On the Miyamoto-Moses Circle.

AUTORES: Manuel Aguilera

Revista de Matemáticas Aleph, Volumen 10, Año 2024

PALABRAS CLAVES: Miyamoto-Moses circle, scalene acute triangle, plane geometry, circles generated, illustrations

RESUMEN

The Miyamoto-Moses circle is a circle derived from a scalene acute triangle, which was introduced in mid-2023. This article showcases illustrations of this circle, certain of its properties, and depictions of other circles and triangles generated from it.

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BIBLIOGRAFÍA

[1] C. Kimberling, Enciclopedia of Triangle Centers: Miyamoto-Moses Points = X(53006)-X(53007), available online at the URL: https://faculty.evansville.edu/ck6/encyclopedia/ETCpart27.html#X53006

[2] E. Jkh, Romantics of Geometry:  Problem 13035, available online at the URL: https://www.facebook.com/groups/1019808738132832/user/100089799874190/

[3] C. Kimberling, Enciclopedia of Triangle Centers: X(39) = Brocard Midpoint, available online at the URL:  https://faculty.evansville.edu/ck6/encyclopedia/ETC.html

[4] C. Kimberling, Enciclopedia of Triangle Centers: X(115) = Center of Kiepert Hyperbola, available online at the URL: https://faculty.evansville.edu/ck6/encyclopedia/ETC.html

[5] E. Weisstein, MathWorld–A Wolfram Web Resource: Kiepert Hyperbola, available online at the URL:  https://mathworld.wolfram.com/KiepertHyperbola.html

[6] C. Kimberling, Enciclopedia of Triangle Centers: X(10489) = Perpsector of ABC and Cross-Triangle of ABC and Mir-Arc Triangle, available online at the URL: https://faculty.evansville.edu/ck6/encyclopedia/ETCPart6.html

[7] E. Weisstein, MathWorld–A Wolfram Web Resource: Contact Triangle, available online at the URL: https://mathworld.wolfram.com/ContactTriangle.html

[8] C. Kimberling, Enciclopedia of Triangle Centers: Miyamoto-Moses Points = X(52805)-X(52834), available online at the URL: https://faculty.evansville.edu/ck6/encyclopedia/ETCpart27.html#X52805

[9] P. Chenghua, T. Kaibin, & C. Xiaoguang. (2017). A class of geometric problems related to Mannheim’s theorem., available online at the URL: https://www.cqvip.com/qk/82667x/201704/671918138.html

[10] H. Zichen, & L. Sheng, Pseudocircle of triangle, Middle School of Xiangshan County, Ningbo, Zhe-jiang, vol 3 (2022)

[11] M. Aguilera., & P. Pavlov, I, Points related to the Aguilera triangle: X(60877)-X(61035). Encyclopedia of Triangle Centers, available online at the URL: https://faculty.evansville.edu/ck6/encyclopedia/ETCPart31.html [12] Altshiller, N. (1915). On the Circles of Apollonius. The American Mathematical Monthly, 22(8), 261-263.

Citar en APA 7:

Aguilera, M. (2024). On the Miyamoto-Moses Circle. Revista de Matemáticas Aleph, 10, 127-146.

Publicado el 14 de noviembre de 2024