The Hypercube is a three-dimensional representation of a polygon existing in the fourth dimension. Mathematicians have been thinking about the fourth dimension for over two centuries. It was during this period that Möbius discovered the unique properties of a two-dimensional strip when twisted in three-dimensional space. Charles Hinton was a mathematician in the mid-1800s interested in what objects existing in the fourth dimension might look like. He wrote an article in New Era of Thought titled "What is the Fourth Dimension?" in which he theorized the ways in which a four-dimensional object could be viewed in three dimensions. He coined the term tesseract from the Greek word meaning four rays of light. This is proven to be difficult for people to visualize. To understand the concept of the fourth dimension (4D), it is useful to start with the simplest construction of space. Dimensions are designated by an "n" plus an integer, representing the dimensional space. For example, n-2 refers to a two-dimensional space. When n equals zero, it results in a geometric point in space. A line connecting two of these points will reside in the first dimension or n-1. This line of the first dimension has only length, but no width or depth. If another line intersects this line perpendicularly, the resulting plane which has length and width, but no depth is in the second dimension. If you add depth to this existing plane, you will get a coordinate system that has both length and depth. In fact, any point in this system can be referenced by a corresponding coordinate (x,y,z). This is the third dimension and is the easiest for humans to visualize because it is the world we live in. If you add another dimension to the cube in the center of the card... difficult to visualize, it becomes increasingly difficult to deal with higher dimensions. This fascinating four-dimensional cube stimulates the mind to look and stretches the mind even further to try to understand the cube. Marvel Studios used the tesseract in their film The Avengers. Marvel used it as a portal to the other side of space, in our world the tesseract has applications of a wormhole. At least that's what the math tells us. While a wormhole is no stretch of the imagination, Marvel could have used the tesseract correctly. The Hypercube leaves everyone speechless because it is so difficult for humans to grasp it and make sense of it. I know I can't visualize anything in the fourth dimension or anything in the other dimensions beyond the fourth. The Tesseract is incredibly cool to study, and the mathematicians who discovered it are brilliant.
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