I'm reading about the Kakeya needle problem. There is the result that the smallest area for a convex set where you can fully turn a needle is the area of an equilateral triangle with height 1.
This was proved in 1928 by Pal and I am looking for a newer version of the proof (it does not matter if it is in a paper, lecture notes or in a book). However so far I only managed to find the original.
Does anyone know where to find extra material on this?
You might try this American Mathematical Monthly article: https://www.jstor.org/stable/2317619?seq=1#page_scan_tab_contents -- that link will even let you read it for free if you don't mind signing up for an account. It has a reasonable amount of detail and develops the problem additionally for star-shaped sets. The list of references is quite short though, suggesting that it might be hard to find a lot of literature on the problem.
F. Cunningham Jr. did write another article on the Kakeya problem three years later (The American Mathematical Monthly Volume 81, 1974 - Issue 6) but the references there go no further.