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Steinerjeva trikotniku včrtana elipsa : diplomsko deloMajcen, Klavdija, 1987-V diplomskem delu je predstavljena elipsa, včrtana trikotniku. Osredotočimo se na Steinerjevo elipso, ki je včrtana v trikotnik in se dotika vseh stranic trikotnika v njihovih razpoloviščih. Oglišča ... trikotnika naj ležijo v kompleksni ravnini in so ničle polinoma. Ničli odvoda tega polinoma sta potem gorišči Steinerjeve trikotniku včrtane elipse. Elipsa ima središče v težišču trikotnika. Premica, ki se najbolj približa ogliščem trikotnika, poteka skozi gorišči trikotniku včrtane elipse in jo imenujemo premica najboljšega prileganja. Diplomsko delo ima v šestih poglavjih. V prvem poglavju je predstavljen Mardenov izrek, ki ga lahko dokažemo šele v kombinaciji z Bôcherjevim delom dokaza. V drugem poglavju smo se osredotočili na Mardenov in Bôcherjev dokaz, ter kombinacijo teh dveh podkrepili s primeri. Mardenov izrek velja za polinome tretje stopnje s kompleksnimi koeficienti; te povezave med ničlami kubičnega polinoma in ničlami njegovega odvoda so opisane v naslednjem, tretjem poglavju. V tem delu je vpeljan tudi Steinerjev izrek, po katerem se imenuje elipsa, včrtana trikotniku. Steinerjev izrek uporabimo pri afini in linearni transformaciji; obe preslikavi sta predstavljeni v četrtem poglavju, v petem poglavju pa smo dokazali Steinerjev izrek in opisali Steinerjevo včrtano elipso. Diplomsko delo smo zaključili z zadnjim, šestim poglavjem, kjer smo se posvetili dokazovanju izreka iz tretjega poglavja. V diplomskem delu sem si pomagala s programom GeoGebra, s pomočjo katerega sem narisala vse priložene slike.Type of material - undergraduate thesis ; adult, seriousPublication and manufacture - Maribor : [K. Majcen], 2013Language - slovenianCOBISS.SI-ID - 20138248
Author
Majcen, Klavdija, 1987-
Other authors
Pagon, Dušan
Topics
Steiner, Jakob, švicarski matematik, 1796-1863 |
Univerzitetna in visokošolska dela |
diplomska dela |
trikotniku včrtana elipsa |
Steinerjev izrek |
Mardenov dokaz |
Bôcherejv dokaz |
ničle polinoma |
afina transformacija |
linearna transformacija
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M DIPL 0000000051 MAJCEN K. Steinerjeva IN: 920130084 M DIPL 51 MAJCEN K. Steinerjeva IN: 920130084 |
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Database name | Field | Year |
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Links to authors' personal bibliographies | Links to information on researchers in the SICRIS system |
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Majcen, Klavdija, 1987- | ![]() |
Pagon, Dušan | 04588 |
Source: Personal bibliographies
and: SICRIS
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