Area and volume in non-Euclidean geometry

Результат исследования: Публикации в книгах, отчётах, сборниках, трудах конференцийглава/разделнаучнаярецензирование

Аннотация

We give an overview old and recent results on areas and volumes in hyperbolic
and 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 concentrate
on 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
Язык оригиналаанглийский
Название основной публикацииEIGHTEEN ESSAYS IN NON-EUCLIDEAN GEOMETRY
Редакторы Alberge, A Papadopoulos
ИздательEUROPEAN MATHEMATICAL SOC
Страницы151-189
Число страниц39
ISBN (печатное издание)978-3-03719-196-5
DOI
СостояниеОпубликовано - 2019

Серия публикаций

НазваниеIRMA Lectures in Mathematics and Theoretical Physics
ИздательEUROPEAN MATHEMATICAL SOC
Том29

Цитировать

Abrosimov, N., & Mednykh, A. (2019). Area and volume in non-Euclidean geometry. В Alberge, & A. Papadopoulos (Ред.), EIGHTEEN ESSAYS IN NON-EUCLIDEAN GEOMETRY (стр. 151-189). (IRMA Lectures in Mathematics and Theoretical Physics; Том 29). EUROPEAN MATHEMATICAL SOC. https://doi.org/10.4171/196-1/11