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́ (. σφαῖρα  , , , . , . 41252.96 . .

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, , , , , , 1:2:3[1]

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S = \ 4\pi r^2 = \pi d^2.
,
V = \frac{4}{3}   \pi r^3.
s = \ 2 \pi r H = 2 \pi r^2 ( 1 - \cos ( \alpha ) ) , H  ,  \alpha  

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(x-x_0)^2+(y-y_0)^2+(z-z_0)^2 = R^2,

(x_0,y_0,z_0)  , R  .

(x_0,y_0,z_0):

\begin{cases}
x = x_0 + R \cdot \sin \theta\cdot \cos \phi,\\
y = y_0 + R \cdot \sin \theta\cdot \sin \phi,\\
z = z_0 + R \cdot \cos \theta,\\
\end{cases}

\theta \in [- \pi/2, \pi/2] \phi \in [0, 2\pi).

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, , , ( ) . ; .

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, :

L = R \cdot \arccos ( \cos \theta_1 \cdot \cos \theta_2 + \sin \theta_1 \cdot \sin \theta_2 \cdot \cos (\phi_1 - \phi_2) ).

, \theta Z , XY ( , ), :

L = R \cdot \arccos ( \sin \theta_1 \cdot \sin \theta_2 + \cos \theta_1 \cdot \cos \theta_2 \cdot \cos (\phi_1 - \phi_2) ).

\theta_1 \theta_2 , \phi_1 \phi_2 .

[] n-

(n-1)- ( n- ) :

\sum_{i=1}^{n}(x_i-a_i)^2=r^2,

(a_1,...,a_n)  , r  .

n- n-1- , .

n- ( ) n+1 .

n- n-1- n-1- .

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  1. [100 , . . ( № 12, 2008). ]