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Thread: What is the topology of a human body, with internal organs?

  1. #1 What is the topology of a human body, with internal organs? 
    Forum Freshman mindissilent's Avatar
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    Apr 2010
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    Human body is not a doughnut, what is it?
    If one excludes the interior, it would leave use with
    ..___.______ .._____._____
    /***|.|*****|.|****|.|*****\<----- THREE INPUT HOLES
    |***|.|*****|.|****|.|*****|
    |***|.|*****|.|****|.|***<--|------ SURROUNDING MESH
    |**/..................................\**|
    |**|..................................|**|
    |**|..................................|**|
    |**|..INTERIOR.WHERE....|**|
    |**|..ALL CONNECTS........|**|
    |**|..................................|**|
    |**\................................../**|
    |***|.|***********|.|*****|
    |***|.|***********|.|*****|
    \***|.|***********|.|*****/<---- TWO OUTPUTS HOLES

    THREE TUBES -> TWO TUBES...
    Can the above be simplified?

    The reason why I asked for the interior is because I think the topology is common among all living things and it would be interesting to know, what are we(or more interesting, what are we like, what can we be bent into) from the perspective of topology.

    I thought, maybe a trumpet(a musical instrument).
    Give me some ideas.


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  3. #2 Three Pairs of Pants, Genus Four, Five Boundary Components 
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    I had the exact same question as you. Unfortunately, the Internet seems to be lacking an answer. Fortunately, I was able to finally track down the information needed to answer this question. It was this article on Wikipedia that finally pointed me in the right direction.

    Model the human body topologically as three pairs of pants sewn together. (See below.) The top pair of pants is inverted so that the legs are pointed up. Those legs represent the human nostrils. The waist of that top pair of pants is sewn to one leg of the next pair of pants. The other leg of this middle pair of pants is sewn to the waist of the lower pair of pants. The waist sticks out to the side and represents the human mouth. The legs on the lower pair of pants represent the "two output holes" of the human body.

    | | | |
    | |_| |
    *\ ' /
    **\ |
    ***\ \__
    ****} __
    ***/ /
    **/ |
    */ _ \
    | | | |
    | | | |

    Those three "inputs" and two "outputs" make up the five boundary components of the Riemann surface. If you don't consider them boundary components, then instead of three pairs of pants, the human body reduces to a sphere punctured five times.

    If you imagine drawing non-intersecting loops from every open hole through every other open hole, you may be able to see that you can cut along at most four of those loops and still have just one connected piece of fabric. This means the genus of the human body is four.

    So there you have it. The human body is three pairs of pants sewn together to form an open surface of genus four with five boundary components.


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