Tsu-2011 - ieeetsu

magaliTi 4. vipovoT albaToba imisa, rom wreSi SemTxveviT Cagdebuli
wertili ar Cavardeba am wreSi Caxazul wesier eqvskuTxedSi.
amoxsna. davuSvaT, rom wris radiusia R , maSin masSi Caxazuli wesieri
eqvskuTxedis gverdic iqneba R . amasTanave, wris farTobia | S | R
2
,
3 3 2
xolo eqvskuTxedis farTobia -- | s | R . amitom saZiebeli albaToba
2
iqneba:
2 3 3 2
R
R
| S | | s | 2 2
3 3
P
0,174.
2
| S | R
2
magaliTi 5. AB monakveTze SemTxveviT agdeben sam wertils C , D
da M . vipovoT albaToba imisa, rom AC, AD da AM monakveTebisagan Sei-
Zleba aigos samkuTxedi?
amoxsna. avRniSnoT AC, AD da AM monakveTebis sigrZeebi Sesabamisad
x, y da z -iT da elementarul xdomilebaTa sivrcis rolSi ganvixiloT
sivrcis wertilTa simravle koordinatebiT ( x , y,
z)
. Tu CavTvliT,
rom AB monakveTis sigrZe tolia 1-is, maSin elementarul xdomilebaTa
sivrce iqneba kubi, romlis wiboa erTi. amave dros, xelSemwyob elementarul
xdomilebaTa simravle (samkuTxedis aqsiomis Tanaxmad )Sedgeba im
wertilebisagan, romelTa koordinatebisaTvis sruldeba samkuTxedis utolobebi:
x +y > z, x + z > y, y + z > x. es ki warmoadgens kubis nawils, romelic
moWrilia misgan sibrtyeebiT: x + y = z, x + z = y, y + z = x
z
х
y
(erT-erTi am sibrtyidan, kerZod x + y = z, moyvanilia naxazze). yoveli ase-
Ti sibrtye kubidan moWris piramidas, romlis moculoba tolia
1 1 1
1
.
3 2 6
Sesabamisad, kubis darCenili nawilis moculoba iqneba
1 1
| v | 13
.
6 2
amitom saZiebeli albaToba, ganmartebis Tanaxmad, iqneba
| v | 1 1
| P | :1
.
| V | 2 2
magaliTi 6 (Sexvedris amocana). ori piri SeTanxmda garkveul adgilze
Sexvdes erTmaneTs 6-dan 7 saaTamde. TiToeuli maTgani SemTxveviT
8