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Динић Љубиша, прпф. математике наствник у ПШ “Ћеле кула” Ниш ЗАПРЕМИНА ПИРАМИДЕ

Piramida - Ljubiša Dinić

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, .

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

- ( 2 2), .- , , - , H = . 11H, , 1 1= 2.

- ( 11H) . - ( , , , ).

- ( , , , ) ( 11H).- ( 11H) - ( 11H) a .

- ( 11H) ( 11H) - :

- ( 11H) ( 11H) :

V = 3 V

? . ( ) ( ) .

- . - . .

a - a, - . (- ) .

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

:1. , . 2. ( )3. - - . . ( axbxc) . .

( )

- - ( )

/ , E E , - , . . . Pi 1 Pi 2. Pi 2. . Pr 1 Pr 2. Pr1 =P d(, ) = 1/2 (axc)xb, Pr2= P d(, ) =1/2 (axc)xb. T d(, ) = b, H. - . , , , . -, . . . ; . - Pi 4 Pi 3. Pi 4. . Pr4 Pr 3. : Pr4=P d(, ) =1/2 (axb)xc Pr3=P d(, ) =1/2 axb)xc. T d(, ) = c. Pi 4 Pi 3 . - Pi 2 Pi 4 . , . o . ( )

Pi 1 , Pi 2 Pi 4 Pi 3 Pr 1 ,Pr 2 Pr 4 Pr 3 Pr1 = Pr2 = 2 (axc)xb Pi 4 = Pr3= 2 (axb)xc . - - . .

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

-- . ABC S, , S (ABC). d(S,(ABC)), S(ABC) SS (ABC) d(S,(ABC)) = d(S,S). ABC - S Pr1 = PABC d(S,(ABC)) = PABC d(S,S). . S - , . C - (ABC) S

d(S,(ABC)) = d(S,S) = d(SC) = SC. Pr2 = PABC d(S,(ABC)) = PABC d(S,C) . d(S,(ABC)) = d(S,S) =d(SC) = SC, Pr1 Pr2 (Pr1= Pr2). 1/3 - , 1/3 () . n ? n- S S (A1A2A3A4 ....An-1 An). A1A2A3A4.... ..An-1 An S. n A1A2S, A2A3 S, A3A4 S,............ . An-2 An-1S, An-1 AnS. S: SA1A2S, SA2A3S, SA3A4S ,.............. .... SAn-2 An-1S, SAn-1 AnS. . SA1A2S,

SA1A2S,

.Vn= P AnA1 S d(S,S).

n-

V =

V = , B , H - .