By Jaan Kalda (TalTech) in collaboration with Máté Vigh
A boy is periodically running around an equilaterally triangular house of side length a on an icy field. What is the minimum duration of one loop around the house, assuming an optimal trajectory? You may assume a constant coefficient of friction \mu between the ice and the boy and that the boy’s stride length is negligible compared to the house’s dimensions. Gravitational acceleration is g.