![]() ![]() Jokes or off-topic top-level comments will be removed. Also, don't be a dick.ĭo not submit top-level comments in posts that are not an attempt at an answer or a request for clarification. Reddit's site-wide rules still apply here. Repeat or egregious offenders will be banned permanently. Rule breaking posts/comments will have a temporary ban that will serve as a first offense "warning". There is no warning for hate speech of any kind. This subreddit has a zero-tolerance policy for hateful or unnecessary language. Try /r/homeworkhelp or /r/cheatatmathhomework instead. Posts which seem to be asking for help on homework will be removed. For more abstract math, try /r/math or /r/learnmath. Posts containing "simple math" will be removed, as well as requests whose answers are easily searchable online, and any other post at the moderators' discretion. How many feet are in a mile?) use Wolfram|Alpha™. " /u/FragTheWhale calculates.".įor easy and quick math results (ex. Give credit where credit is due-include the user who made the calculations in any post you submit: ex. posts must have a calculable answer otherwise, they will be removed. State clearly what is being or what you want calculated in the title. A hint of that complexity can be seen in the accompanying 2D animation of one of the simplest possible regular 4D objects, the tesseract, which is analogous to the 3D cube.Proper title tags are required for all posts or it will be removed! The tags accepted are at the end of the sidebar down there. It is only when such locations are linked together into more complicated shapes that the full richness and geometric complexity of higher-dimensional spaces emerge. Single locations in Euclidean 4D space can be given as vectors or n-tuples, i.e., as ordered lists of numbers such as ( x, y, z, w). Einstein's concept of spacetime has a Minkowski structure based on a non-Euclidean geometry with three spatial dimensions and one temporal dimension, rather than the four symmetric spatial dimensions of Schläfli's Euclidean 4D space. Einstein's theory of relativity is formulated in 4D space, although not in a Euclidean 4D space. Large parts of these topics could not exist in their current forms without using such spaces. Higher-dimensional spaces (greater than three) have since become one of the foundations for formally expressing modern mathematics and physics. The eight lines connecting the vertices of the two cubes in this case represent a single direction in the "unseen" fourth dimension. ![]() This can be seen in the accompanying animation whenever it shows a smaller inner cube inside a larger outer cube. The simplest form of Hinton's method is to draw two ordinary 3D cubes in 2D space, one encompassing the other, separated by an "unseen" distance, and then draw lines between their equivalent vertices. In 1880 Charles Howard Hinton popularized it in an essay, " What is the Fourth Dimension?", in which he explained the concept of a " four-dimensional cube" with a step-by-step generalization of the properties of lines, squares, and cubes. Schläfli's work received little attention during his lifetime and was published only posthumously, in 1901, but meanwhile the fourth Euclidean dimension was rediscovered by others. The general concept of Euclidean space with any number of dimensions was fully developed by the Swiss mathematician Ludwig Schläfli before 1853. published in 1754, but the mathematics of more than three dimensions only emerged in the 19th century. The idea of adding a fourth dimension appears in Jean le Rond d'Alembert's "Dimensions". ![]()
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