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Aebi, Christian, Cairns, Grant. (1403). Equable kites, trapezoids and cyclic quadrilaterals on the Eisenstein Lattice. , (), -. doi: 10.22108/toc.2024.140684.2150
Christian Aebi; Grant Cairns. "Equable kites, trapezoids and cyclic quadrilaterals on the Eisenstein Lattice". , , , 1403, -. doi: 10.22108/toc.2024.140684.2150
Aebi, Christian, Cairns, Grant. (1403). 'Equable kites, trapezoids and cyclic quadrilaterals on the Eisenstein Lattice', , (), pp. -. doi: 10.22108/toc.2024.140684.2150
Aebi, Christian, Cairns, Grant. Equable kites, trapezoids and cyclic quadrilaterals on the Eisenstein Lattice. , 1403; (): -. doi: 10.22108/toc.2024.140684.2150

Equable kites, trapezoids and cyclic quadrilaterals on the Eisenstein Lattice

Transactions on Combinatorics
مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 24 آذر 1403    اصل مقاله (477.48 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/toc.2024.140684.2150
نویسندگان
Christian Aebi1؛ Grant Cairns* 2
1Collège Calvin Geneva, Switzerland
2Department of Mathematical and Physical Sciences, La Trobe University Melbourne, Australia
چکیده
We show that on the Eisenstein lattice, up to Euclidean motions, there is only one infinite family of equable kites, which is given by the Pell-like equation $3x^2-2=y^2$, and only one single equable trapezoid, which also happens to be the only equable cyclic quadrilateral.
کلیدواژه‌ها
quadrilateral؛ Eisenstein lattice؛ equable
مراجع

[1] C. Aebi and G. Cairns, Lattice equable quadrilaterals I: Parallelograms, Enseign. Math., 67 no. 3-4 (2021) 369–401.
[2] C. Aebi and G. Cairns, Lattice equable quadrilaterals II: kites, trapezoids and cyclic quadrilaterals, Int. J. Geom., 11 no. 2 (2022) 5–27.
[3] C. Aebi and G. Cairns, Equable parallelograms on the Eisenstein lattice, Math. Slovaca, 74 no. 4 (2024) 963–982.
[4] C. Aebi and G. Cairns, Equable triangles on the Eisenstein lattice, to appear in the March 2025 issue of Math. Gazette., Preprint available at https://arxiv.org/abs/2309.04476.

[5] C. Aebi and G. Cairns, Less than equable triangles on the Eisenstein lattice, to appear in the July 2025 issue of Math. Gazette., Preprint available at https://arxiv.org/abs/2312.10866.
[6] C. J. Bradley, Challenges in geometry, For Mathematical Olympians past and present, Oxford University Press, Oxford, 2005.
[7] A. Ostermann and G. Wanner, Geometry by its history, Springer, Heidelberg, 2012.
[8] N. J. A. Sloane, The on-line encyclopedia of integer sequences, https:\oeis.org.

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