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2D Cross Sections of a Cube

  1. Dec 12, 2012 #1
    Hey everyone!
    I have the following question for you guys to settle an argument: If you were an inhabitant of Flatland and a cube decided to visit you like the sphere did, would you be able to see more than 2 sides at a time? My answer is no because Mr. Cube could appear as a point, a square with a static side length, or a triangle of varying dimensions among others and it would impossible for Mr. Flatlander to see a 3rd or 4th side because the 2 sides that are in his field of vision are blocking the other side(s) but my friend says that if Mr. Cube descended into Flatland at just the right angle (no pun intended), then one could see 3 sides at the same time. So am I right or is my friend right? Thanks in advance for answering.
    Last edited: Dec 12, 2012
  2. jcsd
  3. Dec 12, 2012 #2
    Draw a cube and then imagine the various intersections of your cube and a plane. We might get a point, a square, a equallaterial triangle, a hexagon, a rectangle and other shapes. Now move and rotate the plane. A google search might come up with an animation.
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