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

In summary, the conversation discusses whether a Flatlander would be able to see more than 2 sides of a cube visiting them, similar to how the sphere visited Flatland in the book "Flatland." One person argues that it would be impossible due to the limited field of vision, while the other suggests that the cube could be seen from a certain angle. The conversation also references visual aids such as drawing a cube and rotating a plane to demonstrate the different perspectives.
  • #1
onlymepa
1
0
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.
 
Last edited:
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  • #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.
 

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

1. What is a 2D cross section of a cube?

A 2D cross section of a cube is a 2-dimensional representation of a cube, which is a 3-dimensional shape. It is created by slicing the cube with a plane in a specific direction, resulting in a flat shape that shows the intersections of the plane and the cube's faces.

2. How many different 2D cross sections can be made from a cube?

There are an infinite number of possible 2D cross sections that can be made from a cube. The direction and location of the slicing plane can vary, resulting in different shapes and sizes of cross sections.

3. What do the different shapes of 2D cross sections represent?

The different shapes of 2D cross sections represent the different orientations and positions of the slicing plane in relation to the cube. For example, a square cross section represents a plane that is perpendicular to the cube's edges, while a rectangle represents a plane that is at an angle to the edges.

4. Can a 2D cross section of a cube be a perfect circle?

No, a 2D cross section of a cube can never be a perfect circle. This is because a cube is a 3-dimensional shape with straight edges and flat faces, so it is not possible for a plane to intersect it and create a curved shape like a circle.

5. How are 2D cross sections of a cube used in real life?

2D cross sections of a cube are used in many fields of science and engineering, such as architecture, computer graphics, and physics. They can help visualize and understand the properties and relationships of 3D objects, and are often used in problem-solving and design processes.

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