Abstract
By the theory of elliptic curves, we show that given a convex angle , there exist, except for finitely many exceptions, infinitely many pairs of rational -triangle and -parallelogram with areas and perimeters in fixed proportions respectively, satisfying that is a previously fixed rational multiple of , where and are positive rational numbers.
Citation
Yangcheng Li. Yong Zhang. "$\theta$-triangle and $\omega$-parallelogram pairs with areas and perimeters in certain proportions." Rocky Mountain J. Math. 50 (3) 1059 - 1071, June 2020. https://doi.org/10.1216/rmj.2020.50.1059
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