Wybrane problemy zadań konstrukcyjnych na płaszczyźnie euklidesowej i wykorzystanie do ich rozwiązywania twierdzeń geometrii rzutowej
Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia (2009)
- Volume: 2, page 131-152
- ISSN: 2080-9751
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Abstract
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topEwa Lubaś. "Wybrane problemy zadań konstrukcyjnych na płaszczyźnie euklidesowej i wykorzystanie do ich rozwiązywania twierdzeń geometrii rzutowej." Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia 2 (2009): 131-152. <http://eudml.org/doc/296328>.
@article{EwaLubaś2009,
abstract = {The article gives examples of construction tasks of first and second degree on a Euclidean plane, which can be solved with the use of a simple ruler. For this purpose, the theoretical backgrounds of projective geometry have been used. It has been proved that in the projective approach some constructions on a Euclidean plane become linear constructions. In particular, a linear construction of this type may be the typical operation of inversion in respect of a circle and an arbitrary conic as well as its generalization, which in reference literature is known under the name of Hirst transformation.},
author = {Ewa Lubaś},
journal = {Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia},
language = {pol},
pages = {131-152},
title = {Wybrane problemy zadań konstrukcyjnych na płaszczyźnie euklidesowej i wykorzystanie do ich rozwiązywania twierdzeń geometrii rzutowej},
url = {http://eudml.org/doc/296328},
volume = {2},
year = {2009},
}
TY - JOUR
AU - Ewa Lubaś
TI - Wybrane problemy zadań konstrukcyjnych na płaszczyźnie euklidesowej i wykorzystanie do ich rozwiązywania twierdzeń geometrii rzutowej
JO - Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia
PY - 2009
VL - 2
SP - 131
EP - 152
AB - The article gives examples of construction tasks of first and second degree on a Euclidean plane, which can be solved with the use of a simple ruler. For this purpose, the theoretical backgrounds of projective geometry have been used. It has been proved that in the projective approach some constructions on a Euclidean plane become linear constructions. In particular, a linear construction of this type may be the typical operation of inversion in respect of a circle and an arbitrary conic as well as its generalization, which in reference literature is known under the name of Hirst transformation.
LA - pol
UR - http://eudml.org/doc/296328
ER -
References
top- Четверухин, Н. Ф.: 1969, Проективная геометрия, Издательство Просвещение, Москва.
- Fudali, S.: 1989, Geometria, Wydawnictwo Naukowe Uniwersytetu Szczecińskiego, Szczecin.
- Комиссарук, А. М.: 1971, Проективная геометрия в задачах, Вышейшая школа, Минск.
- Pedoe, D.: 1963, An Introduction to Projective Geometry, Pergamon Press, Oxford-London-New York-Paris.
- Wieleitner, H.: 1919, Algebraische Kurven. Teil I, II, Walter de Gruyter & Co, Berlin.
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