Grinbergov izrek
na študijskem programu 2. stopnje Matematika
Abstract
Grinbergov izrek trdi, da se krožna cevianska konjugacija izraža kot kompozitum, v katerem nastopajo izotomična in izogonalna konjugacija, razteg s središčem v težišču G in koeficientom -1/2 ter njegov inverz. V magistrskem delu bosta predstavljena sintetični dokaz in direkten dokaz s pomočjo trilinearnih koordinat. Obravnavali bomo vse preslikave, predstavili trilinearne koordinate in poiskali enačbe različnih krožnic v trikotniku.
Keywords
magistrska dela;geometrija trikotnika;krožna cevianska konjugacija;izotomična konjugacija;Grinberg;Darij;1988-;
Data
| Language: | Slovenian |
|---|---|
| Year of publishing: | 2020 |
| Typology: | 2.09 - Master's Thesis |
| Organization: | UM FNM - Faculty of Natural Sciences and Mathematics |
| Publisher: | [V. Štern] |
| UDC: | 514.112.3(043.2) |
| COBISS: |
23990275
|
| Views: | 505 |
| Downloads: | 66 |
| Average score: | 0 (0 votes) |
| Metadata: |
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Other data
| Secondary language: | English |
|---|---|
| Secondary title: | Grinberg's theorem |
| Secondary abstract: | Grinberg's theorem states that cyclocevian conjugation can be expressed as a composition of transformations, in which occur the following transformations: isotomic conjugate, isogonal conjugate, complement and anticomplement. The master's thesis will present synthetic proof and direct proof using trilinear coordinates. We will consider all the mappings involved, present trilinear coordinates and derive equations of diffrent circles in triangle geometry. |
| Secondary keywords: | master theses;triangle geometry;cyclocevian conjugate;isotomic conjugate;isogonal conjugate;Grinberg; |
| Type (COBISS): | Master's thesis/paper |
| Thesis comment: | Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo |
| Pages: | VIII, 49 f. |
| ID: | 11460140 |
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