theroms help

alanoc9

has any1 any advice on how to remember all the theroms

PurpleFistMixer

For a bunch of them, the diagram is fairly self explanatory. So once you've got the diagram and know your basic rules of geometry (some of which okay, are, the results of the theorems, but stuff like the angles opposing equal sides are equal, etc.) it's fairly easy to work out the theorem just by looking at the diagram.

I'd have to check over my theorems, haven't looked at some in a while, but I find loads of the stuff about circles and basically the more complicated theorems all work around congruent triangles. Ie, to prove the theorem you're going to have to prove triangles are congruent in some form or other, and from there a lot of the stuff comes together.

And also, for each theorem there's a kind of 'key' to it, that once you know that bit, the theorem falls into place. The only key I can remember at the minute is that for 'the circle theorem' (ie the one about an angle at the centre of a circle is twice the measure of the angle at the cirumference standing on the same arc), the key is that the 2 triangles you form are isoceles triangles. Ie from there you work out the angles are equal because the sides are equal and then it's all adding and taking away angles, etcetera.

I reckon once you know the theory behind the theorem, it's pretty easy to remember it.
Or at least I hope... I've always hated memorising stuff off.

Fobia

There are two hard theorems : To prove that two similar triangles have same proportions etc etc and Pythagoras' theorem (of which there are two completely different ways to prove it). Other than that it's like PurpleFistMixer says; if you stare at the diagram for about a minute keeping in mind what you're trying to accomplish, the "key" appears in your head and the rest can be done without thinking at all

philologos

purplefistmixer is just naturally smart. For people like me well who arent as intelligent i have to learn it all off

Fobia

Jakkass wrote:

purplefistmixer is just naturally smart. For people like me well who arent as intelligent i have to learn it all off

I wont disagree that she's naturally smart ( ), but what I say reigns true for all levels of intelligence - one of my friends failed maths in the mocks but he can easily write out most of the theorems (bar 2) by using the method above...

alanoc9

[fobia. what part of galway you in

Fobia

alanoc9 wrote:

[fobia. what part of galway you in

Near the city, why?

alanoc9

[just wondering what school you go to. igo to the bish

Fobia

alanoc9 wrote:

[just wondering what school you go to. igo to the bish

I know a few lads in the bish...I guess that your nick is your name? Alan O Connel or O connor or summit? Don't know anyone by the name of Alan O'C

alanoc9

ya its o connor, what school you in.

Fobia

The school of not telling strangers on the internet what school you're in, Westside.

alanoc9

i understand how you feel.soory. i just asked cause theres a thread All about it on this page.

Fobia

No problem, I just can't say who I am/where I go to school due to the FBI being on my back etc

That and I'm a paedophile posing as a student to meet Junior Cert people, don't tell anybody.

declan_lgs

If you *really* wanna know who he is just report this thread to the gardai
That should work.

Victor

Early riser Declan?

spudington16

Fobia wrote:

There are two hard theorems : To prove that two similar triangles have same proportions etc etc and Pythagoras' theorem (of which there are two completely different ways to prove it).

You might find that there are a lot more than to ways to solve Pythagoras' Theorem.

PurpleFistMixer

Fobia wrote:

That and I'm a paedophile posing as a student to meet Junior Cert people, don't tell anybody.

Hey, I knew I recognised you from Paedophiles Posing as Students to Meet Junior Cert People Anonymous... PPSMJCPA!

Victor

Behave you two, back on topic.

Fobia

spudington16 wrote:

You might find that there are a lot more than to ways to solve Pythagoras' Theorem.

To prove, not solve...if there are more than two then could you please explain them? - might be easier than the two I know...

PurpleFistMixer: I thought that was anonymous! Damn them and their lies!

declan_lgs

Fobia wrote:

To prove, not solve...if there are more than two then could you please explain them? - might be easier than the two I know...

http://www.cut-the-knot.com/pythagoras/index.shtml
I'm sticking to the similar triangles one (#19 there)...

Victor wrote:

Early riser Declan?

Well... no

PurpleFistMixer

Jeezus that's a lot of proofs...

The one I learned in school is number 6, probably sticking with that one.

Fobia

Going with number 19 myself, though I'd like to see the look on the examiner's face if you wrote #35 out

modular

I did #4. Dead easy, check it out.

PurpleFistMixer

Yeah, that's the one in the Less Stress More Success book. I was gonna do that but my maths teacher said to do the other one, so meh, probably do the other one. Makes little difference to me really.

Flashling

The one I learned isn't on there....,

oh, and I read somewhere (By somewhere I mean here:http://www.ics.uci.edu/~eppstein/junkyard/euler/) that there are 367 proofs.

declan_lgs

Flashling wrote:

oh, and I read somewhere (By somewhere I mean here:http://www.ics.uci.edu/~eppstein/junkyard/euler/) that there are 367 proofs.

Says that also on the second remark of http://www.cut-the-knot.com/pythagoras/index.shtml

W.Dunham [Mathematical Universe] cites a book The Pythagorean Proposition by an early 20th century professor Elisha Scott Loomis. The book is a collection of 367 proofs of the Pythagorean Theorem and has been republished by NCTM in 1968.

367....

Rozabeez

Do I need any of this for ordinary level?

PurpleFistMixer

According to skool.ie, ordinary maths involves theorems. I'm guessing your teacher would have told you, though? o.O

JBoyle4eva

I can tell you now the reason I had to drop down to ordinary level maths was all because of the bloodty theorms. I was really put off honors by the theorems.

Flashling

declan_lgs wrote:

Says that also on the second remark of http://www.cut-the-knot.com/pythagoras/index.shtml

367....

What are you trying to say.....

And really, you dropped because of theorums? I LOVE THEORUMS! They're so sexy and ...logical. *Sigh*

PurpleFistMixer

No way.

Theorems to actual geometry is like porn is to sex. Writing out a theorem is just someone else's work, but when you apply them to the geometry questions it's all oh so slick and perfect.
Damn, I feel like calculating angles right now...