Hermann Grassmann

n about="#mwt8" data-mw='{"parts":[{"template":{"target":{"wt":"langx","href":"./Template:Langx"},"params":{"1":{"wt":"de"},"link":{"wt":"no"},"2":{"wt":"V-ignore="" lang="de">Graßmann"}},"i":0}}]}' data-ve-no-generated-contents="true" id="mwEw" typeof="mw:Transclusion">German:  Günther Grassmann (Jamusanci: 

Graßmann, mai suna [ˈhɛʁman ˈɡʏntɐ ˈɡʁasman]; 15 ga Afrilu 1809 - 26 ga Satumba 1877) masanin ilimin Jamusanci ne wanda aka sani a zamaninsa a matsayin masanin harshe kuma yanzu kuma a matsayin masaniya. Ya kuma kasance masanin kimiyyar lissafi, babban masanin kimiyya, kuma mai bugawa. Ba a lura da aikinsa na lissafi ba har sai ya kai shekaru sittin. Ayyukansa sun riga sun wuce ra'ayin wanda yanzu aka sani da sararin samaniya. Ya gabatar da Grassmannian, sararin samaniya wanda ke daidaita dukkan sassan layi na <i id="mwHg">k</i>-dimensional na sararin samaniya na n-dimenonal V. A cikin ilimin harshe ya taimaka wa tarihin harshe da tsari daga juna.

 Tarihin rayuwa 
Hermann Grassmann ita ce ta uku cikin 'ya'ya 12 na Johanne Luise Friederike Medenwald da Justus Günter Grassmann, Minista ne wanda ya koyar da lissafi da kimiyyar lissafi a Stettin Gymnasium, inda Hermann ya sami ilimi. Ɗan'uwansa Robert shi ma masanin lissafi ne.

Grassmann dalibi ne mai ban sha'awa har sai da ya sami babban alama a jarrabawar shiga jami'o'in Prussian. Da farko a 1827, ya yi karatun tauhidi a Jami'ar Berlin, kuma yana karatun Harsuna na gargajiya, falsafar, da adabi. Bai bayyana ya dauki darussan lissafi ko kimiyyar lissafi ba.

Kodayake ba shi da horo na jami'a a lissafi, filin ne da ya fi sha'awarsa lokacin da ya koma Stettin a 1830 bayan kammala karatunsa a Berlin. Bayan shekara guda na shiri, ya zauna jarrabawar da ake buƙata don koyar da lissafi a cikin dakin motsa jiki, amma ya sami sakamako mai kyau don ba shi damar koyarwa kawai a ƙananan matakan. A wannan lokacin, ya yi muhimmiyar binciken lissafi na farko, waɗanda suka kai shi ga mahimman ra'ayoyin da ya tsara a cikin takarda ta 1844 Die lineale Ausdehnungslehre, ein neuer Zweig der Mathematik, a nan da ake kira A1, daga baya aka sake shi a 1862 a matsayin Die Ausdehnunglehre: Vollständig und in strenger Form bearbeitet, a nan ana kiransa A2.[1]

A cikin 1834 Grassmann ya fara koyar da lissafi a Gewerbeschule a Berlin, matsayin da Jakob Steiner ya rike a baya. Bayan shekara guda, ya koma Stettin don koyar da lissafi, kimiyyar lissafi, Jamusanci, Latin, da karatun addini a sabuwar makaranta, Otto Schule . A cikin shekaru hudu masu zuwa, Grassmann ya wuce jarrabawa wanda ya ba shi damar koyar da lissafi, kimiyyar lissafi, ilmin sunadarai, da ilimin ma'adinai a duk matakan makarantar sakandare."Hermann Grassmann - Biography". Maths History. Retrieved 2025-08-13.

A shekara ta 1847, an sanya shi "Oberlehrer" ko kuma babban malami. A shekara ta 1852, an nada shi a matsayin mahaifinsa marigayi a Stettin Gymnasium, don haka ya sami taken Farfesa. A shekara ta 1847, ya nemi Ma'aikatar Ilimi ta Prussia da a yi la'akari da shi don matsayin jami'a, inda wannan Ma'aikatu ta tambayi Ernst Kummer don ra'ayinsa game da Grassmann. Kummer ya rubuta a baya yana cewa rubutun kyautar Grassmann na 1846 (duba ƙasa) ya ƙunshi "abubuwa masu kyau da aka bayyana a cikin wani nau'i mara kyau". Rahoton Kummer ya ƙare duk wata dama da Grassmann zai iya samun mukamin jami'a. Wannan labarin ya tabbatar da al'ada; sau da yawa, manyan mutane na zamanin Grassmann sun kasa gane darajar lissafinsa."Hermann Grassmann - Biography". Maths History. Retrieved 2025-08-13.

Farawa a lokacin rikice-rikicen siyasa a Jamus, 1848-49, Hermann da ɗan'uwansa Robert sun buga jaridar Stettin, Deutsche Wochenschrift für Staat, Kirche und Volksleben, suna kira ga Haɗin kan Jamus a ƙarƙashin mulkin mallaka.  (Wannan ya faru a shekara ta 1871.) Bayan ya rubuta jerin labarai game da dokar tsarin mulki, Hermann ya rabu da jaridar, ya sami kansa da rashin jituwa da jagorancin siyasa na jaridar."Hermann Grassmann - Biography". Maths History. Retrieved 2025-08-13.

A shekara ta 1849, ya auri Therese Knappe kuma sun ci gaba da samun 'ya'ya goma sha ɗaya, bakwai daga cikinsu sun kai ga balaga. Ɗansa Hermann Ernst Grassmann ya sami digiri na biyu a lissafi kuma ya zama farfesa a lissafi a Jami'ar Giessen . "Hermann Grassmann - Biography". Maths History. Retrieved 2025-08-13.

Bayan rasuwar mahaifinsa a shekara ta 1852, an nada Grassmann zuwa tsohon matsayin mahaifinsa a Stettin Gymnasium . "Hermann Grassmann - Biography". Maths History. Retrieved 2025-08-13.

 Masanin lissafi 
Ɗaya daga cikin gwaje-gwaje da yawa da Grassmann ya zauna ya buƙaci ya gabatar da wata kasida game da ka'idar raƙuman ruwa. A cikin 1840, ya yi haka, ya ɗauki ka'idar asali daga Traité de mécanique céleste na Laplace da kuma daga Mécanique analytique na Lagrange, amma ya fallasa wannan ka'idar ta yin amfani da hanyoyin da yake tunani tun 1832. Wannan rubutun, wanda aka fara buga shi a cikin Ayyukan da aka tattara na 1894-1911, ya ƙunshi bayyanar farko da aka sani na abin da yanzu ake kira algebra na layi da kuma ra'ayin sararin samaniya. Ya ci gaba da bunkasa waɗannan hanyoyin a cikin Die lineale Ausdehnungslehre, ein neuer Zweig der Mathematik (A1) da kuma sake dubawa daga baya Die Ausdehnunglehre: Vollständig und in strenger Form bearbeitet (A2).

A cikin 1844, Grassmann ya buga aikinsa (A1) wanda aka fi sani da Ausdehnungslehre, wanda ke fassara a matsayin "ka'idar tsawo" ko "ka'idodin Girma gaske". Tun lokacin da A1 ya ba da sabon tushe ga dukkan lissafi, aikin ya fara ne da cikakkun ma'anoni na yanayin falsafa. Grassmann sa'an nan ya nuna cewa da zarar an sanya lissafi a cikin tsarin algebraic da ya ba da shawara, lambar uku ba ta da matsayi mai daraja a matsayin yawan girman sararin samaniya; yawan yiwuwar girman ba shi da iyaka.

Fearnley-Sander ya bayyana tushen Grassmann na algebra na layi kamar haka: 

Bi da ra'ayin mahaifin Grassmann, A1 ya k bayyana samfurin wa<i id="mwmQ">j</i>, wanda ake kira "samfurin haɗuwa" (a cikin Jamusanci: kombinatorisches Produkt ko äußeres Produkt "samfutar waje"), maɓallin aiki na algebra yanzu ana kiranta Algebra na waje.  (Ya kamata mutum ya tuna cewa a zamanin Grassmann, kawai ka'idar 2" href="./Axiom" id="mwig" rel="mw:WikiLink" title="Axiom">axiomatic ita ce geometry na Euclidean, kuma ba a bayyana ra'ayin algebra ba.) A cikin 1878, William Kingdon Clifford ya shiga wannan algebra na waje zuwa quaternions" id="mwjw" rel="mw:WikiLink" title="Quaternions">quaternions na William Rowan Hamilton ta hanyar maye gurbin mulkin Grassmann epep = 0 ta hanyar mulkin epep = 1.  (Don quaternions, muna da doka i2 = j2 = k2 = −1.) Don ƙarin bayani, duba Exterior algebra.

A1 rubutu ne na juyin juya hali, da nisa da lokacinsa don a yaba da shi. Lokacin da Grassmann ya gabatar da shi don neman farfesa a 1847, ma'aikatar ta nemi Ernst Kummer don rahoto. Kummer ya tabbatar da cewa akwai ra'ayoyi masu kyau a ciki, amma ya sami bayyanar ba ta da kyau kuma ya shawarci da ba Grassmann matsayin jami'a. A cikin shekaru 10 masu zuwa, Grassmann ya rubuta ayyuka iri-iri da ke amfani da ka'idarsa ta tsawo, gami da Neue Theorie der Elektrodynamik na 1845 da takardu da yawa a kan layin algebraic da farfajiya, da fatan cewa waɗannan aikace-aikacen za su jagoranci wasu su dauki ka'idonsa da muhimmanci.

A cikin 1846, Möbius ya gayyaci Grassmann don shiga gasa don warware matsalar da Leibniz ya fara gabatar da ita: don tsara lissafin lissafi wanda ba shi da ma'auni da kaddarorin ma'aunin (abin da Leibnit ya kira analysis situs). Grassmann's Geometrische Analyse geknüpft an die von Leibniz erfundene geometrische Charakteristik, shi ne shigarwar da ta ci nasara (kuma shigarwa ɗaya). Möbius, a matsayin daya daga cikin alƙalai, ya soki hanyar da Grassmann ya gabatar da ra'ayoyi ba tare da ba wa mai karatu wani fahimta ba game da dalilin da ya sa waɗannan ra'ayoyin suna da daraja.

A cikin 1853, Grassmann ya buga ka'idar yadda launuka suka haɗu; har yanzu ana koyar da ka'idarsa ta launuka huɗu, kamar yadda Dokokin Grassmann suka haɗu. Ayyukan Grassmann akan wannan batun bai dace da na Helmholtz ba. Grassmann ya kuma rubuta a kan crystallography, electromagnetism, da injiniya.

 Amsa 
A cikin shekarun 1840, masu ilimin lissafi ba su da shiri don fahimtar ra'ayoyin Grassmann. A cikin shekarun 1860 da 1870 masu ilimin lissafi daban-daban sun zo ga ra'ayoyin da suka yi kama da na Grassmann, amma Grassmann da kansa ba shi da sha'awar lissafi. : 46 : 46 

Adhémar Jean Claude Barré de Saint-Venant ya kirkiro lissafin lissafi mai kama da na Grassmann, wanda ya buga a 1845. Daga nan sai ya shiga rikici tare da Grassmann game da wane daga cikin biyun ya fara tunanin ra'ayoyin. Grassmann ya buga sakamakon sa a 1844, amma Saint-Venant ya yi iƙirarin cewa ya fara haɓaka waɗannan ra'ayoyin a 1832.

Ɗaya daga cikin masu ilimin lissafi na farko da suka fahimci ra'ayoyin Grassmann a lokacin rayuwarsa shine Hermann Hankel, wanda 1867 Theorie der complexen Zahlensysteme . 

 Manazarta 

Rukuni:Shafuka masu fassarorin da ba'a duba ba