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Symmetry: Culture and Science
Volume 34, Number 4, pages 407-416 (2023)
https://doi.org/10.26830/symmetry_2023_4_407

THE GEOMETRIC CONSTRUCTIONS OF THE GREEK MEANS

Luděk Spíchal

Czech Forestry Academy Trutnov, Lesnická 9, Trutnov, Czech Republic
Email: spichal@clatrutnov.cz

Abstract: The article deals with the construction of several Greek means which are found using externally touching circles and a common tangent. In the end of the article, some connection between the first contrageometric mean and so-called metallic means is mentioned.

Keywords: Pythagorean means, contraharmonic mean, contrageometric mean, metallic means. MSC 2010: 51M15, 26E60

References:
Gielis, J. (2017) The Geometrical Beauty of Plants, Paris: Atlantis Press. https://doi.org/10.2991/978-94-6239-151-2

Høibakk, R., Lukkassen, D., Meidell, A. and Persson, L. E. (2018) Geometric Construction of Some Lehmer Means, Mathematics, 6, 251. https://doi.org/10.3390/math6110251

Okumura, H. and Saitoh, S. (2018) Harmonic mean and division by zero, Forum Geometricorum, 18, 155-159.

Sivaraman, R. (2020) Exploring Metallic Ratios, Mathematics and Statistics, 8, 4, 388-391. http://dx.doi.org/10.13189/ms.2020.080403

Spíchal, L. (2022) About the Harmonic Mean on the Unit Parabola, Symmetry: Culture and Science, 33(1), 45-54. http://dx.doi.org/10.26830/symmetry_2022_1_45

Spinadel, V. W. (1998) From the Golden Mean to Chaos, Buenos Aires: Editorial Nueva Librería.

Spinadel, V. W., Paz, J. M. (1999) A New Family of Irrational Numbers with Curious Properties, Humanistic Mathematics Network Journal, 19, 14, 33-37. https://doi.org/10.5642/hmnj.199901.19.14

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