The Feuerbach theorem and cyclography in universal geometry
We have another look at the Feuerbach theorem with a view to extending it in an oriented way to finite fields using the purely algebraic approach of rational trigonometry and universal geometry. Our approach starts with the tangent lines to three rational points on the unit circle, and all subsequen...
| Permalink: | http://skupni.nsk.hr/Record/nsk.NSK01001128690/Details |
|---|---|
| Matična publikacija: |
Kog (Online) (2020), 24 ; str. 47-58 |
| Glavni autori: | Beare, William (Author), Wildberger, Norman John |
| Vrsta građe: | e-članak |
| Jezik: | eng |
| Predmet: | |
| Online pristup: |
https://doi.org/10.31896/k.24.5 Hrčak |
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| 005 | 20220224102845.0 | ||
| 006 | m d | ||
| 007 | cr|||||||||||| | ||
| 008 | 220221s2020 ci a |o |0|| ||eng | ||
| 024 | 7 | |2 doi |a 10.31896/k.24.5 | |
| 035 | |a (HR-ZaNSK)001128690 | ||
| 040 | |a HR-ZaNSK |b hrv |c HR-ZaNSK |e ppiak | ||
| 041 | 0 | |a eng |b hrv | |
| 042 | |a croatica | ||
| 044 | |a ci |c hr | ||
| 080 | 1 | |a 51 |2 2011 | |
| 100 | 1 | |a Beare, William |4 aut |9 HR-ZaNSK | |
| 245 | 1 | 4 | |a The Feuerbach theorem and cyclography in universal geometry |h [Elektronička građa] / |c William Beare, Norman J. Wildberger. |
| 300 | |b Ilustr. | ||
| 504 | |a Bibliografija: 10 jed. | ||
| 504 | |a Abstract ; Sažetak. | ||
| 520 | |a We have another look at the Feuerbach theorem with a view to extending it in an oriented way to finite fields using the purely algebraic approach of rational trigonometry and universal geometry. Our approach starts with the tangent lines to three rational points on the unit circle, and all subsequent formulas involve the three parameters that define them. Tangency of incircles is treated in the oriented setting via a simplified form of cyclography. Some interesting features of the finite field case are discussed. | ||
| 520 | |a Dajemo drugačiji pogled na Feuerbachov teorem s ciljem da ga se orijentirano proširi na konačna polja koristeći isključivo algebarski pristup racionalne trigonometrije i univerzalne geometrije. Naš pristup počinje s tangentama u tri racionalne točke na jediničnoj kružnici, i sve naknadne formule uključuju tri parametra koja ih definiraju.Tangencijalnost upisanih kružnica promatra se u orijentiranom okruženju koristeći pojednostavljene forme ciklografije. Promatraju se neka zanimljiva događanja u slučaju konačnih polja. | ||
| 653 | 0 | |a Feuerbachov teorem |a Univerzalna geometrija |a Ciklografija |a Konačna polja |a Upisana kružnica | |
| 700 | 1 | |a Wildberger, Norman John |4 aut | |
| 773 | 0 | |t Kog (Online) |x 1846-4068 |g (2020), 24 ; str. 47-58 |w nsk.(HR-ZaNSK)000628952 | |
| 981 | |b Be2020 |b B04/20 | ||
| 998 | |b tino2202 | ||
| 856 | 4 | 0 | |u https://doi.org/10.31896/k.24.5 |
| 856 | 4 | 0 | |u https://hrcak.srce.hr/248417 |y Hrčak |
| 856 | 4 | 1 | |y Digitalna.nsk.hr |