The dual of Philo's shortest line segment problem
<|reference_start|>The dual of Philo's shortest line segment problem: We study the dual of Philo's shortest line segment problem which asks to find the optimal line segments passing through two given points, with a common endpoint, and with the other endpoints on a given line. The provided solution uses multivariable calculus and geometry methods. Interesting connections with the angle bisector of the triangle are explored. A generalization of the problem using $L_p$ ($p\ge 1$) norm is proposed. Particular case $p=\infty$ is studied. Interesting case $p=2$ is proposed as an open problem and related property of a symedian of a triangle is conjectured.<|reference_end|>
@article{aliyev2024the,
    title={The dual of Philo's shortest line segment problem},
    author={Yagub N. Aliyev},
    journal={arXiv preprint arXiv:2406.05702},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.05702},
    primaryClass={cs.CG}
}