# Euclidean Geometry and Physical Space

## Related Articles

- Large triangles contained in the unit disk of a Minkowski plane. Fabińska, Ewa; Lassak, Marek // Journal of Geometry;2009, Vol. 95 Issue 1/2, p31
We prove that the unit disk C of an arbitrary Minkowski plane contains an equilateral triangle in at least one of the orientations, whose oriented side lengths are $${\frac{3}{2}}$$ . We also prove that C permits to inscribe a triangle whose sides are of lengths at least $${\frac{3}{2}}$$ in the...

- A new characterization of Radon curves via angular bisectors A new characterization of Radon curves via angular bisectors. Düvelmeyer, Nico // Journal of Geometry;2004, Vol. 80 Issue 1/2, p75
We prove that a Minkowski plane is a Radon plane if Busemann's and Glogovskij's definitions of angular bisectors coincide.

- Antipodality in hyperbolic space. Bezdek, Károly; Naszódi, Márton; Oliveros, Deborah // Journal of Geometry;2006, Vol. 85 Issue 1/2, p22
An antipodal set in Euclidean n-space is a set of points with the property that through any two of them there is a pair of parallel hyperplanes supporting the set. In this paper we discuss the various possible ways to translate this notion to hyperbolic space and find the maximal cardinality of...

- Euclid's fifth postulate. // Hutchinson Dictionary of Scientific Biography;2005, p1
States that parallel lines meet only at infinity.

- Ordered Symmetric Minkowski Planes I. Karzel, Helmut; Kosiorek, Jaroslaw; Matraś, Andrzej // Journal of Geometry;2009, Vol. 93 Issue 1/2, p116
Let $${\mathcal{M}}$$ be a symmetric Minkowski plane. By [1, 2, 6] there is a commutative field F such that the circles of $${\mathcal{M}}$$ can be identified with the elements of the projective linear group PGL(2, F). We consider only the case $$char {\mathcal{M}} := char F \neq 2$$. Two...

- Finite reflection groups. Coxeter, H. S. M. // Bulletin (New Series) of the American Mathematical Society;Jan2008, Vol. 45 Issue 1, p157
The article discusses the Euclidean n-space, a finite set of hyperplanes. The author emphasizes that the reflecting hyperplanes will decompose the space into congruent angular regions which is known as the chambers. These chambers will serve as a fundamental region for the group G, a sufficient...

- Propellers in Affine Cayley—Klein Planes. Spirova, Margarita // Journal of Geometry;2009, Vol. 93 Issue 1/2, p164
In the present paper the generalized Propeller theorem from planar Euclidean geometry is extended to all planar affine Cayleyâ€“Klein geometries. Since there are no equilateral triangles in affine Cayleyâ€“Klein planes (except for the Euclidean case), there is no direct extension of...

- Lobachevsky, Nikolai Ivanovich (1792 - 1856). // Hutchinson Dictionary of Scientific Biography;2005, p1
Russian mathematician, one of the founders of non-Euclidean geometry, whose system is sometimes called Lobachevskian geometry.

- Non-Euclidean geometry. // History of Science & Technology;2004, p331
The entry discusses non-Euclidean geometry, particularly the Fifth Postulate developed by mathematician Euclid which deals with the meeting point of two straight lines. Two strategies are generally used to get rid of the postulate: replacing the Fifth Postulate with a different equivalent...