The Polar Triangle, from Ibn ‘Irāq to Euler and Lagrange

Athanase Papadopoulos ()
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Athanase Papadopoulos: Université de Strasbourg et CNRS, Institut de Recherche Mathématique Avancée

Chapter Chapter 10 in Spherical Geometry in the Eighteenth Century I, 2026, pp 223-231 from Springer

Abstract: Abstract The notion of polar triangle plays a central role in spherical geometry. Euler and Lagrange used this triangle in their respective memoirs Trigonometria sphaerica universa, ex primis principiis breviter et dilucide derivata and Solution de quelques problèmes relatifs aux triangles sphériques, avec une analyse complète de ces triangles, when they noticed that we can transform some formulae of spherical trigonometry into others by interchanging the letters for sides and angles after replacing the values of the angles and sides by their supplements to two right angles. This chapter is a historical note on the polar triangle since its discovery by the Arab mathematician Ibn ‘Irāq (10th-11th c.) until the modern period.

Keywords: Polar triangle; Spherical geometry; Spherical trigonometry; Polarity; Duality; Leonhard Euler; Joseph-Louis Lagrange; Ibn ‘Irāq; Naṣı̄r al-Dı̄n al-Ṭūsı̄; 01A30; 01A50; 01A55; 51-03 (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-032-12466-1_10

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DOI: 10.1007/978-3-032-12466-1_10

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