Editing Four-dimensional space (section)

===Cross-sections===
As a three-dimensional object passes through a two-dimensional plane, two-dimensional beings in this plane would only observe a [[Cross section (geometry)|cross-section]] of the three-dimensional object within this plane. For example, if a sphere passed through a sheet of paper, beings in the paper would see first a single point. A circle gradually grows larger, until it reaches the diameter of the sphere, and then gets smaller again, until it shrinks to a point and disappears. The 2D beings would not see a circle in the same way as three-dimensional beings do; rather, they only see a [[One-dimensional space|one-dimensional]] projection of the circle on their 1D "retina". Similarly, if a four-dimensional object passed through a three-dimensional (hyper) surface, one could observe a three-dimensional cross-section of the four-dimensional object. For example, a [[hypersphere]] would appear first as a point, then as a growing sphere (until it reaches the "hyperdiameter" of the hypersphere), with the sphere then shrinking to a single point and then disappearing.<ref>{{cite book|last1=Rucker|first1=Rudy|title=The Fourth Dimension: A Guided Tour of the Higher Universe|date=1996|publisher=[[Houghton Mifflin]]|location=Boston|isbn=978-0-395-39388-8|page=18}}</ref> This means of visualizing aspects of the fourth dimension was used in the novel ''Flatland'' and also in several works of [[Charles Howard Hinton]].<ref name="Hinton"/>{{rp|11–14}} And, in the same way, three-dimensional beings (such as humans with a 2D retina) can see all the sides and the insides of a 2D shape simultaneously, a 4D being could see all faces and the inside of a 3D shape at once with their 3D retina.