@article{19494,
  abstract     = {Starting from any given rational-sided, right triangle, for example, the (3,4,5)-triangle with area 6, we use Euclidean geometry to show that there are infinitely many other rational-sided, right triangles of the same area. We show further that the set of all such triangles of a given area is finitely generated under our geometric construction. Such areas are known as “congruent numbers” and have a rich history in which all the results in this article have been proved and far more. Yet, as far as we can tell, this seems to be the first exploration using this kind of geometric technique.},
  author       = {Chan, Yik Tung},
  issn         = {1930-0972},
  journal      = {The American Mathematical Monthly},
  number       = {8},
  pages        = {689--703},
  publisher    = {Taylor & Francis},
  title        = {{Rational right triangles of a given area}},
  doi          = {10.1080/00029890.2018.1495491},
  volume       = {125},
  year         = {2018},
}

@article{909,
  abstract     = {We study the lengths of curves passing through a fixed number of points on the boundary of a convex shape in the plane. We show that, for any convex shape K, there exist four points on the boundary of K such that the length of any curve passing through these points is at least half of the perimeter of K. It is also shown that the same statement does not remain valid with the additional constraint that the points are extreme points of K. Moreover, the factor ½ cannot be achieved with any fixed number of extreme points. We conclude the paper with a few other inequalities related to the perimeter of a convex shape.},
  author       = {Akopyan, Arseniy and Vysotsky, Vladislav},
  issn         = {0002-9890},
  journal      = {The American Mathematical Monthly},
  number       = {7},
  pages        = {588 -- 596},
  publisher    = {Mathematical Association of America},
  title        = {{On the lengths of curves passing through boundary points of a planar convex shape}},
  doi          = {10.4169/amer.math.monthly.124.7.588},
  volume       = {124},
  year         = {2017},
}

@article{4079,
  author       = {Edelsbrunner, Herbert and Skiena, Steven},
  issn         = {1930-0972},
  journal      = {American Mathematical Monthly},
  number       = {7},
  pages        = {614 -- 618},
  publisher    = {Mathematical Association of America},
  title        = {{On the number of furthest neighbor pairs in a point set}},
  doi          = {10.1080/00029890.1989.11972250},
  volume       = {96},
  year         = {1989},
}