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Three discs for the Mittenpunkt

Published online by Cambridge University Press:  23 August 2024

Martin Lukarevski
Martin Lukarevski*
Affiliation:
Department of Mathematics and Statistics, University “Goce Delcev” - Stip, North Macedonia e-mail: martin.lukarevski@ugd.edu.mk
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The aim of this paper is to give a solution to three conjectures from Euclidean geometry concerning the location of the Mittenpunkt. The first two are solved without dependence on computer technology and with only a moderate amount of calculations. They were initially tackled by heavy calculations using computer algebra systems.

Type
Articles
Information
The Mathematical Gazette , Volume 108 , Issue 572 , July 2024 , pp. 209 - 218
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Copyright
© The Authors, 2024 Published by Cambridge University Press on behalf of The Mathematical Association

References

Lukarevski, M., Marinescu, D. S., A refinement of the Kooi’s inequality, Mittenpunkt and applications, J. Inequal. Appl. 13 (3), (2019) pp. 827–832.CrossRefGoogle Scholar
Kimberling, C., Encyclopedia of triangle centers, available at https://faculty.evansville.edu/ck6/encyclopedia/ETC.html Google Scholar
Leversha, G., The geometry of the triangle, UKMT (2013).Google Scholar
Guinand, A. P., Euler lines, tritangent centers and their triangles, Amer. Math. Monthly 91, pp. 290–300 (1984).CrossRefGoogle Scholar
Altshiller-Court, N., College geometry, Barnes & Noble (1952).Google Scholar
Johnson, R., Advanced euclidean geometry, Dover (1960).Google Scholar
Taylor, G., Applications of the GPAT to triangle geometry (2005) available at: http://maths.straylight.co.uk/triangles/geometry.pdf Google Scholar
Lukarevski, M., Scott, J. A., On the Brocard disc, Math. Gaz. 105 (July 2021) pp. 327–328.CrossRefGoogle Scholar
Yiu, P., The uses of homogeneous barycentric coordinates in plane Euclidean geometry, Int. J. Math. Educ. Sci. Technol. 31(4), pp. 569–578 (2000).CrossRefGoogle Scholar
Lukarevski, M., Scott, J. A., Three discs for the incentre, Math. Gaz. 106 (July 2022) pp. 332–335.CrossRefGoogle Scholar
Klein, F., Vorlesungen über die Entwicklung der Mathematik im 19. Jahrhundert (2 vols.), Springer-Verlag (1926-27).Google Scholar
Boyer, C. B., History of analytic geometry, Scripta Mathematica (1956).Google Scholar
Fauvel, J., Flood, R., Wilson, R., Möbius and his band − mathematics and astronomy in nineteenth-century Germany, Oxford University Press (1993).CrossRefGoogle Scholar
Lukarevski, M., A simple proof of Kooi’s Inequality, Math. Mag. 93 (3), (2020) p. 225.CrossRefGoogle Scholar
Lukarevski, M., Exradii of the triangles and Euler’s inequality, Math. Gaz. 101 (March 2017) p. 123.CrossRefGoogle Scholar
Lukarevski, M., Wanner, G., Mixtilinear radii and Finsler-Hadwiger inequality, Elem. Math. 75(3) (2020) pp. 121–124.CrossRefGoogle Scholar
Finsler, P., Hadwiger, H., Einige Relationen im Dreieck, Commentarii Mathematici Helvetici, 10(1) (1937), pp. 316–326.CrossRefGoogle Scholar
Lukarevski, M., The circummidarc triangle and the Finsler-Hadwiger inequality, Math. Gaz. 104 (July 2020) pp. 335–338.CrossRefGoogle Scholar
Lukarevski, M., Exarc radii and the Finsler-Hadwiger inequality, Math. Gaz. 106 (March 2022) pp. 138–143.CrossRefGoogle Scholar
Rabinowitz, S., A computer algorithm for proving symmetric homogeneous triangle inequalities, International Journal of Computer Discovered Mathematics, 7 (2022) pp. 30–62.Google Scholar