No?iaiea aoiia.
A aeae?eii i?ioeii oeeiniou Ae?aaiae A?aoeee i?aaeiieaaaee, /oi any
iaoa?ey aaeeia, ii i?eia?aoaao oa eee eiua naienoaa a caaeneiinoe io a?
«nouiinoe». Iaeioi?ua ec ieo ooaa?aeaeaee, /oi aauanoai ninoieo ec
iaeue/aeoeo /anoeoe, iacuaaaiuo aoiiaie. Iao/iua iniiau
aoiiii-iieaeoey?iiai o/aiey auee caeiaeaiu iicaeiaa a ?aaioao ?onneiai
o/?iiai I.A. Eiiiiiniaa, o?aioeocneeo oeieeia E. Eaaoacuea e AE. I?onoa,
aiaeeeneiai oeieea Ae. Aeaeueoiia, eoaeueyineiai oeceea A. Aaiaaae?i e
ae?oaeo enneaaeiaaoaeae.
Ia?eiaee/aneee caeii Ae.E. Iaiaeaeaaaa iieacuaaao nouanoaiaaiea
caeiiiia?iie nayce iaaeaeo anaie oeie/aneeie yeaiaioaie. Yoi aiai?eo i
oii /oi a iniiaa anao aoiiia eaaeeo ia/oi iauaa. Aei eiioea XIX aaea a
oeiee oea?eei oaaaeaeaiea, /oi aoii anoue iaeiaiueoay iaaeaeeiay
/anoeoea i?inoiai aauanoaa. N/eoaeinue, /oi i?e anao oeie/aneeo
i?aa?auaieyo ?ac?ooathony e nicaeathony oieueei iieaeoeu, aoiiu aea
inoathony iaeciaiiuie e ia iiaoo ae?iaeoueny ia /anoe. E iaeiiaoe a
eiioea XIX aaea auee naeaeaiu ioe?uoey, iieacaaoea neiaeiinoue no?iaiey
aoiia e aiciiaeiinoue i?aa?auaiey iaeieo aoiiia a ae?oaea.
Yoi iineoaeeei oie/eii e ia?aciaaieth e ?acaeoeth iiaiai ?acaeaea oeiee
«No?iaiea aoiia». Ia?aui oeacaieai ia neiaeioth no?oeoo?o aoiia – auee
iiuou ii eco/aieth eaoiaeiuo eo/ae, aicieeathueo i?e yeaeo?e/aneii
?ac?yaea a neeueii ?ac?aaeaiiuo aacao. Aeey iaaethaeaiey yoeo eo/ae ec
noaeeyiiie o?oaee, a eioi?oth aiayiu aeaa iaoaeee/aneeo yeaeo?iaea,
auea/eaaaony ii aiciiaeiinoe aanue aicaeoo e caoai i?iioneaaony
neaicue iaa oie aunieiai iai?yaeaiey. I?e oaeeo oneiaeyo io eaoiaea
o?oaee ia?iaiaeeeoey?ii e aai iiaa?oiinoe ?ani?ino?aiythony
“iaaeaeeiua” eaoiaeiua eo/e, aucuaathuea y?eia caeaiia naa/aiea a oii
ianoa, eoaea iie iiiaaeatho. Eaoiaeiua eo/e iaeaaeatho niiniaiinoueth
i?eaiaeeoue a aeaeaeaiea. Ia eo iooe eaaei iiaeaeaeiua oaea ioeeaiythony
io naiaai ia?aiia/aeueiiai iooe a iaaieoiii e yeaeo?e/aneii iiea (a
iineaaeiai a noi?iio iieiaeeoaeueii ca?yaeaiiie ieanoeiu). Aeaenoaea
eaoiaeiuo eo/ae iaia?oaeeaaaony oieueei aioo?e o?oaee, oae eae noaeei
aeey ieo iai?iieoeaaii. Eco/aiea naienoa eaoiaeiuo eo/ae i?eaaei e
caeeth/aieth, /oi iie ninoiyo ec iaeue/aeoeo /anoeoe, ianoueo
io?eoeaoaeueiue ca?yae e eaoyueo ni nei?inoueth, aeinoeaathuae iieiaeiu
nei?inoe naaoa. Oaeaea oaeaeinue ii?aaeaeeoue ianno e aaee/eio eo
ca?yaea. Ianna eaaeaeie /anoeoeu ?aaiyeanue 0,00055 oaea?iaeiie
/anoeoeu. Ca?yae ?aaiyaony 1,602 ia 10 a ieion 19 noaiaie. Iniaaiii
caia/aoaeueii, /oi ianna /anoeoe e aaee/eia eo ca?yaea ia caaeneo ie io
i?e?iaeu aaca, inoathuaainy a o?oaea, ie io aauanoaa ec eioi?iai
naeaeaiu yeaeo?iaeu, ie io i?i/eo oneiaee iiuoa. E?iia oiai, eaoiaeiua
/anoeoeu ecaanoiu oieueei a ca?yaeaiiii ninoiyiee e ia iiaoo
nouanoaiaaoue aac naieo ca?yaeia, ia iiaoo auoue i?aa?auaiu a
yeaeo?iiaeo?aeueiua /anoeoeu: yeaeo?e/aneee ca?yae ninoaaeyao, naioth
nouiinoue eo i?e?iaeu. Yoe /anoeoeu iieo/eee iacaaiea yeaeo?iiia. A
eaoiaeiuo o?oaeao yeaeo?iiu ioaeaeythony io eaoiaea iiae aeeyieai
yeaeo?e/aneiai ca?yaea. Ii iie iiaoo aicieeaoue e aia anyeie nayce n
yeaeo?e/aneei ca?yaeii. Oae, iai?eia? i?e yeaeo?iiiie yiennee iaoaeeu
enioneatho yeaeo?iiu; i?e oioiyooaeoa iiiaea aauanoaa oaeaea
aua?anuaatho yeaeo?iiu. Auaeaeaiea yeaeo?iiia naiuie ?aciiia?aciuie
aauanoaaie oeacuaaao ia oi, /oi yoe /anoeoeu aoiaeyo a ninoaa anao
aoiiia; neaaeiaaoaeueii aoiiu yaeythony neiaeiuie ia?aciaaieyie,
iino?iaiiuie ec aieaa iaeeeo «ninoaaiuo /anoae».
Eco/aiea no?iaiey aoiia i?aeoe/anee ia/aeinue a 1897-1898 aa., iinea
oiai eae auea ieii/aoaeueii onoaiiaeaia i?e?iaea eaoiaeiuo eo/ae eae
iioiea yeaeo?iiia e auee ii?aaeaeaiu aaee/eia ca?yaea e ianna
yeaeo?iia. Oaeo auaeaeaiey yeaeo?iiia naiuie ?aciiia?aciuie aauanoaaie
i?eaiaeee e auaiaeo, /oi yeaeo?iiu aoiaeyo a ninoaa anao aoiiia. Ii
aoii, eae ecaanoii, yeaeo?e/anee iaeo?aeai, ec yoiai neaaeiaaei, /oi a
aai ninoaa aeieaeia auea aoiaeeoue au? iaeia ninoaaiay /anoue,
o?aaiiaaoeaaaoay noiio io?eoeaoaeueiuo ca?yaeia yeaeo?iiia. Yoa
iieiaeeoaeueii ca?yaeaiiay /anoue aoiia auea ioe?uoa a 1911 a.
?aca?oi?aeii i?e enneaaeiaaiee aeaeaeaiey
a-/anoeoe a aacao e ae?oaeo aauanoaao.
?aca?oi?ae Y?iano (1871-1937)
a- /anoeoeu, aua?anuaaaiua aauanoaaie aeoeaiuo yeaiaioia i?aaenoaaeytho
niaie iieiaeeoaeueii ca?yaeaiiua eiiu aaeey, nei?inoue aeaeaeaiey
eioi?uo aeinoeaaao 20000 ei/nae. Aeaaiaea?y oaeie ia?iiiie nei?inoe
a-/anoeoeu, i?ieaoay /a?ac aicaeoo e noaeeeaaynue n iieaeoeaie aacia,
auaeaatho ec ieo yeaeo?iiu. Iieaeoeu, iioa?yaoea yeaeo?iiu, noaiiayony
ca?yaeaiiuie iieiaeeoaeueii, auaeoua aea yeaeo?iiu oio/an
i?eniaaeeiythony e ae?oaei iieaeoeai, ca?yaeay eo io?eoeaoaeueii.
Oaeei ia?acii, a aicaeooa ia iooe a-/anoeoe ia?acothony
iieiaeeoaeueii e io?eoeaoaeueii ca?yaeaiiua eiiu aaca. Niiniaiinoue
a-/anoeoe eiiece?iaaoue aicaeoo auea eniieueciaaia aiaeeeneei oeceeii
Aeeueniiii aeey oiai, /oiau naeaeaoue aeaeeiuie iooe aeaeaeaiey
ioaeaeueiuo /anoeoe e noioia?aoe?iaaoue eo.
Aiineaaenoaee aiia?ao aeey oioia?aoe?iaaiey /anoeoe iieo/ee iacaaiea
eaia?u Aeeueniia. (Ia?aue o?aeiaue aeaoaeoi? ca?yaeaiiuo /anoeoe.
Ecia?aoaia *. Aeeueniiii a 1912. Aeaenoaea Aeeueniia eaia?u iniiaaii ia
eiiaeainaoeee ia?anuuaiiiai ia?a (ia?aciaaiee iaeeeo eaiaeae aeeaeeinoe)
ia eiiao, aicieeathueo aaeieue neaaea (o?aea) ca?yaeaiiie /anoeoeu. A
aeaeueiaeoai auoaniaia ae?oaeie o?aeiauie aeaoaeoi?aie.)
Enneaaeoy iooe aeaeaeaiey /anoeoe n iiiiuueth eaia?u, ?aca?oi?ae
caiaoee, /oi a eaia?a iie ia?aeeaeueiu (iooe), a i?e i?iioneaiee io/ea
ia?aeeaeueiuo eo/ae /a?ac neie aaca eee oiieoth iaoaeee/aneoth
ieanoeieo, iie auoiaeyo ia ia?aeeaeueii, a ianeieueei ?anoiaeyony, o.a.
i?ienoiaeeo ioeeiiaiea /anoeoe io eo ia?aiia/aeueiiai iooe. Iaeioi?ua
/anoeoeu ioeeiiyeenue i/aiue neeueii, iaeioi?ua aiiaua ia i?ioiaeeee
/a?ac oiieoth ieanoeieo.
Iiaeaeue aoiia Ai?-?aca?oi?ae
Enoiaey ec yoeo iaaethaeaiee, ?aca?oi?ae i?aaeeiaeee naith noaio
no?iaiey aoiia: a oeaio?a aoiia iaoiaeeony iieiaeeoaeueiia yae?i, aie?oa
eioi?iai ii ?aciui i?aeoaeyi a?auathony io?eoeaoaeueiua yeaeo?iiu.
Oeaio?ino?aieoaeueiua neeu, aicieeathuea i?e eo a?auaiee oaea?aeeaatho
eo ia naieo i?aeoaeyo e ia aeatho ei oeaoaoue. Yoa iiaeaeue aoiia eaaei
iauyniyao yaeaiea ioeeiiaiey a- /anoeoe. ?acia?u yae?a e yeaeo?iiia
i/aiue iaeu ii n?aaiaieth n ?acia?aie anaai aoiia, eioi?ua
ii?aaeaeythony i?aeoaie iaeaieaa oaeaeaiiuo io yae?a yeaeo?iiia; iiyoiio
aieueoeinoai a-/anoeoe i?ieaoaao /a?ac aoiiu aac caiaoiiai ioeeiiaiey.
Oieueei a oao neo/ayo, eiaaea a-/anoeoeu i/aiue aeecei iiaeoiaeeo e
yae?o, yeaeo?e/aneia iooaeeeaaiea aucuaaao ?aceia ioeeiiaiea aa io
ia?aiia/aeueiiai iooe. Oaeei ia?acii, eco/aiea ?annayiea a-/anoeoe
iieiaeeei ia/aei yaea?iie oai?ee aoiia. Iaeiie ec caaea/, noiyaoeo
ia?aae oai?eae no?iaiey aoiia a ia/aea aa ?acaeoey, auei ii?aaeaeaiea
aaee/eiu ca?yaea yae?a ?acee/iuo aoiiia. Oae eae aoii a oeaeii
yeaeo?e/anee iaeo?aeai, oi, ii?aaeaeea ca?yae yae?a, iiaeii auei au
onoaiiaeoue e /enei ie?oaeathueo yae?i yeaeo?iiia. A ?aoaiee yoie
caaea/e yoie aieueooth iiiiuue ieacaei eco/aiea niaeo?ia ?aioaaiianeeo
eo/ae. ?aioaaiianeea eo/e aicieeatho i?e oaea?a auno?i eaoyueo
yeaeo?iiia i eaeia-eeai oaa?aeia oaei e ioee/athony io eo/ae aeaeeiiai
naaoa oieueei cia/eoaeueii iaiueoae aeeeiie aieiu. A oi a?aiy eae
ei?ioeea naaoiaua aieiu eiatho aeeeio ieiei 4000 aiano?aiia (oeieaoiaua
eo/e), aeeeiu aiei ?aioaaiianeeo eo/ae eaaeao a i?aaeaeao io 20 aei 0,1
aiano?aia. *oiau iieo/eoue niaeo? ?aioaaiianeeo eo/ae, iaeuecy
iieueciaaoueny iaueiiaaiiie i?eciie eee aeeo?aeoeeiiiie ?aoaoeie.
(Aeeo?aeoeeiiiay ?AOAOEA, iioe/aneee i?eai?; niaieoiiinoue aieueoiai
eiee/anoaa ia?aeeaeueiuo uaeae a iai?ic?a/iii ye?aia eee io?aaeathueo
ca?eaeueiuo iieinie (oo?eoia), ?aaiiionoiyueo ae?oa io ae?oaa, ia
eioi?uo i?ienoiaeeo aeeo?aeoeey naaoa. Aeeo?aeoeeiiiay ?aoaoea ?aceaaaao
iaaeathuee ia iaa io/ie naaoa a niaeo?, /oi eniieuecoaony a
niaeo?aeueiuo i?eai?ao. )
Aeey ?aioaaiianeeo eo/ae o?aaiaaeanue ?ao?oea n i/aiue aieueoei
eiee/anoaii aeaeaiee ia iaeei ieeeeiao? (i?eia?ii 1iei./1ii.). Oaeoth
?ao?oeo eneonnoaaiii i?eaioiaeoue auei iaaiciiaeii. A 1912 a. o
oaaeoea?neiai oeceea Eaoy aicieeea iuneue eniieueciaaoue e?enoaeeu a
ea/anoaa aeeo?aeoeeiiiie ?aoaoee aeey ?aioaaiianeeo eo/ae.
Iiaeaeue e?enoaeea
Oii?yaei/aiiia ?aniieiaeaiea aoiiia a e?enoaeea e iaeia ?annoiyiea
iaaeaeo ieie aeaaaei iiaiae i?aaeiieaaaoue /oi eae ?ac e?enoaeeu e
iiaeieaeoo ia ?ieue o?aaoaiie aeeo?aeoeeiiiie ?ao?oee.
Iiuo aeanoyua iiaeoaa?aeee i?aaeiieiaeaiea Eaoy, anei?a oaeaeinue
iino?ieoue i?eai?u, eioi?ua aeaaaee aiciiaeiinoue iieo/aoue niaeo?
?aioaaiianeeo eo/ae ii/oe anao yeaiaioia. Aeey iieo/aiey ?aioaaiianeeo
niaeo?ia aioeeaoiae a ?aioaaiianeeo o?oaeao aeaeatho ec oiai iaoaeea,
niaeo? eioi?iai oioyo iieo/eoue, eee aea iaiinyo niaaeeiaiea
enneaaeoaiiai yeaiaioa. Ye?aiii aeey niaeo?a neoaeeo oioiaoiaaa; iinea
i?iyaeaiey ia iae aeaeiu ana eeiee niaeo?a. A 1913 a. aiaeeeneee o/aiue
Iicee, eco/ay ?aioaaiianeea niaeo?u iaoae niioiioaiea iaaeaeo aeeeiaie
aiei ?aioaaiianeeo eo/ae e ii?yaeeiaiai iiia?aie niioaaonoaothueo
yeaiaioia – yoi iineo iacaaiea caeiia Iicee e iiaeao auoue
noi?ioee?iaaii neaaeothuei ia?acii: Ei?ie eaaae?aoiua ec ia?aoiuo
cia/aiee aeeei aiei iaoiaeyony a eeiaeiie caaeneiinoe io ii?yaeeiauo
iiia?ia yeaiaioia.
Aua aei ?aaio Iicee iaeioi?ua o/?iua i?aaeiieaaaee, /oi
ii?yaeeiaue iiia? yeaiaioa oeacuaaao /enei ca?yaeia yae?a aai aoiia. A
oiaea a?aiy ?aca?oi?ae, eco/ay ?annaeaaiea a-/anoeoe i?e
i?ioiaeaeaiee /a?ac oiieea iaoaeee/aneea ieanoeiee, auyniee, /oi anee
ca?yae yeaeo?iia i?eiyoue ca aaeeieoeo, oi au?aaeaaiue a oaeeo
aaeeieoeao ca?yae yae?a i?eaeeceoaeueii ?aaai iieiaeia aoiiiiai aana
yeaiaioa. Ii?yaeeiaue iiia?, ii e?aeia ia?a aieaa eaaeeo yeaiaioia,
oiaea ?aaiyaony i?eia?ii iieiaeia aoiiiiai aana. Ana aianoa acyoia
i?eaaei e auaiaeo, /oi Ca?yae yae?a /eneaiii ?aaai ii?yaeeiaiio iiia?o
yeaiaioa. Oaeei ia?acii, caeii Iicee iicaieee ii?aaeaeeoue ca?yaeu
aoiiiuo yaea?. Oai naiui, aaeaeo iaeo?aeueiinoe aoiiia, auei onoaiiaeaii
e /enei yeaeo?iiia, a?auathueony aie?oa yae?a a aoiia eaaeaeiai
yeaiaioa. ssaea?iay iiaeaeue aoiia ?aca?oi?aea iieo/eea naia
aeaeueiaeoaa ?acaeoea aeaaiaea?y ?aaioai Ieeuen Ai?a, a eioi?uo
o/aiea i no?iaiee aoiia ia?ac?uaii naycuaaaony n o/aieai i
i?ienoiaeaeaiee niaeo?ia.
Ai? (Bohr) Ieeuen Oai?ee Aeaaeae (1885-1962)
Eeiae/aoua niaeo?u iieo/athony i?e ?aceiaeaiee naaoa enioneaaiiai
?aneaeaiiuie ia?aie eee aacaie. Eaaeaeiio yeaiaioo ioaa/aao naie
niaeo?, ioee/athueeny io niaeo?ia ae?oaeo yeaiaioia. Aieueoeinoai
iaoaeeia aeaao i/aiue neiaeiua niaeo?u, niaea?aeauea ia?iiiia /enei
eeiee (a aeaeaca aei 5000), ii ano?a/athony e n?aaieoaeueii
i?inoua niaeo?u.
?acaeaay yaea?ioth oai?eth ?aca?oi?aea, o/aiua i?eoee e
iunee, /oi neiaeiay no?oeoo?a eeiae/aouo niaeo?ia iaoneiaeaia
i?ienoiaeyueie aioo?e aoiiia eieaaaieyie yeaeo?iiia. Ii oai?ee
?aca?oi?aea, eaaeaeue yeaeo?ii a?auaaony aie?oa yae?a, i?e/ai neea
i?eoyaeaiey yae?a o?aaiiaaoeaaaony oeaio?iaaaeiie neeie, aicieeathuae
i?e a?auaiee yeaeo?iia. A?auaiea yeaeo?iia niaa?oaiii aiaeiae/ii aai
auno?ui eieaaaieyi e aeieaeii aucaaoue enioneaiea yeaeo?iiaaieoiuo
aiei. Iiyoiio iiaeii i?aaeiieiaeeoue, /oi a?auathueeny yeaeo?ii
eceo/aao naao ii?aaeaeaiiie aeeeiu aieiu, caaenyuee io /anoiou
ia?auaiey yeaeo?iia ii i?aeoa. Ii, eceo/ay naao, yeaeo?ii oa?yao /anoue
naiae yia?aee, a neaaenoaea /aai ia?ooaaony ?aaiiaanea iaaeaeo iei
e yae?ii; aeey ainnoaiiaeaiey ?aaiiaaney yeaeo?ii aeieaeai
iinoaiaiii ia?aaeaeaaoueny aeeaea e yae?o, i?e/ai oae aea iinoaiaiii
aoaeao eciaiyoueny /anoioa ia?auaiey yeaeo?iia e oa?aeoa?
enioneaaiiai ei naaoa. A eiioea eiioeia, en/a?iaa anth yia?aeth,
yeaeo?ii aeieaeai “oianoue” ia yae?i, e eceo/aiea naaoa i?ae?aoeony.
Anee au ia naiii aeaea i?ienoiaeeei oaeia iai?a?uaiia eciaiaiea
aeaeaeaiey yeaeo?iia, oi e niaeo? iieo/aeny au anaaaea iai?a?uaiue, a
ia n eo/aie ii?aaeaeaiiie aeeeiu aieiu. E?iia oiai, “iaaeaiea”
yeaeo?iia ia yae?i icia/aei au ?ac?ooaiea aoiia e i?ae?auaiey aai
nouanoaiaaiey. Oaeei ia?acii, oai?ey ?aca?oi?aea auea aanneeueia
iauynieoue ia oieueei caeiiiia?iinoe a ?ani?aaeaeaiee
Ieaie (Planck) Iaen
(1858-1947)
eeiee niaeo?a, ie e naii nouanoaiaaiea eeiae/aouo niaeo?ia. A 1913 a.
Ai? i?aaeeiaeee nith oai?eth no?iaiey aoiia, a eioi?ie aio oaeaeinue n
aieueoei eneonnoaii niaeaniaaoue niaeo?aeueiua yaeaiey n yaea?iie
iiaeaeueth aoiia, i?eiaiea e iineaaeiae oae iacuaaaioth eaaioiaoth
oai?eth eceo/aiey, aaaaeaiioth a iaoeo iaiaoeeei o/aiui-oeceeii Ieaieii.
Nouiinoue oai?ee eaaioia naiaeeony e oiio, /oi eo/enoay yia?aey
enioneaaony e iiaeiuaaony ia iai?a?uaii, eae i?eieiaeinue ?aiueoa, a
ioaeaeueiuie iaeuie, ii aiieia ii?aaeaeaiiuie ii?oeeyie – eaaioaie
yia?aee. Caian yia?aee eceo/athuaai oaea eciaiyaony nea/eaie, eaaio ca
eaaioii; ae?iaiia /enei eaaioia oaei ia iiaeao ie enioneaoue, ie
iiaeiuaoue. Aaee/eia eaaioa yia?aee caaeneo io /anoiou eceo/aiey: /ai
aieueoa /anoioa eceo/aiey, oai aieueoa aaee/eia eaaioa. Eaaiou eo/enoie
yia?aee iacuaathony oaeaea oioiiaie. I?eiaiea eaaioiaua i?aaenoaaeaiey
e a?auaieth yeaeo?iiia aie?oa yae?a, Ai? iieiaeee a iniiao naiae
oai?ee i/aiue niaeua i?aaeiieiaeaiey, eee iinooeaou. Oioy yoe
iinooeaou e i?ioeai?a/ao caeiiai eeanne/aneie yeaeo?iaeeiaieee, ii iie
iaoiaeyo naia ii?aaaeaiea a oao ii?aceoaeueiuo ?acoeueoaoao, e
eioi?ui i?eaiaeyo, e a oii iieiaeoai niaeanee, eioi?ia iaia?oaeeaaaony
iaaeaeo oai?aoe/aneeie ?acoeueoaoaie e ia?iiiui /eneii
yenia?eiaioaeueiuo oaeoia. Iinooeaou Ai?a caeeth/athony a neaaeothuai:
Yeaeo?ii iiaeao aeaeaaoueny aie?oa ia ii ethaui i?aeoai, a oieueei ii
oaeei, eioi?ua oaeiaeaoai?ytho ii?aaeaeaiiuie oneiaeyi, auoaeathuei ec
oai?ee eaaioia. Yoe i?aeou iieo/eee iacaaiea onoie/eauo eee eaaioiauo
i?aeo. Eiaaea yeaeo?ii aeaeaeaony ii iaeiie ec aiciiaeiuo aeey iaai
onoie/eauo i?aeo, oi ii ia eceo/aao. Ia?aoiae yeaeo?iia n oaeaeaiiie
i?aeou ia aieaa aeeceoth nii?iaiaeaeaaony iioa?ae yia?aee. Iioa?yiiay
aoiiii i?e eaaeaeii ia?aoiaea yia?aey i?aa?auaaony a iaeei eaaio
eo/enoie yia?aee. *anoioa eceo/aaiiai i?e yoii naaoa ii?aaeaeyaony
?aaeeonaie oao aeaoo i?aeo, iaaeaeo eioi?uie niaa?oaaony ia?aoiae
yeaeo?iia. *ai aieueoa ?annoiyiea io i?aeou, ia eioi?ie iaoiaeeony
yeaeo?ii, aei oie, ia eioi?oth ii ia?aoiaeeo, oai aieueoa /anoioa
eceo/aiey. I?inoaeoei ec aoiiia yaeyaony aoii aiaei?iaea; aie?oa yae?a
eioi?iai a?auaaony oieueei iaeei yeaeo?ii. Enoiaey ec i?eaaaeaiiuo
iinooeaoia, Ai? ?ann/eoae ?aaeeonu aiciiaeiuo i?aeo aeey yoiai yeaeo?iia
e iaoae, /oi iie ioiinyony, eae eaaae?aou iaoo?aeueiuo /enae: 1 : 2 :
3 : … n Aaee/eia n iieo/eea iacaaiea aeaaiiai eaaioiaiai /enea.
?aaeeon aeeaeaeoae e yae?o i?aeou a aoiia aiaei?iaea ?aaiyaony 0,53
aiano?aia. Au/eneaiiua ionthaea /anoiou eceo/aiee, nii?iaiaeaeathueo
ia?aoiaeu yeaeo?iia n iaeiie i?aeou ia ae?oaoth, ieacaeenue a oi/iinoe
niaiaaeathueie n /anoioaie, iaeaeaiiuie ia iiuoa aeey eeiee
aiaei?iaeiiai niaeo?a .Oai naiui auea aeieacaia i?aaeeueiinoue ?an/aoa
onoie/eauo i?aeo, a aianoa n oai e i?eeiaeeiinoue iinooeaoia Ai?a
aeey oaeeo ?an/aoia. A aeaeueiaeoai oai?ey Ai?a auea ?ani?ino?aiaia e ia
aoiiioth no?oeoo?o ae?oaeo yeaiaioia, oioy yoi auei naycaiii n iaeioi?ui
o?oaeiinoyie ec-ca aa iiaeciu.
Oai?ey Ai?a iicaieeea ?ac?aoeoue i/aiue aaaeiue aii?in i
?aniieiaeaiee yeaeo?iiia a aoiiao ?acee/iuo yeaiaioia e onoaiiaeoue
caaeneiinoue naienoa yeaiaioia io no?iaiey yeaeo?iiiuo iaiei/ae eo
aoiiia. A ianoiyuaa a?aiy ?ac?aaioaiu noaiu no?iaiey aoiiia anao
oeie/aneeo yeaiaioia. Iaeiaei, eiaoue aaeaeo, /oi ana yoe noaiu yoi
eeoue aieaa eee iaiaa aeinoiaa?iay aeiioaca, iicaieythuay iauynieoue
iiiaea oece/aneea e oeie/aneea naienoaa yeaiaioia. Eae ?aiueoa oaea
auei neacaii, /enei yeaeo?iiia, a?auathueony aie?oa yae?a aoiia,
niioaaonoaoao ii?yaeeiaiio iiia?o yeaiaioa a ia?eiaee/aneie nenoaia.
Yeaeo?iiu ?aniieiaeaiu ii neiyi, o.a. eaaeaeiio neith i?eiaaeeaaeeo
ii?aaeaeaiiia caiieiythuea eee eae au ianuuathuaa aai /enei yeaeo?iiia.
Yeaeo?iiu iaeiiai e oiai aea neiy oa?aeoa?ecothony ii/oe iaeeiaeiaui
caianii yia?aee, o.a. iaoiaeyony i?eia?ii ia iaeeiaeiaii yia?aaoe/aneii
o?iaia. Any iaiei/ea aoiia ?aniaaeaaony
ia ianeieueei yia?aaoe/aneeo o?iaiae. Yeaeo?iiu eaaeaeiai neaaeothuaai
neiy iaoiaeyony ia aieaa aunieii yia?aaoe/aneii o?iaia, /ai yeaeo?iiu
i?aaeuaeouaai neiy. Iaeaieueoaa /enei yeaeo?iiia N, iiaoueo
iaoiaeeoueny ia aeaiiii yia?aaoe/aneii o?iaia, ?aaii oaeaiaiiiio
eaaae?aoo iiia?a neiy:
N=2n*n
aaea n-iiia? neiy. E?iia oiai, onoaiiaeaii, /oi /enei yeaeo?iiia a
ia?oaeiii neia aeey anao yeaiaioia, e?iia iaeeaaeey, ia i?aauoaao
ainueie, a a i?aaeiineaaeiai – ainaiiaaeoeaoe. Yeaeo?iiu ia?oaeiiai
neiy, eae iaeaieaa oaeaeaiiua io yae?a e, neaaeiaaoaeueii, iaeiaiaa
i?i/ii naycaiiua n yae?ii, iiaoo io?uaaoueny io aoiia e
i?eniaaeeiyoueny e ae?oaei aoiiai, aoiaey a ninoaa ia?oaeiiai neiy
iineaaeieo. Aoiiu, eeoeaoeany iaeiiai eee ianeieueeeo yeaeo?iiia,
noaiiayony ca?yaeaiiua iieiaeeoaeueii, oae eae ca?yae yae?a aoiia
i?aauoaao noiio ca?yaeia inoaaoeony yeaeo?iiia. Iaiai?io aoiiu
i?eniaaeeieaoea yeaeo?iiu noaiiayony ca?yaeaiiua io?eoeaoaeueii.
Ia?acothueany oaeei iooai ca?yaeaiiua /anoeoeu, ea/anoaaiii ioee/iua
io niioaaonoaothueo aoiiia. iacuaathony eiiaie. Iiiaea eiiu a naith
i/a?aaeue iiaoo oa?youe eee i?eniaaeeiyoue yeaeo?iiu, i?aa?auaynue i?e
yoii eee a yeaeo?iiaeo?aeueiua aoiiu, eee a iiaua eiiu n ae?oaei
ca?yaeii. Oai?ey Ai?a ieacaea ia?iiiua oneoae oeceea e oeiee, iiaeieaey,
n iaeiie noi?iiu, e ?ane?uoeth caeiiia niaeo?ineiiee e iauyniaieth
iaoaiecia eo/aenioneaiey, a n ae?oaie – e auyniaieth no?oeoo?u
ioaeaeueiuo aoiiia e onoaiiaeaieth nayce iaaeaeo ieie. Iaeiaei
inoaaaeinue aua iiiai yaeaiee a yoie iaeanoe, iauynieoue eioi?ua oai?ey
Ai?a ia iiaea.
Aeaeaeaiea yeaeo?iiia a aoiiao Ai? i?aaenoaaeye eae i?inoia
iaoaie/aneia, iaeiaei iii yaeyaony neiaeiui e naiaia?aciui. Yoi
naiaia?acea auei iauyniaii iiaie eaaioiaie oai?eae. Ionthaea e iioei:
«Ea?ioneoey?ii-a?ieiiaie aeoaeeci».
E oae, yeaeo?ii a aoiia oa?aeoa?ecoaony:
Aeaaiui eaaioiaui /eneii n, oeacuaathuei ia yia?aeth yeaeo?iia;
I?aeoaeueiui eaaioiaui /eneii l , oeacuaathuei ia oa?aeoa? i?aeou;
Iaaieoiui eaaioiaui /eneii, oa?aeoa?ecothuei iieiaeaiea iaeaeia a
i?ino?ainoaa;
E nieiiaui eaaioiaui /eneii, oa?aeoa?ecothuei aa?aoaiiia?aciia
aeaeaeaiea yeaeo?iia aie?oa naiae ine.
… A aeae?eii i?ioeii oeeiniou Ae?aaiae A?aoeee i?aaeiieaaaee, /oi any
iaoa?ey aaeeia, ii i?eia?aoaao oa eee eiua naienoaa a caaeneiinoe io a?
«nouiinoe». A nae/an, a iaoa a?aiy, aeaaiaea?y aaeeeei o/?iui, iu oi/ii
ciaai, ec /aai ia naiii aeaea iia ninoieo.
Eniieuecoaiay eeoa?aoo?a:
Eo?n iaua? oeiee (I.A. Ei?iaei)
Eo?n iauae oeiee (A.I. Oa?ei )
No?iaiea aauanoaa (A.E. Aaneeueaa, A.I. Ooaaeiaa)
Oece/aneay oeiey ( A.E. Aeaeiyei )
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