Completing Brahmagupta’s Extension of Ptolemy’s Theorem

Richard Askey ()
Additional contact information
Richard Askey: University of Wisconsin, Department of Mathematics

A chapter in The Legacy of Alladi Ramakrishnan in the Mathematical Sciences, 2010, pp 191-197 from Springer

Abstract: Summary Brahmagupta extended Ptolemy’s theorem on cyclic quadrilaterals to find the lengths of the diagonals, the segments made when they are cut at the point of intersection of the diagonals, and the lengths of the sides of the needles, the figures formed when opposite sides of the quadrilateral are extended until they meet. Proofs of these results are given, and a derivation of the 19th century result of the length of the third diagonal is given. This “diagonal” is formed by connecting the tips of the needles with a line segment.

Keywords: Ptolemy’s theorem; Brahmagupta; Third diagonal of cyclic quadrilateral (search for similar items in EconPapers)
Date: 2010
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:978-1-4419-6263-8_11

Ordering information: This item can be ordered from
http://www.springer.com/9781441962638

DOI: 10.1007/978-1-4419-6263-8_11

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 ().