Wikipedia:Reference desk/Archives/Mathematics/2014 February 24
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February 24 edit
Question on what the name of a step is edit
Simply, I have forgotten the name of what the mathematical steps of solving a problem are; for example:
4(x+4) = 6(x+5)-x 4x+16 = 6x+30-x 4x+16 = 5x+30 16 = x + 30 -14 = x
What is the term used to describe the solving of "6(x+5)" to "6x+30", as well as the canceling on each side of the equation (i.e. "4x+16 = 5x+30", subtracting 4x from 5x and subtracting 30 from 16 to get "-14 = x")? Thanks :) -- 140.202.10.134 (talk) 19:50, 24 February 2014 (UTC)
- "6(x+5)" to "6x+30" is the distribution of multiplication over addition (i.e. using the distributive property). RJFJR (talk) 20:52, 24 February 2014 (UTC)
- Is this for an assignment, in which case you would want to refer to your book or teacher. If not, when you are subtracting 4x from 5x, you are really subtracting 4x from each side of the equality, you can do this because equal numbers are identical; so you could say this is justified by the identity of equals, or something to that effect - you could also say that you are using the cancellative property of addition, if you wanted to. Why are you looking for the names? If you are looking for some specific idea/rule that you have forgotten, and need, we may be able to help you given more context. :-) Phoenixia1177 (talk) 08:53, 25 February 2014 (UTC)
Animated GIFs of complex 4D rotations? edit
Our article tesseract has wonderful animated gifs of rotations of these simple 4D objects. Do we have any more complex gifs, with more or different objects, or are any available on the web? Thanks. μηδείς (talk) 21:08, 24 February 2014 (UTC)
- If you look at Category:Featured animations, there are other nice animations at WP. --Mark viking (talk) 21:24, 24 February 2014 (UTC)
- A quick google of tasseract gif or 4d gif shows a huge amount of gifs. I am sure that you have already done such a search, so I was hoping that you might clarify what more you are asking for. They are wonderful, aren't they? I especially like this 4D image. http://www.moillusions.com/wp-content/uploads/2009/11/greatestgifever.gif . Please delete my comment if it is irrelevant to what you are looking for. I will not mind, since I am not sure what you are after. DanielDemaret (talk) 21:32, 24 February 2014 (UTC)
- Commons has commons:Category:Animations_of_polyhedra with a lot of similar models. This is a sub-sub category to commons:Category:Mathematical animations with many other animations. --Salix alba (talk): 22:43, 24 February 2014 (UTC)
- If you look at the bottom of my home page, there's a few I created. (One is 3D, and requires red/blue 3D glasses.) StuRat (talk) 02:15, 25 February 2014 (UTC)
- Just to confirm your intuition, an animation of the 4D sphere is just as boring as an animation of a rotating 3D sphere [1]. You can get animations for any of the Convex regular polychoron by searching google with their proper names (though I think we have animations for all of them.) SemanticMantis (talk) 21:31, 26 February 2014 (UTC)
- Thanks for the answers so far. I guess what I am really looking for is something like a Penrose tiling of the plane in a rotating 4D analog, with pentagonal faces being dodecagons, or the like. A sea of boiling hyper-dodecahedra. The 4D torus was excellent, hadn't seen that before. Even two rotating tesseracts that touch at a face would be excellent. μηδείς (talk) 21:34, 26 February 2014 (UTC)