surface area of a cone

[WDIK]

Well carry on man!

Indeed, some of these surfaces are path-connected, which means that you could trace a continuous route from any point on it to any other point. The only type that isn't path-connected is the hyperbola of 2 sheets, since there is a gap between these two sheets.

interesting, where does leave the mobius strip?

 

[tim west]

Shouldnt this thread have been started by conn(e)y?

 

[dextrous]

the cooling tower thing made with straight steel..
that's the same thing you get if you take a buch of spaghetti in two hands and twist each hand in the oposite direction?

Pretty much

interesting, where does leave the mobius strip?

The interesting thing about a Mobius strip created by a single half twist (other than it also being path connected as it's only got 1 side), is that if you join two of them edge to edge, then you get a 4-dimensional Klein bottle, which has a curious property of having its inside on the outside, and vice-versa

 

[Stivino]

Does a Mobius strip look like a conveyor?

 

[dextrous]

Does a Mobius strip look like a conveyor?

Sort of, but a conveyor has two sides to it - one that sits on the rollers and one that carries the goods. If you cut the conveyor belt, twisted one edge so that it is "upside down" and rejoined it the the other cut edge, you get a "mobius band with 1 twist". If you get a pen and started to draw along it, you would eventually end up back where you started, which demonstrates that it only has 1 side! Mobius bands with differing nuber of twists have different such properties.

 

[LaminatePro]

It only demonstrates that the sides rotate it still has 2 sides.

Well I will know where to come for a little light bedtime reading now.

 

[Johnmelad502]

Mobius strip pictures

http://www.wikihow.com/Explore-a-Mobius-Strip

 

[Space cat]

that's the same thing you get if you take a buch of spaghetti in two hands and twist each hand in the oposite direction?

Yes it is. For a better model, take two discs (old freebie CDs will do) and fix the strands of spaghetti all the way around their edges to form a cylinder. Now, if you twist one disc relative to the other, you will generate the hyperboloid of one sheet. Twist it the the other way and you get the same shape but with the strands angled the other way.

In a cooling tower, two sets of (steel) spaghetti strands are fitted, one for each twist. The resulting structure is then very rigid since each set prevents the other one from twisting.

 

[Space cat]

It only demonstrates that the sides rotate it still has 2 sides.

No, it has only one side - and, less obviously, only one edge!

Edit: Since we started on the subject of areas ---

The circumference of a circle is 2 x pi x r (that is pi x d) and its area is pi x r^2.

The area of a sphere is 4 x pi x r^2 (that is pi x d^2) and its volume is 4 x pi x r^3 / 3.

Do you see a pattern here? Is the 'surface' of a 4D 'sphere' 8 x pi x r^3 (pi x d^3) and is its 'volume' 2 x pi x r^4? Does anybody know, because I haven't got the time right now to go looking.

 

[WDIK]

 

[conny]

can some one tell me whats the face area of a cone shape to the total surface area is please

Do you realise what you have started with your innocent question?


But very educational all the same!

 

[tim west]

Im busy halfway through knitting the headband

 

[conny]

Wife's wearing mine!

 

[dextrous]

It only demonstrates that the sides rotate it still has 2 sides.

No, it has only one side - and, less obviously, only one edge!

Edit: Since we started on the subject of areas ---

The circumference of a circle is 2 x pi x r (that is pi x d) and its area is pi x r^2.

The area of a sphere is 4 x pi x r^2 (that is pi x d^2) and its volume is 4 x pi x r^3 / 3.

Do you see a pattern here? Is the 'surface' of a 4D 'sphere' 8 x pi x r^3 (pi x d^3) and is its 'volume' 2 x pi x r^4? Does anybody know, because I haven't got the time right now to go looking.

Am afraind the pattern is unlikely to be that simple since the "volume" would be worked out by using a "volume of rotation" method, which requires integration on a level which I have long forgot how to go about, and can't really be bothered to reacquaint myself with

 

[bengasman]

two blobs of ice cream on the cone it doesn't matter what the area is.

Oh yes it does!

They have to big big ones!
Ask my grandkids!

(more grandad, more!)

Nope, it does not matter the slightest, unless you are a politician. The surface determines how much is visible, not how much is in it. The principle is known as: spreading yourself thin. Compare: gordon brown's empty promises
The invisible volume determines how much is in it: compare gordon brown's legacy of highest number of people feeding from the government's coffers after he is booted out.