Результаты исследований: Публикации в книгах, отчётах, сборниках, трудах конференций › глава/раздел › научная › Рецензирование
Area and volume in non-Euclidean geometry. / Abrosimov, Nikolay; Mednykh, Alexander.
EIGHTEEN ESSAYS IN NON-EUCLIDEAN GEOMETRY. ред. / Alberge; A Papadopoulos. EUROPEAN MATHEMATICAL SOC, 2019. стр. 151-189 (IRMA Lectures in Mathematics and Theoretical Physics; Том 29).Результаты исследований: Публикации в книгах, отчётах, сборниках, трудах конференций › глава/раздел › научная › Рецензирование
}
TY - CHAP
T1 - Area and volume in non-Euclidean geometry
AU - Abrosimov, Nikolay
AU - Mednykh, Alexander
PY - 2019
Y1 - 2019
N2 - We give an overview old and recent results on areas and volumes in hyperbolicand spherical geometries. First, we observe the known results about Heron’s and Ptolemy’s theorems. Then we present non-Euclidean analogues of the Brahmagupta’s theorem for a cyclic quadrilateral. We produce also hyperbolic and spherical versions of the Bretschneider’s formula for the area of a quadrilateral. We give hyperbolic and spherical analogues of the Casey’s theorem which is a generalization of the Ptolemy’s equation. We give a short historical review of volume calculations for non-Euclidean polyhedra. Then we concentrateon recent results concerning Seidel’s problem on the volume of an ideal tetrahedron, Sforza’s formula for a compact tetrahedron in H3 or S3 and volumes of non-Euclidean octahedra with symmetries
AB - We give an overview old and recent results on areas and volumes in hyperbolicand spherical geometries. First, we observe the known results about Heron’s and Ptolemy’s theorems. Then we present non-Euclidean analogues of the Brahmagupta’s theorem for a cyclic quadrilateral. We produce also hyperbolic and spherical versions of the Bretschneider’s formula for the area of a quadrilateral. We give hyperbolic and spherical analogues of the Casey’s theorem which is a generalization of the Ptolemy’s equation. We give a short historical review of volume calculations for non-Euclidean polyhedra. Then we concentrateon recent results concerning Seidel’s problem on the volume of an ideal tetrahedron, Sforza’s formula for a compact tetrahedron in H3 or S3 and volumes of non-Euclidean octahedra with symmetries
KW - CYCLIC POLYGONS
KW - SEIDEL PROBLEM
KW - FORMULA
KW - THEOREM
U2 - 10.4171/196-1/11
DO - 10.4171/196-1/11
M3 - Chapter
SN - 978-3-03719-196-5
T3 - IRMA Lectures in Mathematics and Theoretical Physics
SP - 151
EP - 189
BT - EIGHTEEN ESSAYS IN NON-EUCLIDEAN GEOMETRY
A2 - Alberge, null
A2 - Papadopoulos, A
PB - EUROPEAN MATHEMATICAL SOC
ER -
ID: 23654700