๐ Astronomers discuss the large-scale structure of the cosmos and refer to space as curved or the universe as finite but unbounded.

๐ณ Imagine living in a flat land where everyone is exceptionally flat and has no height, only width and length.

๐ In this hypothetical concept, Edwin Abbott, a Shakespearean scholar, created the concept of flatland.

๐ The concept of dimensions and how we perceive them.

๐ณ The encounter between a 3D creature and a 2D square in Flatland.

๐ The confusion and unease of the square when interacting with the 3D creature.

๐ A three-dimensional creature enters the two-dimensional world of Flatland and can only be seen as a cross-section.

๐ The presence of the three-dimensional creature in Flatland is represented by gradually revealing higher slices of an Apple.

๐ The square in Flatland observes objects mysteriously appearing and changing shape, leading to the conclusion of entering a different dimension.

๐ A contact between dimensions causes a square in flatland to see inside closed rooms, giving him a new perspective on his world.

๐ The square's descent back to flatland creates confusion among his friends, who believe he mysteriously appeared from another place.

๐ The video discusses the concept of dimensions and explores the idea of the fourth dimension.

๐ง A cube can be used to explain the concept of dimensions. Moving a line segment at right angles to itself creates a square, and moving that square at right angles to itself creates a cube.

๐ The cube casts a shadow, which represents the three-dimensional projection of the cube in our world.

๐ก The representation of a three-dimensional object in two dimensions is not perfect due to the loss of a dimension.

๐ When a three-dimensional cube is projected through a fourth physical dimension, it forms a four-dimensional hypercube called a tesseract.

๐ Although we cannot visualize a tesseract in three dimensions, we can observe its shadow.

๐ The tesseract is a four-dimensional object consisting of two nested cubes.

๐๏ธโ๐จ๏ธ In four dimensions, the lines of the tesseract would all be equal in length and all angles would be right angles.

๐ We can think about the concept of a four-dimensional universe, even though we cannot imagine it.

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