Euler chithunzi. Euler chithunzi - zitsanzo mfundo

Leonhard Euler (1707-1783) - wotchuka Swiss ndi Russian masamu, membala wa St. Petersburg Academy of Sciences, moyo wake mu Russia. The odziwika bwino mu kusanthula masamu, ziwerengero zambiri, ndi mfundo za imatengedwa bwalo Eulerian (Euler-Venn chithunzi) posonyeza kuchuluka kwa mfundo ndi zinthu kukukhala lapansi.

Dzhon Venn (1834-1923) - English nzeru zapamwamba ndi logician, co-Mlembi wa Euler-Venn zithunzi.

Zikhulupiriro Yogwirizana ndi yosemphana

Mawu akuti mfundo amatanthauza mawonekedwe a maganizo, kusonyeza zinthu zofunika kwambiri pa gulu la zinthu zofanana. Iwo amadziwika ndi munthu kapena gulu la mawu, "map", "The kvintseptakkord Lalikulu", "Monday" ndi ena.

Ngati kumene zinthu buku ndi maganizo kwathunthu kapena pang'ono m'manja mwa voliyumu ya ena, kuyankhula za mfundo n'zogwirizana. Ngati mbali iliyonse ya buku kumatanthauza mfundo sikuli kwa kuchuluka kwa mzake, tili ndi malo ndi mfundo atakwatirana.

Zikatero, aliyense wa mitundu mfundo waika yake ya maubwenzi zotheka. izo n'zogwirizana kwa mfundo zotsatirazi:

• amadziwikira (pazikhala kufanana) mabuku;
• mphambano (alipo) mabuku;
• subordination (subordination).

Pakuti atakwatirana:

• subordination (mgwirizano);
• Mosiyana (contraries);
• kutsutsana (kontradiktornost).

Schematically, ubale malingaliro maganizo angathe kukonzedwa ntchito mabwalo a Euler-Venn.

Mugone pazikhala kufanana

Pankhaniyi, mfundo zikutanthauza chinthu chomwecho. Choncho, kuchuluka kwa mfundo deta ali ofanana. Mwachitsanzo:

A - Sigmund Freud;

Mu - woyambitsa wa psychoanalysis.

mwina;

A - lalikulu;

B - ndi equilateral rectangle;

C - equiangular rhombus.

Ntchito pofotokoza mabwalo kwathunthu zofanana Euler.

The mphambano (alipo)

gulu Izi zikuphatikizapo mfundo kugawana zinthu wamba amapezeka mu ubale ndi pa mphambano. Kuti ndi kuchuluka kwa imodzi mwa mfundo ndi pang'ono m'gulu kuchuluka kwa wina:

A - mphunzitsi;

B - nyimbo fani.

Malinga pa nkhani imeneyi, buku mfundo alipo: aphunzitsi gulu akhoza kukhala nyimbo okonda, ndi mosemphanitsa - pakati mafani nyimbo kungakhale nthumwi za chiphunzitso ntchito. A chiŵerengero ofanana adzakhala choncho kumene lingaliro A amachita Mwachitsanzo, "nzika" ndipo monga B - "autodriver".

Kugonjera (subordination)

Schematically anasonyeza osiyana lonse Euler chithunzi. Kubverana malingaliro Pankhaniyi yodziwika ndi chakuti mfundo Kumvetsela (buku kochepa) amadziwa mbali ya subordinating (buku zikuluzikulu). Pankhaniyi, kapolo sakhala kuutsiriza zosiyana complies kwathunthu.

Mwachitsanzo:

A - mtengo;

B - pine.

Lingaliro adzakhala pansi pa mfundo A. Popeza paini imakhudzanso mitengo, mawu A amakhala subordinating muchisanzo chimenechi, "kungolandira" Lingaliro buku V.

Subordination (mgwirizano)

Chiŵerengero limasonyeza mfundo ziwiri kapena zambiri zosiyana kwenikweni, koma wachokera momwe mwachindunji nawo generic osiyanasiyana. Mwachitsanzo:

A - clarinet;

Mu - gitala;

C - zeze;

D - chida choimbira.

Lingaliro la A, B, C si toyalana ndi ulemu wina ndi mnzake, Koma iwo onse a gulu zoimbira (lingaliro D).

Zotsutsana (contraries)

Kutsutsana ubale malingaliro zikutanthauza mfundo relatedness deta kwa mtundu womwewo. Choncho imodzi mwa mfundo ili katundu (zinthu), pamene ena awo wokanayo m'malo ufalikire khalidwe. Choncho, ife tikuchita ndi otsutsana nawo. Mwachitsanzo:

A - ndi nyenyezi yaing'ono;

B - chimphona.

Euler bwalo pa ubwenzi zosiyana pakati pa mawu lagawidwa zigawo zitatu, woyamba wa Chofanana mfundo A, wachiwiri - mu lingaliro, ndi wachitatu - zina zotheka limaphunzitsa.

Vutolo (kontradiktornost)

Pankhaniyi, mfundo onse ndi maganizo a mtundu womwewo. Monga mu chitsanzo yapita, imodzi mwa mfundo zikusonyeza makhalidwe ena (makhalidwe), pamene winayo adawatsutsa. Komabe, mosiyana ndi maganizo anyamata, wachiwiri, mfundo zosiyana, osati m'malo katundu anakana ina. Mwachitsanzo:

A - yovuta;

B - ntchito yosavuta (sanali A).

Posonyeza kuchuluka kwa malingaliro a mtundu uwu, bwalo Euler lagawidwa pawiri - wachitatu m'khalapakati Pankhaniyi kulibe. Choncho, mfundo komanso ndi otsutsana nawo. Pankhaniyi, mmodzi wa iwo (A) amakhala zabwino (kuvomereza chilichonse chosonyeza) ndi wachiwiri (B kapena A) - zoipa (kumakana chizindikiro yoyenera), "White Paper" - "si pepala woyera", "mbiri ya dziko" - "mbiri zakunja," etc ...

Choncho, buku chiŵerengero mfundo poyerekezera ndi mzake ndi khalidwe kiyi kudziwa Euler mabwalo.

Relations pakati akanema

Tiyenera kusiyanitsa pakati pa zinthu ndi kuchuluka kwa buku akuimira Euler mabwalo. Lingaliro anaitenga ku kuchuluka kwa sayansi masamu ndipo ali mokwanira waukulu. Zitsanzo maganizo ndi masamu kusonyeza ngati akonzedwa ena a zinthu. Akutsutsa okha ndi mfundo za Anatipatsa. "Zambiri A zambiri, monga akanakhalapo" (Georg Cantor, woyambitsa wa chiphunzitso zanu).

Akuti adzabweretse ikuchitika ndi likulu makalata A, B, C, D ... etc., zinthu kukukhala ndi - lowercase: .. A, b, c, anthu d ... etc. Zitsanzo za akonzedwa mwina ophunzira ili mu kalasi imodzi, mabuku ataima. pa alumali yeniyeni (kapena Mwachitsanzo, mabuku onse mu laibulale makamaka), masamba mu zolemba za, zipatso mu glade nkhalango, ndi zina zotero. d.

Nayenso ngati akonzedwa ena lilibe zinthu iliyonse, ndiye iwo akutchedwa chizindikiro osalembapo ndipo amasonyeza inu. Mwachitsanzo, kuchuluka kwa mfundo mphambano ya mizere yomweyi, ndi kuchuluka kwa njira zothetsera aone kuti pali × ² = -5.

Kukwaniritsa mavuto

Kuti athetse ambiri ntchito ankagwiritsa ntchito Euler chithunzi. Zimasonyeza nzeru kulankhulana ntchito mfundo anapereka chiphunzitso. Iwo amagwiritsa malingaliro a tebulo choonadi. Mwachitsanzo, bwalo amaimira dzina A choonadi ankalamulira. Choncho, malo ena panja bwalo adzakhala bodza. Pofuna kudziwa malo a tchati kuti ntchito mfundo ayenera aswa zigawo liwulo Euler chithunzi chimene zake kuti zinthu A ndi B ndi zoona.

Kugwiritsa Euler mabwalo anapeza lonse othandiza ntchito m'mafakitale zosiyanasiyana. Mwachitsanzo, zinthu kusankha katswiri. Ngati nkhaniyo ndi nkhawa za kusankha ntchito m'tsogolo, akhoza kutsogoleredwa ndi muyezo zotsatirazi:

W - zimene ndimakonda kuchita?

D - ndichondiyenera?

P - kuposa ine ndalama wabwino?

Tikuimira izi mu mawonekedwe a zithunzi: Euler chithunzi (zitsanzo mu mfundo - ndi mphambano chiŵerengero):

The chifukwa adzakhala amene kudzinenera kuti adzakhala pa mphambano ya mabwalo atatu.

Osiyana malo awa Euler-Venn otani masamu (mnyumba chiphunzitso) mu mawerengedwe a ma ndi katundu. Euler chithunzi kuchuluka kwa zinthu chithunzi unazunguliridwa mu rectangle zimasonyeza chilengedwe akonzedwa (U). M'malo mabwalo Angagwiritsidwenso ntchito mafanizo ena chatsekedwa, koma chofunika akanali yemweyo. Ziwerengero intersect ndi mzake, monga mwa zikhalidwe za vutoli (zinachitikira kwambiri general). Komanso, ziwerengero deta iyenera zaikidwa mogwirizana. Pamene nyengo pansi pa kuganizira akhoza kuchita waika mfundo ili mkati zigawo zosiyana za taperekachi. Ofotokoza mungathe mthunzi malo enieni, potero kusonyeza kuika utangoyamba kumene.

Ndi akanema deta ndi chovomerezeka kuchita zazikulu ntchito masamu: Kuwonjezera (Uwerenge likulowa wa zinthu), wochotsera (kusiyana), chulutsa (mankhwala). Komanso, kuthokoza kwa Euler-Venn zithunzi angachichite ntchito pa malo poyerekeza ndi kuchuluka kwa zinthu zawo constituent, osati kuwerengera iwo.