Analytical descriptions of Perseus spirics
type: Item
instance of: scholarly article
title: Analytical descriptions of Perseus spirics
published in: Journal of Geometry and Symmetry in Physics
publication date: 2022-12-23T00:00:00Z
review text: The ancient Greek geometer Perseus investigated around 150\,BC the plane sections of tori such that the planes are parallel to the symmetry axes of the tori. The resulting curves are called \textit{spiric sections} and they can be partitioned into five different types, depending on the inner radius and outer radius of the torus on which they lie. The article presents explicit parametrizations for each of the five cases using elliptic and circular functions. Additionally, some historical context is provided.
reviewed by: Niels Lubbes
Mathematics Subject Classification ID: 53A04
Mathematics Subject Classification ID: 53-03
Mathematics Subject Classification ID: 51-03
Mathematics Subject Classification ID: 51M25
Mathematics Subject Classification ID: 26B15
zbMATH DE Number: 7636583
zbMATH Keywords: Bernoullian and Booth lemniscates
zbMATH Keywords: Cassinian oval
zbMATH Keywords: Hippopede
zbMATH Keywords: spiric sections
author: Ivaïlo Mladenov
MaRDI profile type: Publication
full work available at URL: jgsp-63-2022-65-75
OpenAlex ID: W4225474432
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DOI: 10.7546/JGSP-63-2022-65-75
description: scientific article; zbMATH DE number 7636583