2019/10/15 by Makhul, Mehdi
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1910.06888
Richard Guy asked the following question: can we find a triangle with rational sides, medians, and area? Such a triangle is called a perfect triangle and no example has been found to date. It is widely believed that such a triangle does not exist. Here we use the setup of Solymosi and de Zeeuw about rational distance sets contained in an algebraic curve, to show that for any angle 0