![]() ![]() The material looks uniform throughout, there does not seem to be any internal energy generation, and the range of temperature is narrow. The temperature distribution also seems stable with respect to time. You rotate around the wall, drill a few more holes, and find that the temperature distribution is the same at each location. ![]() You install your thermocouples and measure the temperature distribution of the wall in the radial direction: T(r) = 50☌ + 1800☌ in Góm) Your equation gives the temperature distribution of the wall at any radius, r, between the limits of rį and ro. Based on the length of your drill bit, you estimate the inner radius of the shell, ri, to be 9.9 m. You feel your drill bit punch through the wall, so it must be either a spherical or cylindrical shell. ![]() The wizard's voice booms, “Is the object in front of you a sphere, or is it a cylinder?" You may not be able to perceive the third dimension, but you do have your trusty drill and thermocouples. By counting your paces around the circumference, you estimate the outer radius of the wall, ro, to be 10.0 m. You walk around it, feeling the continuous curve of the wall until you arrive back at where you started. From your perspective you only see a wall that curves away from you in both directions. The wizard snaps his fingers, and an object appears in front of you. If you can solve the wizard's riddle, you will be returned to the real world. An evil wizard has banished you to Flatland, a two-dimensional plane intersecting the real world. ![]()
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