Theorem kalma ce ta asalin Girkanci wanda a shawara wanda ke nuna gaskiya ga wani fannin kimiyya, wanda ke da keɓaɓɓen abin nunawa ta hanyar yin amfani da wasu shawarwarin da aka nuna a baya, waɗanda ake kira axioms. Yawanci theorems suna tallafawa ilimin da ake kira ''daidai’, musamman 'na tsari' (lissafi, dabaru), waɗanda su ne waɗanda ke amfani da abubuwan da suka dace don zana ƙarshe.
Tunanin da ke bayan manufar theorem shine, muddin dai an kafa su ne akan shawarwari na gaskiya da aka bayyana a hankali da kuma daidai, abin da theorem ya bayyana gaskiya ce ingantacciya.. Wannan shi ne daidai abin da ke ba su damar yin hidima a matsayin tallafi don ci gaban kowane ka'idar kimiyya, ba tare da buƙatar sake tabbatar da hakan ba.
Babban ingancin theorems shine halayen su ma'ana. Gabaɗaya, kuma a sake gwadawa da sauran nau'ikan ilimin kimiyya (kamar waɗanda ake samarwa ta hanyar tunani ko kallo), asalinsa daga aiwatar da hanya mai ma'ana ce da za a iya yin oda cikin sauƙi. A wannan ma'anar, theorems suna farawa daga a hasashe na asali, wanda shine abin da kuke son nunawa; rubutun, wanda shine daidai da zanga -zanga, da lissafin, wanda shine ƙarshe ana kaiwa da zarar an kammala muzaharar.
Kamar yadda aka ce, babban ra'ayin theorems shine tambayar yiwuwar yuwuwar ci gaba da yuwuwar sake yin rajista da karɓa a kowane lokaci. Koyaya, idan yanayi guda ya taso wanda theorem ya rasa matsayinsa na duniya baki ɗaya, theorem ɗin nan da nan ya zama mara inganci.
An dauki manufar ka'idar sauran kimiyyar (tattalin arziki, ilimin halin dan Adam ko kimiyyar siyasa, da sauransu) don tsara wasu muhimman ra'ayoyi ko tushe waɗanda ke mulkin waɗannan fannoni, koda kuwa waɗannan ba su taso ta hanyar hanyar da aka bayyana ba. A cikin waɗannan lamuran, ba a amfani da axioms amma a maimakon haka abubuwan da aka yi ta hanyoyin kamar kallo ko ma samfurin ƙididdiga.
Jerin mai zuwa yana tara misalan ka'idoji da taƙaitaccen bayanin abin da yake aikawa:
- Theorem na Pythagoras: alaƙa tsakanin ma'aunin hypotenuse da na ƙafafu, a cikin yanayin triangles na dama.
- Theorem lambar lambar: Yayin da layin lamba ke ƙaruwa, za a yi ƙarancin lambobi kaɗan daga wannan rukunin.
- Ka'idar Binomial: dabara don warware ikon binomials (ƙari ko ragi na abubuwa).
- Ka'idar Frobenius: dabarun warwarewa don tsarin daidaitattun layika.
- Ka'idar Thales: halaye dangane da kusurwoyi da ɓangarorin triangles iri ɗaya, da sauran kaddarorin su.
- Ka'idar Euler: adadin kusoshi da adadin fuskoki sun daidaita adadin gefuna da 2.
- Ka'idar Ptolemy: Jimlar samfuran diagonals daidai yake da jimlar samfuran sabanin haka.
- Ka'idar Cauchy-Hadamard: Kafa radius na haduwar jerin madafan iko wanda ya kusan aiki kusa da aya.
- Ka'idar Rolle.
- Ma'anar ƙimar darajar.
- Ka'idar Cauchy Dini: Sharuɗɗa don lissafin abubuwan da aka samo asali a cikin yanayin ayyuka na ɓoye.
- Kaidar lissafi: Ƙirƙirawa da haɗewar aiki aiki ne na juyi.
- Ka'idar Arithmetic: Kowane lamba mai kyau ana iya wakilta ta azaman samfuran manyan abubuwa.
- Bayes theorem (ƙididdiga): Hanyar samun yuwuwar sharaɗi.
- Cobweb theorem (tattalin arziki): Theorem don bayyana samuwar samfuran da aka yi bisa farashin da ya gabata.
- Ka'idar Marshall Lerner (tattalin arziki): Tattaunawa kan tasirin faduwar darajar kuɗi dangane da yawa da farashi.
- Coase theorem (tattalin arziki): Magani ga lamuran abubuwan waje, suna fuskantar ƙa'ida.
- Ka'idar masu jefa ƙuri'a ta Mediya (kimiyyar siyasa): Tsarin zaɓe mafi rinjaye yana nuna fifikon zaɓen tsakiyar.
- Ka'idar Baglini (kimiyyar siyasa, Argentina): Dan siyasan yana da burin kawo shawarwarinsa zuwa cibiyar idan ya kusanci mukamai.
- Thomas theorem (ilimin zamantakewa): Idan mutane sun ayyana yanayi a matsayin na gaske, za su zama na gaske a sakamakon su.
