Math Is Fun Forum

bossk171

Member

Registered: 2007-07-16

Posts: 305

2D cone

I'm a little stuck here, and could certainly use some help...

Start with a hollow cone [A] , cut off the top and cut a slit down the side (the blue line) [b]. Discard the circle base and unfold [C -- obviously not to scale].

Both the top and the bottom of [C] are curved lines, what is the curve? Instinct dictates they're part of a circle (I can't explain why, it just does), if that's the case, what's the radius of those circles? I need this for a project I'm doing, and I'm really stumped.

An answer would be great, but an explanation/derivation of the answer would make me one of the happiest people in the world.

Also, is there a "math word" for a cone with the top chopped off?

Thank you!

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luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: 2D cone

truncated cone i believe is the correct mathematical term.

Ill have to think longer about finding the curves.

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simron

Real Member

Registered: 2006-10-07

Posts: 237

Re: 2D cone

Does that answer your question? Do I need to elaborate?
I agree with luca's "truncated cone" idea although if we're talking about those circles, it's a conic section.

Last edited by simron (2008-05-19 14:15:22)

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bossk171

Member

Registered: 2007-07-16

Posts: 305

Re: 2D cone

Thanks simron, but I pretty much knew all that, my issue was more of what is the function that describes the curve? I'm reasonably sure it's a circle at this point (but I can't prove it).

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There are 10 types of people in the world, those who understand binary, those who don't, and those who can use induction.

Identity

Member

Registered: 2007-04-18

Posts: 934

Re: 2D cone

I'm a little stuck here, and could certainly use some help...

http://img502.imageshack.us/img502/2228/conevf2.th.gif

Start with a hollow cone [A] , cut off the top and cut a slit down the side (the blue line) [b]. Discard the circle base and unfold [C -- obviously not to scale].

Both the top and the bottom of [C] are curved lines, what is the curve? Instinct dictates they're part of a circle (I can't explain why, it just does), if that's the case, what's the radius of those circles? I need this for a project I'm doing, and I'm really stumped.

An answer would be great, but an explanation/derivation of the answer would make me one of the happiest people in the world.

Also, is there a "math word" for a cone with the top chopped off?

Thank you!

Here's my approach, but I'm not sure how valid it is
Think of the net of the cone before it has been truncated. It is a sector of a circle. How do you know this? Let the height of the cone tend to zero, then the arc length of the sector will tend to a circumference - the circumference of a circle.