On the distance between the centers of the inscribed and circumscribed circles for a triangle and a quadrilateral

Гетманенко, Людмила Миколаївна (2024) On the distance between the centers of the inscribed and circumscribed circles for a triangle and a quadrilateral Grail of Science (44). pp. 380-384. ISSN 2710–3056

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Abstract

This article discusses two well-known and widely popular formulas. The first formula was discovered and proven by the English mathematician William Chapple in 1746 and was named after the great Leonhard Euler, which is why it is rightfully called the Euler-Chapple formula. An analogue of this formula was found and proven by Euler's student, Nikolai Fuss (1755–1825), and the proof of this formula can be found in mathematical literature. At an open mathematical seminar, the Ukrainian scientist, renowned educator, and founder of formulaic geometry I. A. Kushnir, together with his student O. A. Cherkassky, discovered their own method for proving this formula. We are pleased to present it in this article.

Item Type:	Article
Additional Information:	DOI 10.36074/grail-of-science.04.10.2024
Uncontrolled Keywords:	Euler's formula; Fuss's formula; distance between the centers of the inscribed and circumscribed circles of a triangle; distance between the centers of the inscribed and circumscribed circles of a quadrilateral; product of chord segments
Subjects:	Статті у базах даних > Index Copernicus
Divisions:	Інститут післядипломної освіти > Кафедра природничо-математичної освіти і технологій
Depositing User:	Людмила Гетманенко
Date Deposited:	10 Oct 2024 11:48
Last Modified:	08 Jan 2025 09:09
URI:	https://elibrary.kubg.edu.ua/id/eprint/49818

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