This construction is intended to help visualize the premise of a challenging puzzle, found at https://mindyourdecisions.com/blog/2018/03/28/can-you-solve-a-hard-korean-test-question-cone-shaped-mountain-puzzle/[br][br]The track for a sightseeing train is to be constructed, making one full turn around a cone-shaped mountain.[br]The track starts at point A on the base of the mountain and ends at point B, directly uphill from point A.[br]Drag the various points on the 2D net to adjust the parameters of the mountain.[br][br]Questions one may explore:[br][list][*]Under what conditions does the shortest track ascend first and then descend? Explain in simple language why this is sometimes shorter than a strictly-uphill track.[/*][*]For some given set of parameters, what is the shortest possible length of the track? How long are both the ascending and descending sections of track?[/*][*]What is the shortest track length when the central angle of the cone's net exceeds 180°?[/*][/list]