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Math Help - Looking for a word similar to concentric

  1. #1
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    Looking for a word similar to concentric

    Hello, I hope I am in the right forum; if not, please feel free to move my topic with my apologies!

    I am wondering if there is a word to denote that two shapes exist within the same larger shape. An analogy is concentric. I am looking for a word that means two shapes which share the same larger shape, just not necessarily the same center. I feel like there might be a word for it, but I just can't think of it and it has come up a few times in the past month or so where I wanted to use such a word. It's bugging me quite a bit.

    I was trying to build the word myself, and the two best candidates I could conceive of were autogenous and homomorphic. Autogenous seems primarily referenced in medicine; however, homomorphic seems to have mathematical significance and is further divided into the following subset terms: "automorphic," "endomorphic," and "isomorphic." Do any of these fulfill the role I am looking for, or did I just imagine I once knew a term with this definition?

    Here is the Wiki page from homomorphism: https://en.wikipedia.org/wiki/Homomorphism

    Unfortunately, I don't understand it when I read it, which I fear indicates they're incompatible.

    Thank you!
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  2. #2
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    Re: Looking for a word similar to concentric

    Hey blaisem.

    Do you mean that the two shapes can be rotated, scaled, and translated into each other so that they have a perfect overlap?

    If this is the case then you will need to look at whether a transformation involving all of these (which can be written as matrices) exists and also if an inverse transformation exists (which it should).

    Basically you have to prove that a transformation exists such that Ax = x' (transform each vertex so that you map x in shape A to x' in shape B) and that its inverse exists (determinant will be non-zero).

    If you need more information look at matrix structures for translation, rotation, and scaling and compose them in the right order.
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  3. #3
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    Re: Looking for a word similar to concentric

    I would say that the word you are looking for is one you used: "similar".
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