The paper this article is about: * A Closed-Form Solution to the Geometric Goat Problem, by Ingo Ullisch in The Mathematical Intelligencer. https://doi.org/10

The paper this article is about: * A Closed-Form Solution to the Geometric Goat Problem, by Ingo Ullisch in The Mathematical Intelligencer. https://doi.org/10.1007/s00283-020-09966-0 https://doi.org/10.1007/s00283-020-09966-0 The illustration in the article (I mean the top half of https://d2r55xnwy6nx47.cloudfront.net/uploads/2020/12/Grazing-goat-figure.svg https://d2r55xnwy6nx47.cloudfront.net/uploads/2020/12/Grazin...) was really helpful to understand what the question is. I know Quanta Magazine articles sometimes get some negative comments here on HN from readers who expect a different kind of exposition than what is suitable for a magazine of that sort, but for my part I'm really grateful to Quanta Magazine for bringing attention to papers like this, and writing nice articles about them with history, good illustrations, quotes from other mathematicians, etc. For the impatient, Wikipedia has a short article on the problem and earlier progress: https://en.wikipedia.org/w/index.php?title=Goat_problem&oldid=993368252 https://en.wikipedia.org/w/index.php?title=Goat_problem&oldi... From this it's more clear in what sense this is progress: whereas earlier the answer r=1.1587284730181215178... (https://oeis.org/A133731 https://oeis.org/A133731) was known via more than one formula of the form r = (some function of r), only now do we have a closed-form expression of the form r = (some expression not involving r).