Is it mathematically correct to call a sphere the 3-d equivalent of a circle?

[John Cuthber]

I think that a circle is all the points at a given distance ® from the origin. In 1 dimension it's a bit meaningless but x^2 =r^2 works (2 points at + and - r)

In a plane you get a circle x^2 + y^2 =r^2.

A sphere has x^2 + y^2 + z^2 =r^2

 

I's even go on to speculate that in 4D you would need to add w^2 as well.

[MrSandman]

You guys are making a discussion out of nothing. The call a circle a circle and a sphere a sphere. A cube a cube, and a square a square. they would relate their names if they really wanted you to know the relation. Want another problem take a Pryamid and Triangle, what about those?

[the tree]

You guys are making a discussion out of nothing.

That is, largely, the point of maths.

they would relate their names if they really wanted you to know the relation.

"They" would, would "they?". Well if "they" are going to be so helpful when crafting the English language (which I assume is "their" job), then why doesn't the word 'brick' share more with the word 'clay'?

Want another problem take a [pyramid] and Triangle, what about those?

What about them? A pyramid is not the 3D analogue of a triangle, if that's what you're asking.

[YT2095]

as far as I`m concerned a Circle has 360 degrees of "Freedom" a Sphere has 720 degrees.

[MrSandman]

The pryamid was just another thing to keep you guys going.

 

"They" as the people mad this load of crap. Don't think our math is perfect.

[the tree]

The [pyramid] was just another thing to keep you guys going.

It was off topic and not particularly interesting, then.

"They" as the people [made] this load of crap.

Names, like the rest of language, form naturally over thousands of years. No-one ever sat down and gave a name to each individual shape, words come into being as they are needed and as this happens all over the world there far from being one source for the particular concoction of terms that English speakers use to use to talk about geometry.

Don't think our math is perfect.

What would perfect maths be then? What possible state could maths be aiming for?

[Xerxes]

as far as I`m concerned a Circle has 360 degrees of "Freedom" a Sphere has 720 degrees.

Uh - this is a joke, right? (Remember that jokes are hard to smuggle through Customs).

[bobhexa]

Could a sphere be more correctly described as a three dimensional point?

[ajb]

Could a sphere be more correctly described as a three dimensional point?

 

No.

 

A point is zero-dimensional.

 

The zero-sphere consists of two points, if that is what you are trying to "generalise" to 3-d.

[YT2095]

Uh - this is a joke, right? (Remember that jokes are hard to smuggle through Customs).

 

not at all, learn to Fly, you`ll have X,Y and Z axis` to contend with, AKA Pitch , Roll and Yaw.

 

720 degrees of freedom.

[the tree]

Well yes but the phrase degrees of freedom: "is the number of parameters which may be independently varied. " according to mathworld, which I guess explains the shock on Xerxes' part.

[ajb]

You only have two degrees of freedom on a sphere as it is 2-dimensional, [math] \{ \theta, \phi\} [/math] (or something similar depending on your choice of coordinates)

[bobhexa]

Rhombic dodecahedrons..........compressed spheres .....what shape would a big bang make and what would it geometrically generate in 3d space?

Just like soap bubbles.......lots of RD's.(All things being equal).

The most elegant geometries generally encompass the Golden Section ratio.

 

Does anyone know of a G.S. inherent in the RD?

Is there a relationship between a RD and the placement of the twelve pentagons of a C60?(truncated icosahedron)

How many degrees of freedom are there in a RD?

 

You know , if the caveman who was the initial twerp who sat in the river mud and fashioned an orthogonal brick that unfortunately caught on in popularity for dwellings....well if only.............. he had sat there a litlle longer and had discovered the RD.....we would have had a far better and greater understanding of our planet energy with a far more interesting architecture to work from.