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Re: So you think your good at math... [Re: exagram]
    #6784158 -

Quote:
Consider the pentagon, where n = 5 and the number of diagonals is 2 (according to your definition, as far as I can see).


a pentagon does have 5 diagonals.

geometry is probably my least favorite of all mathematics. linear algebra and differential equations are very interesting though.

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Re: So you think your good at math... [Re: daba]
    #6784161 -

You can look at it this way,

There are N ways to go from a vertex including it'self, that is N*N possible ways.

Now take away the "outer edges", For each vertex there are 3 outer edge including the edge to it'self. This gives us N^2 - 3*N, but you are still over counting the "interior edges". At each vertex you are counting an interior edge twice. Thus, divide by 2.

(N^2 - 3N)/2


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Be like water my friend!

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Re: So you think your good at math... [Re: SymmetryGroup8]
    #6784170 -

Hmm yeah Daba explained it better.

You need to find a more rigorous proof good luck...

I think about this some more... I'm gonna burn some weed and get back to you :tongue: Probably not tho...

I didn't take the geometry class so I don't really know how the "machineries" they use in geometry, anyway good luck.


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Be like water my friend!

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Re: So you think your good at math... [Re: iateshaggy]
    #6784176 -

iateshaggy said:
if u want to have some fun w/ geometry, figure this one out.



wtf? they both have an area of 32 as well as 32.5

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Re: So you think your good at math... [Re: bigtee212]
    #6784229 -

The green and red triangles have different slopes which makes the large "triangle" not a triangle because the hypotenuse has to be a straight line.


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Those who would give up a little freedom to get a little security shall soon have neither.
-Benjamin Franklin

Edited by Legend9123 (04/13/07 08:14 PM)

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Re: So you think your good at math... [Re: daba]
    #6784231 -

daba, you just owned my homework. Muchos kudos for you. Now I can actually enjoy my weekend and not have to fret with this.

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Re: So you think your good at math... [Re: Legend9123]
    #6784498 -

Legend9123 said:
The green and red triangles have different slopes which makes the large "triangle" not a triangle because the hypotenuse has to be a straight line.


congrats, that is the fastest i've seen someone notice that the "triangles" are really trapezoids.


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I can flash/jtag/repair 360's, pm for details.

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Re: So you think your good at math... [Re: iateshaggy]
    #6784880 -

I have a life?


Anyway, I couldn't get this stupid problem out of my head. Here is how you the more rigorous proof:

Lemma:

(n^2-3n)/2 = (n-1)^2-3(n-1) + n-2

Geometrically speaking this is saying, when you have an N convex polygon, by adding one more vertex, you are in effect adding a triangle. Thus, if you have an (n-1) convex polygon you add vertex, which have n-2 connectivity.

X = (N^2 - 3n) /2 With N>=3

N=3 is true.

Assume N(k). We want to show N(k+1)

That is, by Lemma, we want to show

k^2-3k+(k+1)-2 = [(k+1)^2 -3(k+1)]/2
= k^2 - k - 2

On the left hand side we get:

k^2-3k+k-1 = k^2-3k+2k-2 = k^2 - k -2

Equals the right hand side.

Thus, we have shown N(k+1)

QED.


--------------------
Be like water my friend!

Edited by SymmetryGroup8 (04/13/07 11:11 PM)

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Re: So you think your good at math... [Re: ChiefGreenLeaf]
    #6784907 -

Well I know you're not good at spelling. However, good luck with the math.

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Re: So you think your good at math... [Re: Legend9123]
    #6785884 -

Legend9123 said:
Counterexamples are used to prove something is wrong. By your logic I can say that since a triangle has three sides a square does too.


The theorem can be either true or false. If you start by assuming that it is true, then provide a counterexample to it, the only other thing it could be is false.

Anyway, doesn't matter, since I'm wrong. My geometrical education so far has been mostly Euclidian (if only that retard had a ruler).


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Raoul Duke: What Leary took down with him was the central illusion of a whole lifestyle that he helped create - a generation of permanent cripples, failed seekers, who never understood the essential old-mystic fallacy of the acid culture: the desperate assumption that somebody, or at least some force, is tending the light at the end of the tunnel.

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