Can a Flatlander See More Than 2 Sides of a Cube at Once?

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SUMMARY

In the discussion regarding whether a Flatlander can see more than two sides of a cube simultaneously, the consensus is that it is not possible. The Flatlander perceives the cube as a point, square, or triangle, with only two sides visible at any given time due to occlusion. However, one participant suggests that if the cube descends at a specific angle, it may be possible to perceive three sides. The debate hinges on the geometric interpretations of dimensional visibility in a two-dimensional space.

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  • Understanding of two-dimensional and three-dimensional geometry
  • Familiarity with the concept of dimensionality in mathematics
  • Knowledge of visual perception in different dimensions
  • Basic skills in geometric visualization and spatial reasoning
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  • Research geometric projections and their implications in different dimensions
  • Explore the concept of dimensionality in mathematics and physics
  • Investigate visual perception theories related to dimensional occlusion
  • Learn about animations and simulations that illustrate geometric intersections
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This discussion is beneficial for mathematicians, educators, students of geometry, and anyone interested in the philosophical implications of dimensionality and perception.

onlymepa
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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.
Chris.
 
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Physics news on Phys.org
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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