Equations, Codes, Siphers, Mathematics and Poetry

Michal Shurek ya ce game da kansa: “An haife ni a shekara ta 1946. Na sauke karatu a Jami’ar Warsaw a shekarar 1968 kuma tun daga nan nake aiki a Faculty of Mathematics, Informatics and Mechanics. Ƙwarewar kimiyya: lissafi na algebra. Kwanan nan na yi ma'amala da tarin vector. Menene ma'anar vector? Don haka, vectors suna buƙatar a ɗaure su tam tare da zaren, kuma muna da bunch. Abokina masanin kimiyya Anthony Sim ya sanya ni shiga cikin Matashin Technician (ya yarda ya kamata ya sami sarauta daga kudade na). Na rubuta wasu kasidu sannan na zauna, kuma tun 1978 kuna iya karanta kowane wata abin da nake tunani game da lissafi. Ina son duwatsu kuma, duk da kiba, ina ƙoƙarin tafiya. Ina tsammanin malamai sune mafi mahimmanci. Zan ajiye ’yan siyasa, ko wane irin zabin su, a cikin wani wurin da ke da tsaro sosai don kada su tsere. Ciyar da sau ɗaya a rana. Wani beagle daga Tulek yana so na.

Ma'auni kamar ma'ajin lissafi ne. Magance ma'auni, ainihin mathematics, shine karatun rubutu. Masana tauhidi sun lura da wannan tun ƙarni na XNUMX. John Paul II, wanda ya san ilimin lissafi, ya rubuta kuma ya ambata wannan sau da yawa a cikin wa'azinsa - abin baƙin ciki, an goge gaskiyar daga tunanina.

A kimiyyar makaranta, ana wakilta shi Pythagoras a matsayin marubucin ka'idar akan wasu dogara a cikin madaidaicin alwatika. Don haka ya zama wani ɓangare na falsafancin mu na Eurocentric. Kuma duk da haka Pythagoras yana da kyawawan halaye masu yawa. Shi ne ya dora wa dalibansa aikin "koyan duniya", daga "menene bayan wannan tudun?" kafin nazarin taurari. Shi ya sa Turawa suka “gano” tsoffin wayewa, ba akasin haka ba.

Wasu masu karatu suna tunawaViète alamukuma"; Manya manyan masu karatu suna tunawa da kalmar kanta daga makaranta kuma kusan gaskiyar cewa tambayar ta bayyana a cikin ma'auni. Waɗannan ƙa'idodi na yau da kullun suna "akida" boye-boye bayani.

Ba mamaki daya Francois Vietnam (1540-1603) ya tsunduma cikin aikin cryptography a kotun Henry IV (Sarkin Faransa na farko daga daular Bourbon, 1553-1610) kuma ya yi nasarar karya taswirar da Burtaniya ke amfani da shi a yakin da Faransa. Don haka ya taka rawa iri ɗaya da ƴan lissafin Poland (wanda Marian Rejewski ke jagoranta), wanda ya gano sirrin na'urar sifa ta Jamus Enigma kafin yakin duniya na biyu.

fashion jigo

Daidai. Taken "lambobi da ƙididdiga" ya daɗe ya zama abin salo a koyarwa. Na riga na rubuta game da wannan sau da yawa, kuma a cikin watanni biyu za a sami wani jerin. A wannan karon ina rubutawa a ƙarƙashin kallon wani fim game da yaƙin 1920, inda nasarar ta kasance mafi yawa saboda karya ka'idar sojojin Bolshevik da wata tawagar karkashin jagorancin matashin lokacin. Vaclav Sierpinski (1882-1969). A'a, ba Enigma ba tukuna, gabatarwa ce kawai. Na tuna wani fage daga fim ɗin inda Józef Piłsudski (wanda Daniil Olbrychski ya buga) ya ce wa shugaban sashen rubutun:

Saƙonnin da aka yanke suna ɗauke da saƙo mai mahimmanci: Sojojin Tukhachevsky ba za su sami tallafi ba. Kuna iya kai hari!

Na san Vaclav Sierpinski (idan zan iya faɗi haka: Ni ɗan ɗalibi ne, shi mashahurin farfesa ne), ya halarci laccoci da karawa juna sani. Ya ba da ra'ayin wani gurguwar malami, ba shi da tunani, mai shagaltuwa da tarbiyyarsa, ba ya ganin duniya. Ya yi lacca ta musamman, yana fuskantar allo, bai kalli masu sauraro ba ... amma ya ji kamar kwararre ne. Wata hanya ko wata, yana da wasu iyawar ilimin lissafi - alal misali, don magance matsaloli. Akwai wasu-masana kimiyya waɗanda ba su da kyau a warware wasanin gwada ilimi, amma waɗanda ke da zurfin fahimtar dukkanin ka'idar kuma suna da ikon fara dukkan fagagen kerawa. Muna buƙatar duka biyun - kodayake na farko zai yi sauri.

Vaclav Sierpinski bai taba magana game da nasarorin da ya samu ba a 1920. Har zuwa 1939, wannan tabbas ya kasance a asirce, kuma bayan 1945, waɗanda suka yi yaƙi da Soviet Rasha ba su ji tausayin hukumomin lokacin ba. Hukunci na cewa ana buƙatar masana kimiyya, kamar sojoji, an tabbatar da cewa: "kawai idan." Ga Shugaba Roosevelt yana kiran Einstein:

Fitaccen masanin lissafi na kasar Rasha Igor Arnold a fili da bakin ciki ya ce yakin yana da matukar tasiri a ci gaban ilmin lissafi da kimiyyar lissafi (radar da GPS kuma suna da asalin soja). Ba na shiga cikin yanayin halin kirki na amfani da bam din bam: a nan ne tsawaita yakin har tsawon shekara guda da kuma mutuwar da dama na sojojinsu - akwai wahalar da fararen hula marasa laifi.

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Na gudu zuwa wuraren da aka saba - k. Yawancinmu suna wasa da lambobin, watakila suna leko, watakila haka. Sauƙaƙan sifofi, bisa ƙa'idar maye gurbin haruffa da wasu haruffa ko wasu lambobi, ana karyewa akai-akai idan muka sami 'yan alamu kaɗan (misali, muna zato sunan sarki). Binciken kididdiga kuma yana taimakawa a yau. Mafi muni, lokacin da komai ya canza. Amma mafi munin abu shine lokacin da babu daidaituwa. Yi la'akari da lambar da aka kwatanta a cikin Kasadar Soja Mai Kyau Schweik. Ɗauki littafi, alal misali, Ambaliyar. Ga shawarwarin a shafi na farko da na biyu.

Muna so mu ɓoye kalmar "CAT". Muna buɗewa a shafi na 1 da sakan na gaba. Mun sami cewa a shafi na 1, harafin K ya fara bayyana a wuri na 59. Mun sami kalmar hamsin da tara a akasin haka, daya bangaren. Kalmar "a" ce. Yanzu harafin O. A gefen hagu shine kalma ta 16, kuma ta goma sha shida a hannun dama shine "Mr." Harafin T yana a matsayi na 95, idan na ƙidaya daidai, kuma kalmar casa'in da biyar daga dama ita ce "o". Don haka, CAT = 1 Yahweh O.

Siffar “mara zato”, duk da jinkirin jinkirin duka don ɓoyewa da ... don zato. A ce muna so mu wuce harafin M. Za mu iya bincika ko mun ɓoye shi da kalmar "Wołodyjowski". Kuma bayan mu sun riga sun shirya ɗakin kurkuku. Za mu iya kawai ƙidaya a kan maye! Bugu da ƙari, rashin hankali ya lura da rahotanni na ma'aikatan sirri cewa abokan ciniki sun daɗe suna sayen juzu'in farko na Ambaliyar.

Labari na yana ba da gudummawa ga wannan bita: har ma da mafi yawan ra'ayoyin masu ilimin lissafi na iya samun aikace-aikace a cikin aikin da aka fahimta sosai. Misali, shin zai yiwu a yi tunanin binciken ilimin lissafi mara amfani fiye da gwajin rarrabawa ta ... ta 47?

Yaushe muke bukata a rayuwa? Kuma idan haka ne, zai kasance da sauƙi a gwada raba shi. Idan ya raba, to yana da kyau, idan ba haka ba, to ... na biyu yana da kyau (mun san cewa ba ya rarraba).

Yadda ake raba kuma me yasa

Bayan wannan gabatarwar, bari mu ci gaba, shin masu karatu kun san alamun rarrabuwa? Tabbas. Hatta lambobi suna ƙarewa a 2, 4, 6, 8, ko sifili. Ana iya raba lamba da uku idan jimlar lambobinta ke raba uku. Hakazalika, tare da alamar rarraba ta tara - jimlar lambobi dole ne a rarraba ta tara.

Wanene yake bukata? Zan yi karya idan na gamsar da mai karatu cewa yana da kyau ga wani abu banda... makaranta assignment. To, da kuma wani sifa na rarrabawa ta 4 (kuma menene, Mai karatu? Wataƙila za ku yi amfani da shi lokacin da kuke son sanin shekara ta gaba Olympiad ta faɗo a kan ...). Amma fasalin rarraba ta 47? Wannan tuni ciwon kai ne. Shin za mu taɓa sanin idan wani abu yana raba ta 47? Idan eh, to, ɗauki kalkuleta ka gani.

Wannan shine. Kai gaskiya mai karatu. Duk da haka, karanta a kan. Barka da zuwa.

Alamar rarraba ta 47: Lambobin 100+ ana raba su ta 47 idan kuma kawai idan 47 ya raba ta +8.

Masanin lissafin zai yi murmushi tare da gamsuwa: "Gee, kyakkyawa." Amma lissafin lissafi ne. Shaida tana da mahimmanci, kuma muna kula da kyawunta. Yadda za a tabbatar da halinmu? Yana da sauqi qwarai. Rage daga 100 + lamba 94 - 47 = 47 (2 -). Muna samun 100+-94+47=6+48=6(+8).

Mun rage adadin da ake raba shi da 47, don haka idan 6 (+ 8) ya zama 47, to haka 100 + ne. Amma lambar 6 tana da inganci sosai zuwa 47, wanda ke nufin cewa 6 (+ 8) yana rarraba ta 47 idan kuma idan + 8 ne kawai.

mu duba Wasu misalai.

8805685 ana iya raba ta 47? Idan da gaske muna sha'awar sa, za mu gano da wuri kawai ta hanyar rarraba mu kamar yadda aka koya mana a makarantar firamare. Wata hanya ko wata, yanzu akwai kalkuleta a kowace wayar hannu. Raba? Da, masu zaman kansu 187355.

To, bari mu ga abin da alamar rarrabuwa ta gaya mana. Muna cire haɗin lambobi biyu na ƙarshe, ninka su ta 8, ƙara sakamakon zuwa "lambar da aka yanke" kuma muyi haka tare da lambar da aka samu.

8805685 → 88056 + 8 · 85 = 88736 → 887 + 8 · 36 = 1175 → 11 + 8 · 75 = 611 → 6 + 8 · 11 = 94.

Mun ga cewa 94 yana rarraba ta 47 (launi shine 2), wanda ke nufin cewa ainihin lambar kuma tana iya rarrabawa. Lafiya. Amma idan muka ci gaba da jin daɗi fa?

94 → 0 + 8 94 = 752 → 7 + 8 52 = 423 → 4 + 8 23 = 188 → 1 + 8 88 = 705 → 7 + 8 5 = 47.

Yanzu dole mu daina. Ana raba arba'in da bakwai ta 47, daidai ne?

Shin muna bukatar mu daina? Idan muka kara gaba fa? Ya Allah, komai na iya faruwa... Zan bar cikakkun bayanai. Wataƙila kawai farkon:

47 → 0 + 8 47 = 376 → 3 + 8 76 = 611 → 6 + 8 11 = 94 → 0 + 8 94 = 752.

Amma, abin takaici, yana da jaraba kamar tauna iri...

752 → 7 + 8 * 52 = 423 → 4 + 8 * 23 = 188 → 1 + 8 * 88 = 705 → 7 + 8 * 5 = 47.

Ah, arba'in da bakwai. Ya faru a baya. Menene na gaba? . Haka. Lambobin suna tafiya cikin madauki kamar haka:

Yana da ban sha'awa sosai. Madaukai da yawa.

Biyu bin misalai.

Muna so mu sani idan 10017627 yana rarraba ta 47. Me yasa muke buƙatar wannan ilimin? Muna tunawa da ka'idar: kaiton ilimin da ba ya taimakon mai sani. Ilimi koyaushe yana nan don wani abu. Zai zama don wani abu, amma yanzu ba zan bayyana ba. Wasu ƙarin asusun:

10017627 → 100176 + 8 27 = 100392.

"Ya canza kawunsa daga gatari zuwa sanda." Menene muke samu daga duk wannan?

To, bari mu sake maimaita tsarin shari'ar. Wato za mu ci gaba da yin haka (wato kalmar “iterate”).

100392 → 1003 + 8 92 = 1739 → 17 + 8 39 = 329 → 3 + 8 29 = 235.

Mu dakatar da wasan, mu raba kamar a makaranta (ko a kan ma'auni): 235 = 5 47. Bingo. Asalin lambar 10017627 ana rarraba ta 47.

Sannu da aikatawa!

Idan muka kara gaba fa? Ku amince da ni, za ku iya duba shi.

Kuma wata hujja mai ban sha'awa. Muna so mu bincika idan 799 yana rarraba ta 47. Muna amfani da aikin rarrabawa. Muna cire haɗin lambobi biyu na ƙarshe, mu ninka sakamakon lambar da 8 kuma mu ƙara zuwa abin da ya rage:

799 → 7 + 8 99 = 7 + 792 = 799.

Me muke da shi? Shin 799 za'a iya raba ta 47 idan kuma kawai idan 799 yana raba ta 47? Haka ne, amma ba a buƙatar lissafi don wannan !!! Man yana da mai (akalla wannan mai yana da mai).

Game da ganye, 'yan fashi da kuma ƙarshen barkwanci!

Karin labarai guda biyu. A ina ne ya fi kyau a ɓoye ganye? Amsar a bayyane take: a cikin daji! Amma ta yaya za ku same shi a lokacin?

Na biyu mun sani daga littattafai game da 'yan fashin teku da muka karanta da dadewa. ‘Yan fashin sun yi taswirar wurin da suka binne dukiyar. Wasu kuma ko dai sun sace ko kuma sun yi nasara a yakin. Amma taswirar ba ta nuna tsibirin da aka nufa ba. Kuma nemi kanku! Tabbas, 'yan fashin teku sun shawo kan wannan (azabtarwa) - abubuwan da nake magana akai kuma ana iya fitar da su ta amfani da irin waɗannan hanyoyin.

Karshen barkwanci. Mai karatu! Mun ƙirƙira sifa. Ni ɗan leƙen asiri ne kuma ina amfani da "Junior Technician" azaman akwatin lambata. Aiko min da rufaffen sakonni kamar haka.

Da farko, canza rubutun zuwa jerin lambobi ta amfani da lambar: AB CDEFGH IJ KLMN ON RST UWX Y Z1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Kamar yadda kake gani, ba ma amfani da yarukan Yaren mutanen Poland (watau ba tare da ą, ę, ć, ń, ó, ś) da waɗanda ba Yaren mutanen Poland q, v - amma waɗanda ba Yaren mutanen Poland x suna can kawai idan akwai. Bari mu haɗa wani 25 a matsayin sarari ( sarari tsakanin kalmomi). Oh, abu mafi mahimmanci. Da fatan za a yi amfani da lamba mai lamba 47.

Kun san abin da hakan ke nufi. Za ka je wurin wani abokin aikin lissafi.

Ido abokin ya zaro cike da mamaki.

Kuna amsa da alfahari:

Masanin ilimin lissafi yana ba ku wannan sifa… kuma kun riga kun san cewa ana amfani da aikin da ba a iya gani ba don ɓoyewa.

saboda irin wannan tsari aiki ne da aka siffanta

100 + → + 8.

Don haka, lokacin da kake son sanin ma'anar lamba, kamar 77777777 a cikin saƙon da aka ɓoye, kuna amfani da aikin.

100 + → + 8

har sai kun sami lamba tsakanin 1 da 25. Yanzu duba lambar haruffa bayyane. Bari mu ga: 77777777 →… Na bar muku wannan a matsayin aiki. Amma bari mu ga wace harafi 48 ke ɓoye? Mu karanta:

48 → 0 + 8 48 = 384.

Sai mu koma bi da bi:

384 → 3 + 8 84 = 675 → 6 + 8 75 = 606 → 6 + 8 6 = 54 → 0 + 8 54 = 432…

Ƙarshen ba a gani. Sai bayan lokacin sittin (!) adadin da bai wuce 25 ba, wannan shine 3, wanda ke nufin 48 shine harafin C.

Kuma menene wannan saƙon ya ba mu? (Ina so in tunatar da ku cewa muna amfani da lambar lamba 47):

80 – 152 – 136 – 546 – ​​695719 – 100 – 224 – 555 – 412 – 111 – 640 – 102 – 152 – 12881 – 444 – 77777777 – 59 – 408 – 373.

To, yi tunani game da shi, abin da ke da rikitarwa, wasu asusun. Mun fara. Farkon 80. Sanann doka:

80 → 0 + 8 80 = 640 → 6 + 8 40 = 326.

Ya ci gaba kamar haka:

326 → 211 → 90 → 720 → 167 → 537 → 301 → 11.

Ku ci! Harafin farko na saƙon shine K. Phew, mai sauƙi, amma yaushe zai ɗauki?

Mu kuma duba irin wahalar da muka sha da lamba 1234567. Sai a karo na goma sha shida za mu samu lamba kasa da 25, wato 12. Don haka 1234567 shine L.

To, mutum zai iya cewa, amma wannan aikin lissafin yana da sauƙi don tsara shi akan kwamfuta zai karya lambar nan take. E gaskiya ne. Waɗannan ƙididdigar kwamfuta ce mai sauƙi. ra'ayi da sifar jama'a sannan kuma batun sanya lissafin ya yi wahala ga kwamfuta. Bari yayi aiki aƙalla shekaru ɗari. Shin zai warware saƙon? Ba komai. Ba zai dade ba. Wannan shine (mafi ko ƙasa da haka) abin da bayanan jama'a ke game da shi. Za a iya karya su idan kun yi aiki na dogon lokaci ... har sai labarin bai dace ba.

 ko da yaushe ta haifi "maganin rigakafi". An fara da takobi da garkuwa. Sabis na Asirin suna biyan kuɗi masu yawa ga ƙwararrun masu ilimin lissafi don ƙirƙira hanyoyin ɓoyewa waɗanda kwamfutoci (ciki har da waɗanda muka ƙirƙira) ba za su iya fashe ba a ƙarni na XNUMX.

karni na ashirin da biyu? Ba shi da wuya a san cewa akwai mutane da yawa a duniya waɗanda za su rayu a wannan kyakkyawan ƙarni!

Oh yaya? Idan na tambaya (ni, Jami'in Asirin da “Masanin Fasaha na Matasa” ya tuntube shi) don ɓoyewa da lambar lamba 23 fa? Ko 17? Mai sauƙi:

Kada mu taɓa yin amfani da lissafi don irin waɗannan dalilai.

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Taken labarin game da waka ne. Menene ruwanta da wannan?

Kamar me? Waka kuma tana rufawa duniya asiri.

Ta yaya?

Ta hanyoyin su - kama da na algebraic.