Why Is Pi Less Than Twice Phi?

Alejandro H. Morales, Igor Pak, Greta Panova. Why Is Pi Less Than Twice Phi?. The American Mathematical Monthly, 125(8):715-723, 2018. [doi]

@article{MoralesPP18-1,
  title = {Why Is Pi Less Than Twice Phi?},
  author = {Alejandro H. Morales and Igor Pak and Greta Panova},
  year = {2018},
  doi = {10.1080/00029890.2018.1496757},
  url = {https://doi.org/10.1080/00029890.2018.1496757},
  researchr = {https://researchr.org/publication/MoralesPP18-1},
  cites = {0},
  citedby = {0},
  journal = {The American Mathematical Monthly},
  volume = {125},
  number = {8},
  pages = {715-723},
}