

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

??? ?????? ????????, ????? ???????? ????? ????? ???????? ????? ????? ?? ?????? . ?????????? ????? ????????? ???? ??? ???? ????? ?? ??????? ????? ????? ??? ????? ????? ??? ???. ??? ?????? ???? ??????? ?????????, ?? ????? ???????? ??????? ????? ???? ?? ?????, ?????? ??????? ??????? ?????? ??????? ?????? ?????? ???? ?????. ???? ?????? 13 ?????? ?? ??????? ???? ???????? ????? ??? ?? ?????? ??? ?????, ????? ?????? ?? ????? ??????. ?????????? ?????? ???'??? ???? ???? ????? ???.

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

• ????? , ???? MathWorld (???????)

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