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Преобразования плоскости, движение

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I?aia?aciaaiey ieineinoe

Ioia?aaeaiea ieineinoe ia naay

Ioia?aaeaiai ieininoe ia naay iacuaaaony oaeia i?aia?iciaaiea, /oi
eaaeaeie oi/ea enoiaeiie ieineinoe niiinoaaeyaony eaeay-oi oi/ea yoie
aea ieineinoe, i?e/ai ethaay ethaay oi/ea ieineinoe ieacuaaaony
niiinoaaeaiie ae?oaie oi/ea. Anee i?e ioia?aaeaiee ieineinoe ia naay
oeao?a F i?aia?aciauaaaony a oeao?o F’, oi aiai?yo, /oi oeao?a F’ –
ia?ac oeao?u F, a oeao?a F – i?iia?ac oeao?u F’. Anee iaeiei
ioia?aaeaieai oeao?a F ia?aaiaeeony a oeao?o F’, a caoai oeao?a F’
ia?aaiaeeony a oeao?o F”, oi ioia?aaeaiea, ia?aaiaeyuaa F a F”
iacuaaaony eiiiiceoeeae aeaoo ioia?aaeaiee. Iaiiaeaeaeiie oi/eie
ioia?aaeaiey iacuaaaony oaeay oi/ea A eioi?ay yoei ioia?aaeaieai
ia?aaiaeeony naia a naay. Ioia?aaeaiea, ana oi/ee eioi?iai iaiiaeaeaeiua
iacuaaaony oiaeaeanoaaiiui ioia?aaeaieai. Anee i?e aeaiiii ioia?aaeaiee
?aciui oi/eai oeao?u niioaaonoaotho ?aciua ia?acu, oi oaeia ioia?aaeaiea
iacuaaaony acaeiii iaeiicia/iui. Ionoue oeao?a F’ iieo/aia ec oeao?u F
acaeiii iaeiicia/iui ioia?aaeaieai f, oi iiaeii caaeaoue ioia?aaeaiea
ia?aoiia ioia?aaeaieth f, eioi?ia ii?aaeaeyaony oae: eiiiiceoeey
ioia?aaeaiey f e ioia?aaeaiey, ia?aoiiai f yaeyaony oiaeaeanoaaiiui
ioia?aaeaieai. Nouanoaoao iiiaeanoai aeaeia ioia?aaeaiey ieineinoe ia
naay, ?anniio?ei iaeioi?ua ec ieo:

Aeaeaeaiey

Ia?aeeaeueiue ia?aiin

Inaaay neiiao?ey

Iiai?io aie?oa oi/ee

Oeaio?aeueiay neiiao?ey

Iiaeiaea

Aiiioaoey

Aeaeaeaiea

Aeaeaeaieai iacuaaaony ioia?aaeaiea ieineinoe ia naay i?e eioi??ii
nio?aiaythony ana ?annoiyiey iaaeaeo oi/eaie. Aeaeaeaiea eiaao ?yae
aaaeiuo naienoa:

O?e oi/ee, eaaeauea ia iaeiie i?yiie, i?e aeaeaeaiee ia?aoiaeyo a o?e
oi/ee, eaaeauea ia iaeiie i?yiie, e o?e oi/ee, ia eaaeauea ia iaeiie
i?yiie, ia?aoiaeyo a o?e oi/ee, ia eaaeauea ia iaeiie i?yiie.

Aeieicaoaeuenoai: ionoue aeaeaeaiea ia?aaiaeeo oi/ee A, B, C a oi/ee A’,
B’, C’. Oiaaea auiieiythony ?aaainoaa

A’B’=AB , A’C’=AC , B’C’=BC (1)

Anee oi/ee A, B, C eaaeao ia iaeiie i?yiie, oi iaeia ec ieo, iai?eia?
oi/ea B eaaeeo iaaeaeo aeaoiy ae?oaeie. A yoii neo/aa AB+BC=AC, e ec
?aaainoa (1) neaaeoao, /oi A’C’+B’C’=A’C’. A ec yoiai neaaeoao, /oi
oi/ea B’ eaaeeo iaaeaeo oi/eaie A’ e C’. Ia?aia ooaa?aeaeaiea aeieacaii.
Aoi?ia ooaa?aeaeaiea aeieaaeai iaoiaeii io i?ioeaiiai: I?aaeiieiaeei,
/oi oi/ee A’, B’, C’ eaaeao ia iaeiie i?yiie aeaaea a oii neo/aa, anee
oi/ee A, B, C ia eaaeao ia iaeiie i?yiie, oi anoue yaeythony aa?oeiaie
o?aoaieueieea. Oiaaea aeieaeiu auiieiyony ia?aaainoaa o?aoaieueieea:

AB0 iacuaaaony ioia?aaeaiea ieineinoe, i?e
eioi?ii ethaui aeaoiy oi/eai X e Y niioaaonaotho oaeea oi/ee X’ e Y’,
/oi X’Y’=kXY.

Ioiaoei, /oi i?e k=1 iiaeiaea yaeyaony aeaeaeaieai, oi anoue aeaeaeaiea
anoue /anoiue neo/ae iiaeiaey.

Oeao?a F iacuaaaony iiaeiaiie oeao?a F’ n eiyooeoeeaioii k, anee
nouanoaoao iiaeiaea n eiyooeoeeaioii k, ia?aaiaeyuaa F a F’.

I?inoaeoei, ii aaaeiui i?eia?ii iiaeiaey yaeyaony aiiioaoey

Aiiioaoey

Aiiioaoeae n oeaio?ii a oi/ea O e eiyooeoeeaioii k iacuaaaony oaeia
ioia?aaeaiea ieineinoe, i?e eioi?ii eaaeaeie oi/ea X niiinoaaeyaony
oaeay oi/ea X’, /oi OX’ = kOX, i?e/ai ia eneth/aaony e aiciiaeiinoue
k<0.I?e k =(1 iieo/aaony oeaio?aeueiay neiiao?ey n oeaio?ii a oi/ea O, i?e k =1 iieo/aaony oiaeaeanoaaiiia i?aia?aciaaiea.Iniiaiia naienoai aiiioaoeeI?e aiiioaoee n eiyoooeoeeaioii k eaaeaeue aaeoi? oiiiaeaaony ia (. Iiae?iaiaa: anee oi/ee ( e ( i?e aiiioaoee n eiyooooeoeeaioii ( ia?aoee a oi/ee (' e (', oi('(' = (((Aeieacaoaeuenoai.Ionoue oi/ea ( ( oeaio? aiiioaoee. Oiaaea ((' = (((, ((' = (((. Iiyoiio ('(' = ((' ( ((' = ((( ( ((( = (((( ( (() = (((.Ec ?aaiaonaa ('(' = ((( neaaeoao, /oi A'B' = |k|AB, oi anoue aiiioaoey n eiyooeoeeaioii k yaeyaony iiaeiaeai n eiyoooeoeeaioii |k|.Ioiaoei, /oi ethaia iiaeiaea n eiyooeoeeaioii ( iiaeii i?aaenoaaeoue a aeaea eiiiiceoeee aiiioaoee n eiyooeoeeaioii ( e aeaeaeaiey.Iaeioi?ua naienoaa aiiioaoeeAiiioaoey io?acie ia?aaiaeeo a io?acie.Aiiioaoey nio?aiyao aaee/eio oaeia..Eiiiiceoeey aeaoo aiiioaoee n iauei oeaio?ii e eiyooeoeeaioaie k1 e k2 ,aoaeao aiiioaoeae n oai aea oeaio?ii e eiyooeoeeaioii I?aia?aciaaiea, ia?aoiia aiiioaoee n eiyooeoeeaioii ( aoaeao aiiioaoeae n oai aea oeaio?ii e eiyooeoeeaioii 1/k.Naienoaa iiaeiaey.Iiaeiaea io?acie ia?aaiaeeo a io?acie.Iiaeiaea nio?aiyao aaee/eio oaeia.Iiaeiaea o?aoaieueiee ia?aaiaeeo a o?aoaieueiee. Niioaaonaaiiua noi?iiu yoeo o?aoaieueieeia i?iii?oeeiiaeueiu, a niioaaonaaiiua oaeu ?aaiuA ?acoeueoaoa iiaeiaey n eiyooeoeeaioii ( ieiuaaee oeao? oiiiaeathony ia (2.Eiiiiceoeey iiaeiaee n eiyooeoeeaioaie k1 e k2 anoue iiaeiaea n eiyooeoeeaioii k1k2.Iiaeiaea ia?aoeii. Ioia?aaeaiea, ia?aoiia iiaeiaeth n eiyooeoeeaioii ( anoue iiaeiaea n eiyooeoeeaioii 1/(.- PAGE 6 -

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