?????
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?????????	${\displaystyle \pi r^{2}}$

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????? ?????? ??????? ???? ??????? ??? ???? ????? ???????? ??????? ????? ???? ????????? ?????????, ????: ???? , ????? ??????? ????????? ????????? ???? , ?? ???? ??????? ????????? ?????? ????? ??????, ?? ?????????? ????? ???? ????????? ??? ???? ????????, ???? ?????? , ???? ???????? ?????????? ????? ??????? ??????? ??????????? ???????? ? ???????????? ?? ?????? ????????? ???????? ????? ?????? ? ?????????? ???????, ????? ??? ???????? ??? ??????? ??????? ??? ??????????????? ?????????? ????????? ??????? ??????? ???? ???????? ???? ??? ?????? ??????? "???????" ?? "???????" ??? ??????? ????? ^{[?] [?]}

??????? ??????? ??????? ???????????? ???? [ ???????? ]

• ???? ????????????: ??????? ?????? ?????????????? ?????????? (??????: Rhind Mathemetical Papyrus ) ??????? ????????? ??????? ???? ?????? ???????? ??? ? ??? ???/??(?.?????....)?? π ?? ???????? ??? ?????? ??????? ??? ???? ^[?]
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????????? ????? ???? [ ???????? ]

?????? ??????? [ ???????? ]

?????? ??? ???? ?? ??????? ????? ? ??????? ?????? ??? ???? ?????? ??????? ??? ????? ???? ${\displaystyle \pi }$ ( ??? ) ??? ???? ${\displaystyle \pi }$ ???? ????? ?????? ? ??? ???????????????? ?????? ? ?????? ??? ????? ???? ?????????? ???????? ??????? ?????? ??? ???? ??? ????? ??????? ??????? ???????? ?? ??? ?????? ?.?????????? ?????? ??????? C , ????????? r ? ????? d ??? ${\displaystyle \pi }$ ?? ?????????????,

${\displaystyle C=\pi d=2\pi r.\,}$

????????? [ ???????? ]

???????????? ?????? ???????, ??????? ???????? ????????? ????????? ???? ????????? ????, ??? ???? ??????? ????? ? ?????? ??????? ??????????? ???? ???? ^[?] ??????, ${\displaystyle \pi }$ ?? ???? ??????????? ?????? ?????? ??????? ?????????:

${\displaystyle \mathrm {Area} =\pi r^{2}.\,}$

????? d ?????? ?????? ????:

${\displaystyle \mathrm {Area} ={\frac {\pi d^{2}}{4}}\approx 0{.}7854d^{2},}$

???????? ??? ?????? ??? ???, ??? ??????? ??????? n ?????? ??????? ???? ?????? ???? ??? n ??? ??? ???, ??? ??????? ?????? ???? ??????? ?????? ??????? ??? ????? ????? C ??? ?? ??????? ????????? C/n. ???, ?? ??????? ????????? ??????? ????????? ???? ??? ???? ?????? ??????? ????????? ?????? ???? C/n ??? ???? ??????????? ????? ????? ??????? ????????? ????????? Cr/(2n), ??? ????? ??????? ????????? ??? n ?????? ??????? ???????????? ??????? ??????, ?????????=½Crn/n=½Cr. ?????????? ??? ????? ?????

x - y ?????????? ????????? ???????????, ( a , b ) ??????? ??? r ????????? ??????? ??????? ?????? ?? :

${\displaystyle \left(x-a\right)^{2}+\left(y-b\right)^{2}=r^{2}.}$

?? ???????? "???????? ??????" ????? ???????

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

${\displaystyle x^{2}+y^{2}=r^{2}.\!\ }$

???????? ??????? ???????? ??? ??? :

${\displaystyle x=a+r\,\cos t,\,\!}$

${\displaystyle y=b+r\,\sin t\,\!}$

??? t, 0 ???? 2π ??????? ?????????? ???????????, ??? ????????? ???????? ???????? (a,b) ? (x,y) ?????? ?????? ????? X-???? ???? ???? ??????? ???? ?????? ?????????? ??:??

${\displaystyle x=a+r{\frac {1-t^{2}}{1+t^{2}}}\,}$

${\displaystyle y=b+r{\frac {2t}{1+t^{2}}}.\,}$

?? ??????????? t ? r ?? ???????? ????????? ????????? ???? ???????? ??? ???? ??????? ??????????? ??????????? ???????, ?? X-???? ????? ????????? ?????????? ???? ??????? ????????

?????? ?????????? ??????? ????? ???? ??????? ?????? ?????? ???????? ????

${\displaystyle ax^{2}+ay^{2}+2b_{1}xz+2b_{2}yz+cz^{2}=0.\,}$

??? ?????? ??? ???? ??, ????? ???? ????? ??? ??? ????????? ????? I(1: i: 0) ??? J(1: ?i: 0) ?????? ???? ???????? ????? ?? ???????????? ???? ????????? ?????? ??? ????

??????? ??????? [ ???????? ]

????? ????????? ??????????, ??????? ?????? ???:

${\displaystyle r^{2}-2rr_{0}\cos(\theta -\phi )+r_{0}^{2}=a^{2}\,}$

????? ${\displaystyle a}$ ??? ??????? ?????????, ${\displaystyle (r,\theta )}$ ??????? ???? ?????? ??????? ????? ?????????, ${\displaystyle (r_{0},\phi )}$ ??????? ????????? ????? ????????? ( r ₀ ??? ????????? ???? ??????? ????????? ?????? ??? φ ??? ????????? ?????? ???, ?? X-?????? ??????? ??????? ???? ????????? ? ????????? ?????? ???????? ???? ???????)? ?????????????????? ???? ??????? ???? r ₀ = 0, ??? r = a ? ??? r ₀ = a ?? ????????? ? ??????? ??? ??? ?????? ??? ??? ????????:

${\displaystyle r=2a\cos(\theta -\phi ).\,}$

???????, ???????? r ?? ???? ?????? ??? ????:

${\displaystyle r=r_{0}\cos(\theta -\phi )+{\sqrt {a^{2}-r_{0}^{2}\sin ^{2}(\theta -\phi )}},}$

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

???? ?? [ ???????? ]

???? ?? ??????????, c ??????? ? r ????????? ??????? ??????? ?????? ????

${\displaystyle |z-c|=r\,}$

?????????? ???? ??? ?????? ??? ?????

${\displaystyle z=re^{it}+c}$

??????? ??????? ????????? ${\displaystyle pz{\overline {z}}+gz+{\overline {gz}}=q}$ ?????? ?????? p , q ? ???? ?????? g ?? ???? ????? "?????????? ?????" ? ??? ???? ?? ???????? ???? ????????? ?????????? ???? ?????

${\displaystyle p=1,\ g=-{\overline {c}},\ q=r^{2}-|c|^{2}}$, ??? ${\displaystyle |z-c|^{2}=z{\overline {z}}-{\overline {c}}z-c{\overline {z}}+c{\overline {c}}}$

??? ?????????? ?????? ?????? ????? ???; ??? ?????? ????????? ?????, ??? ?? ??????? ?

????????? [ ???????? ]

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• ??????? ????? ? ??????? ?????? ???? ????? ??????, ??? π ?????? ?????? ??? ??? ?
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??? ????? [ ???????? ]

????-?? ?????

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???? ?????? ?? ???????? ????????? ? ???? ????? ????? ??????????? ??? ????????????? ??????? ???? ?????? ?? ?