Are There Flaws and Restrictions in Geometry Theorems?

[TsunamiJoe]

First off - id just like to say hello to everyone and I am 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 I am not positive whether or or theyre applicable, mainly because I've experienced that my instructor has quite the closed mind and doesn't question mathmatics.

also

another thing i have noticed is that currently a lot 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 I am 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 don't intend to bash or hurt the values of geometry, it has a nice addition to mathematics - i personaly have found errors and/or restrictions in its applications

 

[Chi Meson]

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.

 

[TsunamiJoe]

well this was really just trying to see if I am crazy or if others share opinions - btw halls of ivy I am 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?

 

[TsunamiJoe]

ok guys I am 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 don't 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 - shouldn't 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 ?

 

[AKG]

ok guys I am 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 don't 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 - shouldn't 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 ?

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.

 

[NateTG]

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.

 

[Janitor]

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.

 

[TsunamiJoe]

I don't have my geometry book with my atm but ill look and try and find the theorum number for the "hinge theorum."

 

[physics phan]

First off - id just like to say hello to everyone and I am sorry if this has possibly already been posted - but i looked around to check a bit and didnt see anything of the sort

Aw no prob we forgive you