Problematics | Walking with a dinosaur

Although dinosaurs went extinct millennia before humans evolved, their old fossils and modern simulations have given us a fair idea of how gigantic some of them were compared to the humans of today. I have no idea how long it will take us, though.” “If we walk long enough, we will eventually reach one end of the flat earth,” says the human. “Let’s keep walking and we will eventually return where we started.” “I have walked long enough,” says the human, “and so have you.” “My feet have travelled as far as your feet,” the dinosaur agrees, “but my head has travelled a longer distance than your head.” This confuses the human, so the brachiosaurus explains: “Your feet and mine have walked the same arc on the surface of the earth. But my head, being at a height of 18m compared to your height of 1.8m, has described the arc of a larger circle than your head has done.” “No,” says the human, “we walked along a straight line, so it’s been the same distance for both of us, head and foot.” The brachiosaurus ignores him. — Sampath Kumar V, Coimbatore Although only two of Sampath’s methods are being published here, let us acknowledge him for having tried three approaches: two using similar triangles and one using coordinates.