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ParthKohli
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I discovered an obvious thing some days back, but is there a solid proof for it? Prove that there are \(\rm x + 1\) faces if the base of a pyramid has \(\rm x\) sides. I know the concept of it, but just need to know if there's a proof.
 one year ago
 one year ago
ParthKohli Group Title
I discovered an obvious thing some days back, but is there a solid proof for it? Prove that there are \(\rm x + 1\) faces if the base of a pyramid has \(\rm x\) sides. I know the concept of it, but just need to know if there's a proof.
 one year ago
 one year ago

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lgbasallote Group TitleBest ResponseYou've already chosen the best response.0
there is.
 one year ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.0
Please.
 one year ago

CliffSedge Group TitleBest ResponseYou've already chosen the best response.4
You mean for pyramids?
 one year ago

ujjwal Group TitleBest ResponseYou've already chosen the best response.0
The base of a cube has 4 sides but it has 4+2 faces.. I didn't get it!
 one year ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.0
Oops, yes, pyramids.
 one year ago

CliffSedge Group TitleBest ResponseYou've already chosen the best response.4
It seems pretty obvious. There is one face attached to each of the base polygon's sides, plus the base itself.
 one year ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.0
Yeah... but I am asking for a solid proof.
 one year ago

ujjwal Group TitleBest ResponseYou've already chosen the best response.0
@ParthKohli needs a proof involving serious 'mathematics'
 one year ago

CliffSedge Group TitleBest ResponseYou've already chosen the best response.4
For a pentagonal prism: dw:1350485379807:dw
 one year ago

CliffSedge Group TitleBest ResponseYou've already chosen the best response.4
Pfft, drawing pictures is serious enough for me.
 one year ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.0
Oh Lord, a solid proof.
 one year ago

CliffSedge Group TitleBest ResponseYou've already chosen the best response.4
LOL, I get it.
 one year ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.0
Induction?
 one year ago

ujjwal Group TitleBest ResponseYou've already chosen the best response.0
Well, @CliffSedge , your diagram says it all...
 one year ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.0
I need serious mathematics, sire, serious mathematics.
 one year ago

CliffSedge Group TitleBest ResponseYou've already chosen the best response.4
Euler's formula might come into play if you want to get all fancy about it. VE+F=2
 one year ago

lgbasallote Group TitleBest ResponseYou've already chosen the best response.0
to prove something, you need an equation
 one year ago

ujjwal Group TitleBest ResponseYou've already chosen the best response.0
And that formula is valid also for a cube!!
 one year ago

CliffSedge Group TitleBest ResponseYou've already chosen the best response.4
Euler's formula is valid for all polyhedra, so it will be applicable to the special case of pyramids. Here F=x+1
 one year ago

CliffSedge Group TitleBest ResponseYou've already chosen the best response.4
The number of vertices, V, also equals x+1 (x for the vertices of the base polygon, plus the top vertex of the pyramid).
 one year ago

CliffSedge Group TitleBest ResponseYou've already chosen the best response.4
And the number of edges, E = 2x (x for each side of the base polygon, plus the x edges coming up from its x vertices). These are all based on definitions of pyramids, so VE+F=2 F=x+1 V=x+1 E=2x (x+1)2x+(x+1)=2 Simplify and identity is verified.
 one year ago

CliffSedge Group TitleBest ResponseYou've already chosen the best response.4
Or since your task is to show that F=x+1, start with (x+1)2x+F=2, and solve for F. This all seems quite circular, since it is merely restating definitions of pyramids.
 one year ago
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