ParthKohli
  • ParthKohli
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.
Meta-math
schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this
and thousands of other questions

lgbasallote
  • lgbasallote
there is.
ParthKohli
  • ParthKohli
Please.
anonymous
  • anonymous
You mean for pyramids?

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

ujjwal
  • ujjwal
The base of a cube has 4 sides but it has 4+2 faces.. I didn't get it!
ParthKohli
  • ParthKohli
Oops, yes, pyramids.
anonymous
  • anonymous
It seems pretty obvious. There is one face attached to each of the base polygon's sides, plus the base itself.
ParthKohli
  • ParthKohli
Yeah... but I am asking for a solid proof.
ujjwal
  • ujjwal
@ParthKohli needs a proof involving serious 'mathematics'
anonymous
  • anonymous
For a pentagonal prism: |dw:1350485379807:dw|
anonymous
  • anonymous
Pfft, drawing pictures is serious enough for me.
ParthKohli
  • ParthKohli
Oh Lord, a solid proof.
anonymous
  • anonymous
LOL, I get it.
ParthKohli
  • ParthKohli
Induction?
ujjwal
  • ujjwal
Well, @CliffSedge , your diagram says it all...
ParthKohli
  • ParthKohli
I need serious mathematics, sire, serious mathematics.
anonymous
  • anonymous
Euler's formula might come into play if you want to get all fancy about it. V-E+F=2
lgbasallote
  • lgbasallote
to prove something, you need an equation
ujjwal
  • ujjwal
And that formula is valid also for a cube!!
anonymous
  • anonymous
Euler's formula is valid for all polyhedra, so it will be applicable to the special case of pyramids. Here F=x+1
anonymous
  • anonymous
The number of vertices, V, also equals x+1 (x for the vertices of the base polygon, plus the top vertex of the pyramid).
anonymous
  • anonymous
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 V-E+F=2 F=x+1 V=x+1 E=2x (x+1)-2x+(x+1)=2 Simplify and identity is verified.
anonymous
  • anonymous
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.

Looking for something else?

Not the answer you are looking for? Search for more explanations.