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Geometric flaws/restriction?

  1. May 4, 2004 #1
    First off - id just like to say hello to everyone and im sorry if this has possibly already been posted - but i looked around to check a bit and didnt see anything of the sort

    ok i supose i ought to explain what i mean: i am only in a sophomore geometry class(high school) but i have tended to notice many restrictions in theorums and/or flaws. now im not positive whether or or theyre applicable, mainly because ive experienced that my instructor has quite the closed mind and doesnt question mathmatics.

    also

    another thing i have noticed is that currently alot of the circle theorums we are dealing with tend to be incomplete in what they intend or are illogical in what they say is true

    now the reason im not including examples at the moment is because not only would it take too long for me to explain but also because this topic is mainly me asking - is geometry flawed? or have i just not been introduced into a better form of geometry at my low grade level

    ok now to the restriction part of my question

    i have noticed again in many of the circle theorums that they say only a certain thing can be prooved by using it - when in fact there can be several others also prooved

    now if in the end anyone would like examples and/or my reasoning behind my statements please email me or PM me and i will contact you with a thorough answer

    so with that said i am wondering if anyone can help me or if anyone shares these veiws as i do.

    remember this is just my opinion and i dont intend to bash or hurt the values of geometry, it has a nice addition to mathmatics - i personaly have found errors and/or restrictions in its applications
     
  2. jcsd
  3. May 7, 2004 #2

    Chi Meson

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    A lot of folks, myself included, do not go in for personal contact via email or PM. You will get a much greater response by posting an example of what you mean here.
     
  4. May 7, 2004 #3
    well this was really jsut trying to see if im crazy or if others share opinions - btw halls of ivy im getting a big list of things together ok so itll be couple of days before you get a responce

    also

    ill rerespond in here in a couple of days with what i sent ivy ok?
     
  5. May 21, 2004 #4
    ok guys im seriously sorry for the latency of this reply but my internet went down for a while there - ok here is a perhaps incompleteness of geometry

    now i dont know if this is apllicable because its 2 differint figures- but the hinge theorum and its opposite - when they are applied to circles and well everything else - shouldnt there be an equation to figure out the length of a specified line with just using hinge? my schoolyear is generaly over and i have yet to see any real equation that denotes this

    also what i think is completely stupid in geometry is the fact that remotely its entire structure is based mostly off of postulates...which in definition are unprooved (thus not neccisarely true) statements

    and in the prooving of a theorum you use such things - how is that possible ?
     
  6. May 21, 2004 #5

    AKG

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    All of mathematics are based on postulated axioms. If they weren't, then there would be no mathematics to start with! This doesn't make them flawed, this makes them valid given the axioms. Accepting the axioms doesn't mean believing something false, it simply means that you agree that we are talking about mathematics.

    Also, you might want to provide some (better) examples. I looked at mathworld.com and searched for "hinge theorem"; it returned no results.
     
  7. May 21, 2004 #6

    NateTG

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    AKG -
    Our typographically/gramatically challenged guest appears to be looking for something like the law of cosines, or the Side-Angle-Side theorem, and not claiming that a particular theorem is invalid.

    Tsunamijoe -
    Please take the time to punctuate, capitalize, and check your spelling. Everyone makes errors, but the more anoying it is to decipher your posts, the less likely you are to get any responses at all. -- People generally think that if it's not important to you to make an effort, it's certainly not important for them to make one either.
     
  8. May 21, 2004 #7

    Janitor

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    Euclid did a phenomenally good job of compiling what was known about geometry in his day, and trying to fit it all into a deductive structure. It seems like they say he wrote 13 books. I am not sure if all of them survived to modern times, and I think some may be more number theory than geometry.

    IIRC, Euclid based his entire plane geometry on five axioms. Early in the 20th century David Hilbert polished up Euclid's work, and found he needed something like 21 axioms. (I am going by memory and may be a bit off.)

    I will hazard a guess that the geometry presented in high schools these days is still heavily based on Euclid, rather than on a more modern version such as Hilbert.
     
  9. May 21, 2004 #8
    I don't have my geometry book with my atm but ill look and try and find the theorum number for the "hinge theorum."
     
  10. May 28, 2004 #9
    Aw no prob we forgive you :biggrin: :biggrin: :biggrin: :biggrin: :biggrin:
     
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