Results 1 to 10 of about 61 (36)
Formulae connected with the Radii of the Incircle and the Excircles of a Triangle [PDF]
Proceedings of the Edinburgh Mathematical Society, 1893 The notation employed in the following pages is that recommended in a paper of mine on “The Triangle and its Six Scribed Circles”* printed in the first volume of the Proceedings of the Edinburgh Mathematical Society. It may be convenient to repeat all that is necessary for the present purpose.
J. S. Mackay
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, 2021 This paper introduces the unique geometric features of 1:2: right triangle, which is observed to be the quintessential form of Golden Ratio (φ). The 1:2: triangle, with all its peculiar geometric attributes described herein, turns out to be the real ...
Rajput, Dr. Chetansing
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Triads of Conics Associated with a Triangle [PDF]
, 2022 Podsjećamo na konstrukcije temeljene na trijadama konika sa žarištima u parovima vrhova referetnog trokuta. Nalazimo da njihovih 6 vrhova leži na dobro poznatim konikama čiji tip analiziramo.
Garcia, Ronaldo +3 more
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Area and perimeter relationship for different shapes with an inradius [PDF]
, 2022 In this paper, we show that an interesting relationship for a triangle, which is Area/Perimeter = r/2, extends to other shapes with an inradius r (i.e., shapes with an inscribed circle). These shapes include squares, circles, rhombuses, regular polygons,
Kaufman, Richard
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Synthetic foundations of cevian geometry, III: The generalized orthocenter [PDF]
, 2015 In this paper, the third in the series, we define the generalized orthocenter $H$ corresponding to a point $P$, with respect to triangle $ABC$, as the unique point for which the lines $HA, HB, HC$ are parallel, respectively, to $QD, QE, QF$, where $DEF ...
Minevich, Igor, Morton, Patrick
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An App for Visual Exploration, Discovery, and Sharing of Poncelet 3-Periodic Phenomena
, 2021 We describe a browser-based application built for the real-time visualization of the beauteous dynamic geometry of Poncelet 3-periodic families. The focus is on highly responsive, visually smooth, "live" experimentation with old and new phenomena ...
Darlan, Iverton, Reznik, Dan
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Trokuti iz Feuerbachovog trokuta [PDF]
, 2000 We prove four unusual theorems about the Feuerbach triangle A_dB_dC_d of the given triangle ABC whose vertices are points A_d, B_d, and C_d in which the excircles touch from outside the nine-point circle.
Zvonko Čerin
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Euler’s inequality for the circumradius and inradius of a triangle [PDF]
, 2020 For any arbitrary triangle ABC, let R denote its circumradius and r its inradius (Figure 1). It was the Swiss-German mathematician Leonhard Euler who first observed that regardless of the shape of the triangle, the following inequality is invariably ...
Shirali, Shailesh
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A family of hyperbolas associated to a triangle [PDF]
, 2019 In this note, we explore an apparently new one parameter family of conics associated to a triangle. Given a triangle we study ellipses whose one axis is parallel to one of sides of the triangle.
Zięba, Maciej
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Things to do with a broken stick. [PDF]
, 2013 In this article we consider variations of a classical geometric probability question in Euclidean Geometry. Our work is tightly related to the problem of constructing a triangles given three of its elements.
Ionascu, Eugen J.
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