![]() This is where Professor Frink's explanation picks up, because the two-dimensional square can be pulled in the z direction, which is perpendicular to its face, to form a three-dimensional cube (or Frinkahedron). Next, the one-dimensional line can be pulled in the perpendicular y direction to form a two-dimensional square. This point can be pulled in, say, the x direction to trace a path that forms a one-dimensional line. If we start with zero dimensions, we have a zero-dimensional point. In fact, his approach can be used to explain the relationship between all dimensions. Professor Frink: This forms a three-dimensional object known as a cube, or a Frinkahedron in honour of its discoverer.įrink's explanation illustrates the relationship between two and three dimensions. Professor Frink: But suppose we extend the square beyond the two dimensions of our universe along the hypothetical z-axis. Professor Frink: Here is an ordinary square.Ĭhief Wiggum: Whoa, whoa! Slow down, egghead! With the help of a blackboard, Frink goes on to explain the concept of higher dimensions: ![]() Help is at hand in the form of Professor John Nerdelbaum Frink, Jr, who explains "Well, it should be obvious to even the most dimwitted individual, who holds an advanced degree in hyperbolic topology, that Homer Simpson has stumbled into. Marge cannot fathom what has happened to Homer, because she can hear him but not see him. Well, better make the most of it." And promptly belches. I feel like I'm wasting a fortune just standing here. When Homer approaches a signpost indicating the x, y, and z axes in his new three-dimensional universe, he alludes to the fact that he is standing within the most sophisticated animated scene ever to have appeared on television: "Man, this place looks expensive. Instead of being drawn in the classic flat-animation style of The Simpsons, scenes set in this higher dimension have a sophisticated three-dimensional appearance. Homer is utterly perplexed by his new extra dimensionality and notices something shocking: "What's going on here? I'm so bulgy. Diving through the portal he leaves behind his two-dimensional Springfield environment and enters an incredible three-dimensional world. Keen to avoid them, Homer hides behind a bookcase, where he encounters a mysterious portal that seems to lead into another universe. The storyline begins quite innocently with Patty and Selma, Homer's sisters-in-law, paying a surprise visit to the Simpsons. But "Homer 3" is without doubt the most intense and elegant integration of mathematics into an episode since the series began a quarter of a century ago. Mathematical references and in-jokes are peppered throughout The Simpsons, thanks to a swag of physics and maths degrees amongst the show's writers. Odds on: the maths behind game shows, Science Online,.
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