Relevant bibliographies by topics / Lemoine’s Circles

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Academic literature on the topic 'Lemoine’s Circles'

Author: Grafiati
Published: 2 June 2025
Last updated: 31 July 2025

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Journal articles on the topic "Lemoine’s Circles"

1

Natchev, Vladislav. "Apollonian Sphere and Properties of Stereographic Projection around the Lemoine Point." Mathematics and Informatics 68, no. 1 (2025): 35–50. https://doi.org/10.53656/math2025-1-3-apo.

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The definition and some of the properties of the Apollonian circle in the plane find their analogies in the Euclidean three-dimensional space. Thus, we manage to introduce a new concept in solid geometry that we call an “Apollonian sphere”. It appears that the Apollonian sphere not only possesses classical properties similar to the Apollonian circle such as orthogonality and coaxiality, but also analogies of its lesser-known connection with the Lemoine point and the circumcenter. We also discover two notable properties of stereographic projection that we prove with an Apollonian sphere. They i
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2

DeTemple, Duane W. "Carlyle Circles and the Lemoine Simplicity of Polygon Constructions." American Mathematical Monthly 98, no. 2 (1991): 97. http://dx.doi.org/10.2307/2323939.

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3

DeTemple, Duane W. "Carlyle Circles and the Lemoine Simplicity of Polygon Constructions." American Mathematical Monthly 98, no. 2 (1991): 97–108. http://dx.doi.org/10.1080/00029890.1991.11995711.

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4

Bradley, Christopher. "Conics twinned with two special circles." Mathematical Gazette 96, no. 536 (2012): 236–42. http://dx.doi.org/10.1017/s0025557200004472.

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Throughout the article we use areal (or barycentric) coordinates. The side lengths ofBC, CA, ABare denoted as usual bya, b, cand for brevity and ease of reading we writea2= p, b2= q, c2= r. The symmedian pointKthen has coordinates (a2, b2, c2) replaced by (p, q, r), it being the isogonal conjugate of the centroid, and the circumcentreOthen has coordinates (a2(b2+ c2− a2), b2(c2+ a2− b2), c2(a2+ b2− c2)) replaced by (p(q + r − p), q(r + p − q), r(p + q − r)). The construction of the triplicate ratio circle (also known as the Lemoine circle) and the Brocard circle is replicated but starting with
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5

Patrascu, Ion, and Florentin Smarandache. "Lemoine’s Circles Radius Calculus." February 12, 2016. https://doi.org/10.5281/zenodo.57712.

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For the calculus of the first Lemoine’s circle, we will first prove: The first Lemoine’s circle divides the sides of a triangle in segments proportional to the squares of the triangle’s sides.
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6

Patrascu, Ion, and Florentin Smarandache. "Radical Axis of Lemoine’s Circles." February 12, 2016. https://doi.org/10.5281/zenodo.57790.

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7

Ion, Patrascu, and Smarandache Florentin. "Generating Lemoine Circles." April 2, 2013. https://doi.org/10.5281/zenodo.30175.

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8

Ion, Patrascu, and Smarandache Florentin. "Lemoine Circles." November 9, 2012. https://doi.org/10.5281/zenodo.30201.

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9

Ion, Pătrașcu, and Smarandache Florentin. "Lemoine Circles Radius Calculus." September 2, 2015. https://doi.org/10.5281/zenodo.30202.

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10

Ion, Patrascu, and Smarandache Florentin. "Radical Axis of Lemoine Circles." September 2, 2013. https://doi.org/10.5281/zenodo.30252.

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