Novel Tools to Determine Hyperbolic Triangle Centers

Abraham Albert Ungar ()
Additional contact information
Abraham Albert Ungar: North Dakota State University, Department of Mathematics

A chapter in Essays in Mathematics and its Applications, 2016, pp 563-663 from Springer

Abstract: Abstract Recently discovered tools to study analytic hyperbolic geometry in terms of analogies with analytic Euclidean geometry are presented and employed. Special attention is paid to the study of two novel hyperbolic triangle centers that we call hyperbolic Cabrera points of a hyperbolic triangle and to the way they descend to their novel Euclidean counterparts. The two novel hyperbolic Cabrera points are the (1) Cabrera gyrotriangle ingyrocircle gyropoint and the (2) Cabrera gyrotriangle exgyrocircle gyropoint. Accordingly, their Euclidean counterparts to which they descend are the two novel Euclidean Cabrera points, which are the (1) Cabrera triangle incircle point and the (2) Cabrera triangle excircle point.

Keywords: Euclidean Geometry; Hyperbolic Geometry; Line Parameter; Lorentz Boost; Full Analogy (search for similar items in EconPapers)
Date: 2016
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-31338-2_18

Ordering information: This item can be ordered from
http://www.springer.com/9783319313382

DOI: 10.1007/978-3-319-31338-2_18

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().