Euler chithunzi: Zitsanzo ndi mwayi

Masamu makamaka ndi sayansi umboni, ngati inu kuchoka mfundo zofunika kwambiri. Choncho, peyala ya maapulo patatu akhoza zimaonetsa akamachita zinthu zikuluzikulu zimene zili maziko a masamu, koma mwamsanga pamene ndege ya ntchito zambiri, awa zinthu si kokwanira. Winawake anayesa kusonyeza pa ntchito maapulo pa waika malire? Mfundo za nkhaniyo ndi chakuti palibe. Zovuta zambiri malingaliro, amene umagwira ntchito pa masamu chiweruzo chake, ndi mabvuto kwambiri izo zinkawoneka mawu awo zithunzi, zimene kutikonza atsogolere kumvetsetsa. Komabe, chimwemwe ana masiku ano, sayansi ambiri, akhala kudzipatula zotsatirazi Euler, zitsanzo ndi mwayi umene tikambirana pansipa.

A mbiri pang'ono

April 17, 1707 anapereka dziko sayansi Leonarda Eylera - wasayansi kwambiri amene zopereka masamu, sayansi shipbuilding ndipo ngakhale chiphunzitso nyimbo si kukambapo. ntchito zake akuzindikiridwa ndi mu ankafuna kuti lero padziko lonse, ngakhale kuti sayansi alibe kuima. Makamaka zoseketsa n'chakuti Bambo Euler unkagwira ntchito chitukuko cha sukulu Russian a masamu apamwamba kwambiri chifukwa chakuti chifuniro cha tsoka, iye kawiri atabwerera wathu. Wasayansi anali ndi luso lapadera kumanga chimaonekera mu ma aligorivimu ake mfundo, kudula onse kosafunikira ndipo palibe nthawi amayenda ndi ambiri kwa yeniyeni. Ife sitikhala ati ubwino onse, monga adzakhala kutenga yambiri ya nthawi, tibwerere ku phunziro nkhaniyo. Ndipo Iye adafotokoza ntchito chifaniziro mawonekedwe ntchito pa waika. Euler chithunzi njira yothetsera, ngakhale ntchito yovuta kwambiri anakonza, akhoza kusonyeza zowoneka.

Kodi chofunika?

Zochita za izi Euler chithunzi cha chomwe chili m'munsimu angagwiritsidwe ntchito osati masamu, monga mfundo 'adzakhazikitsa "sali wapadera chilangocho. Choncho, akhala bwino ntchito anira.

Chiwembu amasonyeza ubale pamwamba amakhazikitsa A (nambala zopanda chilungamo), B (zomveka integers) ndi C (manambala zachilengedwe). Anzanu amasonyeza amene anakhala ali m'gulu kuika B, ndiye amaika nkhabe intersect nawo. Chitsanzo cha yosavuta, akufotokozera limatchula za 'adzakhazikitsa ubwenzi "amene umboni kwambiri kuyerekezera weniweni ngati chifukwa cha malire awo.

mfundo ajebura

Kudera limeneli maganizo masamu ukugwira ntchito mawu, zomwe zimakhala khalidwe woona ndi wabodza. Mwachitsanzo, ku pulayimale ndi: chiwerengero 625 ndi divisible ndi 25, chiwerengero 625 ndi divisible ndi 5, chiwerengero 625 yosavuta. Woyamba ndi wachiwiri chiyanjo - choonadi, pamene yotsirizira - bodza. Kumene, kuchita n'zovuta kwambiri, koma mfundo kumaonekeranso bwino. Ndipo, ndithudi, kusankha kachiwiri nawo Euler chithunzi zitsanzo za ntchito yawo yabwino kwambiri ndi mwachilengedwe kunyalanyaza.

A pang'ono chiphunzitso:

• Tiyeni amapereka ndi B kulibe ndipo sali kanthu, ndiye kuti ntchito mphambano izi kumatanthauza kucheza ndi negation.
• Mphambano kukukhala A ndi B tichipeza zinthu za nthawi yomweyo monga kuika A ndipo anapereka B.
• Osakaniza A ndi B tichipeza zinthu za kuika A kapena B.
• A negation wa Anatipatsa - akonzedwa kuti tichipeza zinthu zomwe si za kuika A.

Zonse izi kachiwiri limafanizira Euler chithunzi mu mfundo, ndi iwo lililonse ntchito, kaya mlingo wa movutikira imaonekera ndipo kuwoneka.

Axioms wa ajebura maganizo

Musamachite 1 ndi 0 anafotokozedwa ndi kukhalapo mu zosiyanasiyana A, ndiye:

• A negation wa negation a akonzedwa ndi ya A;
• A kuchuluka wogwirizana ndi ne_A 1;
• A kuchuluka kwa mgwirizano 1 1;
• A mgwirizano wa anakhala ndi palokha ndi kuika A;
• Association of A 0 kuika A;
• A kuchuluka mphambano ne_A 0;
• A kuchuluka kwa mphambano palokha ndi kuika A;
• mphambano za A 0 0;
• mphambano za A 1 chili A.

The katundu yaikulu ya ajebura maganizo

Tiyeni likulowa A ndi B kulibe ndipo sali kanthu, ndiye:

• chifukwa mphambano ndi chilumikizano kukukhala A ndi B amachita malamulo commutative;
• chifukwa mphambano ndi chilumikizano kukukhala A ndi B amachita malamulo associative;
• chifukwa mphambano ndi chilumikizano kukukhala A ndi B amachita malamulo distributive;
• kukana kwa mphambano za A ndi B ndi mphambano ya negations la A ndi B;
• kukana mgwirizano kukukhala A ndi B ndi mgwirizano wa negations la A ndi B.

Pansipa amaoneka zotsatirazi Euler mphambano zitsanzo ndi kaphatikizidwe likulowa A, B ndi C.

ziyembekezo

Ntchito Leonarda Eylera zapamwamba maziko a masamu ano, koma tsopano iwo ali bwinobwino ntchito m'madera a zochita za anthu amene watsopano, kuti osachepera ulamuliro makampani: Euler chithunzi, zitsanzo ndi matchati kufotokoza njira zitsanzo chitukuko, kaya Russian kapena Anglo-American Baibulo .