A community for students.
Here's the question you clicked on:
 0 viewing
ParthKohli
 4 years ago
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.
ParthKohli
 4 years ago
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.

This Question is Closed

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0You mean for pyramids?

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

ParthKohli
 4 years ago
Best ResponseYou've already chosen the best response.0Oops, yes, pyramids.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0It seems pretty obvious. There is one face attached to each of the base polygon's sides, plus the base itself.

ParthKohli
 4 years ago
Best ResponseYou've already chosen the best response.0Yeah... but I am asking for a solid proof.

ujjwal
 4 years ago
Best ResponseYou've already chosen the best response.0@ParthKohli needs a proof involving serious 'mathematics'

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0For a pentagonal prism: dw:1350485379807:dw

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Pfft, drawing pictures is serious enough for me.

ParthKohli
 4 years ago
Best ResponseYou've already chosen the best response.0Oh Lord, a solid proof.

ujjwal
 4 years ago
Best ResponseYou've already chosen the best response.0Well, @CliffSedge , your diagram says it all...

ParthKohli
 4 years ago
Best ResponseYou've already chosen the best response.0I need serious mathematics, sire, serious mathematics.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Euler's formula might come into play if you want to get all fancy about it. VE+F=2

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0to prove something, you need an equation

ujjwal
 4 years ago
Best ResponseYou've already chosen the best response.0And that formula is valid also for a cube!!

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Euler's formula is valid for all polyhedra, so it will be applicable to the special case of pyramids. Here F=x+1

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0The number of vertices, V, also equals x+1 (x for the vertices of the base polygon, plus the top vertex of the pyramid).

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0And 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.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Or 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.
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.