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So you think your good at math...
    #6783694 -

In my math class we were covering some analytical geometry.
I am supposed to prove (or disprove) that the number of diagnols a convex n-gon has is equal to (n^2-3n)/2

I think I will need to use a summation formula, but from other then that I have no idea.
Any thoughts?...

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Re: So you think your good at math... [Re: ChiefGreenLeaf]
    #6783708 -

My thoughts? Thank Christ I don't have to take another geometry class for as long as I live.


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"The Highways of Life are Paved with Flat Squirrels who Couldn't Make Up Their Minds"

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Re: So you think your good at math... [Re: DrCamacho89]
    #6783728 -

^ Yeah, it sucks.

I know there is someone on here though that wants to flex ther brain.

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Re: So you think your good at math... [Re: DrCamacho89]
    #6783740 -

Geometry and Trig were my least favorite classes ever. :thumbdown:

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Re: So you think your good at math... [Re: VoidOfsPg]
    #6783745 -

Fuck math.

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Re: So you think your good at math... [Re: ChiefGreenLeaf]
    #6783765 -

Quote:
I think I will need to use a summation formula, but from other then that I have no idea.
Any thoughts?...


Seems simple enough that it should be possible to resolve using geometric definitions.

What exactly do you mean by 'diagonals'?


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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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Re: So you think your good at math... [Re: exagram]
    #6783812 -

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


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You are a filipina sex goddess who wants to fuck me until I fall asleep, so then you can tickle my balls and see if the legend of my diamond filled nutsuck is true.  I am a white man from costa rica, who smells like lime jello.


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

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Re: So you think your good at math... [Re: exagram]
    #6783820 -

ya define diagonals cause i was looking at it under what i thought was meant by diagonal and calculated n factorial diags


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If you're frightened of dying and you're holding on.you'll see devils tearing your life away.
But...if you've made your peace, then the devils are really angels
Freeing you from the earth.

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Re: So you think your good at math... [Re: iateshaggy]
    #6783828 -

the hole in it occurs as a result of switching the green and red triangles. the slope is 2 and the red triangle has a length exactly 2 larger than the green one so it results in a gap of 1 (due to 2/2)


--------------------
If you're frightened of dying and you're holding on.you'll see devils tearing your life away.
But...if you've made your peace, then the devils are really angels
Freeing you from the earth.

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Re: So you think your good at math... [Re: Eightball]
    #6783876 -

A diagonal is a segment that joins two nonconsecutive vertices. If anyone knows what that means...
Example: a square has 2 diagonls, while a triangle has none

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Re: So you think your good at math... [Re: Eightball]
    #6783915 -

Eightball said:
the hole in it occurs as a result of switching the green and red triangles. the slope is 2 and the red triangle has a length exactly 2 larger than the green one so it results in a gap of 1 (due to 2/2)


so where is the hole in the top triangle?


--------------------
You are a filipina sex goddess who wants to fuck me until I fall asleep, so then you can tickle my balls and see if the legend of my diamond filled nutsuck is true.  I am a white man from costa rica, who smells like lime jello.


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

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Re: So you think your good at math... [Re: DrCamacho89]
    #6783920 -

DrCamacho89 said:
My thoughts? Thank Christ I don't have to take another geometry class for as long as I live.


thumbs up to that.


--------------------
OP is now RP!  Read about it here!


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Re: So you think your good at math... [Re: ChiefGreenLeaf]
    #6783936 -

Well, seems simple enough to me. Consider the pentagon, where n = 5 and the number of diagonals is 2 (according to your definition, as far as I can see).

Plug in numbers, and you get the number of diagonals to be 5, which isn't right. There's your counterexample.


--------------------
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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Re: So you think your good at math... [Re: exagram]
    #6784006 -

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.


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

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Re: So you think your good at math... [Re: Legend9123]
    #6784014 -

Did you try induction? Here are some thing I have noticed.

First, given any convex shape in 2-dimensions with n sides, you can draw precisely n-3 diagonals from that point. Also note that a convex polygon with n sides also has n points, but drawing diagonals from one vertex constitutes that you have already drawn diagonals from other vertices as well, precisely n/2 of them. Therefore, the total number of diagonals capable of being drawn is (n-3)n/2 = (n^2-3n)/2.

Thinking in 3-dimensions, you can try the same thing. I think this is the proof.


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Fold for The Shroomery!

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Re: So you think your good at math... [Re: ChiefGreenLeaf]
    #6784029 -

One second.


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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 07:20 PM)

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Re: So you think your good at math... [Re: Legend9123]
    #6784041 -

Those proofs are not applicable for his problem, Legend 9123. That is assuming no diagonals intersect. His is assuming diagonals may intersect.


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Fold for The Shroomery!

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Re: So you think your good at math... [Re: daba]
    #6784044 -

Also, in n-dimensions I'm assuming that, for this formula to work, that a diagonal is NOT a line defined by two points in any n-space, but instead a hyperplane defined by precisely n-points in the n-dimensional space. EDIT: Actually this is also wrong.

EDIT: OOPS... you're working only in two dimensional space. My bad. Then yea the proof is my first post above!

EDIT: one more quick correction to my proof. If you draw all the diagonals in an n-gon you have drawn precisely n(n-3) diagonals. However, since you have drawn exactly TWICE the number of diagonals you actually have (note by drawing in all the diagonals then you have effectively drawn over the same diagonal TWICE -- you can verify this -- MOREOVER, by drawing in each diagonal you have assured that you have AT LEAST 2 edges emitting from each vertex (this is only the case in the triangle) and in general GREATER THAN OR EQUAL to 3 you know this is true since your n-gon is convex -- consider it thusly every CONVEX n-gon in 2-d only has 2 edges emitting from each vertex (otherwise it wouldn't be a polygon) -- by drawing in diagonals you have agreed that there are at least 3 except for a triangle coming from each vertex -- this should help you make your proof more rigorous.) then divide the answer by two. Therefore, the number of diagonals in a convex polygon is (n(n-3))/2. QED.


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Fold for The Shroomery!

Edited by daba (04/13/07 07:43 PM)

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Re: So you think your good at math... [Re: daba]
    #6784055 -

That works.


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

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Re: So you think your good at math... [Re: daba]
    #6784059 -

OK that's a bit handwavy ... I'm going to the gym now if I think of something more rigorous there I'll be back... otherwise that's your answer I don't know if it's rigorous enough though.


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Fold for The Shroomery!

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