Envelope of the Wallace-Simson Lines with Signed Angle <TEX>${\alpha}$</TEX>
نویسندگان
چکیده
منابع مشابه
The envelope of the Wallace-Simson lines of a triangle. A simple proof of the Steiner theorem on the deltoid
A simple proof is presented of a famous, and difficult, theorem by Jakob Steiner. By means of a straightforward transformation of the triangle, the proof of the theorem is reduced to the case of the equilateral triangle. Several relations of the Steiner deltoid with the Feuerbach circle and the Morley triangle appear then as obvious. La envolvente de las rectas de Wallace-Simson de un triángulo...
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Let K,L,M be orthogonal projections of a point P onto the sides of a triangle ABC. Then the locus of P such that K,L,M are collinear, is the circumcircle of ABC. This theorem has several generalizations [4], [5], [10],[6], [7], [9]. A generalization of the Simson–Wallace theorem which is by [2] ascribed to J. D. Gergonne is as follows: Let K,L,M be orthogonal projections of a point P onto the s...
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ژورنال
عنوان ژورنال: Journal of the Chosun Natural Science
سال: 2012
ISSN: 2005-1042
DOI: 10.13160/ricns.2012.5.1.038