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mips
December 22nd, 2006, 04:49 PM
http://news.bbc.co.uk/2/hi/science/nature/6201373.stm

dbbolton
December 22nd, 2006, 05:59 PM
that should have been easy enough. the answer is nullity.

dbbolton
December 22nd, 2006, 07:25 PM
speaking of math, i have a question of my own.

let's say that you have a sphere resting on a plane. how much of that sphere's surface area actually "touches" the plane ? what about a circle and a line ?

raul_
December 22nd, 2006, 07:42 PM
I liked the photo.

Aren't you speaking of tangents? :rolleyes:

sonny
December 22nd, 2006, 08:00 PM
speaking of math, i have a question of my own.

let's say that you have a sphere resting on a plane. how much of that sphere's surface area actually "touches" the plane ? what about a circle and a line ?
I think you can solve that with an integer or a derived, because you have to calculate the area of the smallest circle in the sphere that touches the plane.

sonny
December 22nd, 2006, 08:05 PM
Don't complicate this things... just do the experiment for yourself.. and then try to imagine how to calculate it. :confused: :confused: :confused: :confused:

raul_
December 22nd, 2006, 08:33 PM
I think you can solve that with an integer or a derived, because you have to calculate the area of the smallest circle in the sphere that touches the plane.

Isn't it a single point? :P

dbbolton
December 22nd, 2006, 08:35 PM
Isn't it a single point? :P
that's what i thought.

raul_
December 22nd, 2006, 08:40 PM
that's what i thought.

For real or are you being sarcastic? lol :)

sonny
December 22nd, 2006, 08:48 PM
Isn't it a single point? :P
How big is a point??? If you take a pencil and "draw" a point and then take a pen and "draw" an other point those two will have different sizes, but they're still a point... you need and integer to calculate the area of that point.

raul_
December 22nd, 2006, 09:18 PM
Now you're going phylosophical. I mean a mathematical point :P When you draw a line tangent to a circle in one given point, you can't calculate how much of the line actually touches the circle, because by it's very definition it is a point (an area is a sum of points, as small as you draw it). So, mathematically speaking, the table would be the tangent plane to the ball, so by mathematical definition, if the world was perfect, the plane is tangent to the ball in one point: where the ball is supported.

Pretty interesting question though. I guess i'll have to ask my math mentor about it :-k but i'm pretty sure that's the answer

red_Marvin
December 22nd, 2006, 09:36 PM
A mathematical sphere placed on a mathematical plane touches it only in a mathematical point with the following effect that if the sphere has an arbitrary weight the pressure on the plane in that point will be infinite.

dbbolton
December 22nd, 2006, 09:44 PM
so it depends on whether the sphere in question is geometrical, or physical.

or real.

JAPrufrock
December 23rd, 2006, 03:47 AM
The area of a point approaches zero (i.e. is infinitely small). So the area of a sphere that is actually touching the surface of a plane approaches zero, but never reaches zero.

raul_
December 23rd, 2006, 04:39 AM
That's the very definition of point :)

JAPrufrock
December 26th, 2006, 04:51 AM
Yes, the sphere touches the plane at a point.

.t.
December 26th, 2006, 10:31 AM
A point has position but no area. Surely?

Scott A
January 2nd, 2007, 03:13 PM
isnt a point an infinitely small, dimensionless location in space?
It has no area, no volume, it is simply a location.
Or am I missing the "point" of this discussion. (Sorry for the pun)
Red Marvin seemed to express the geometry of it well.

Nonno Bassotto
January 2nd, 2007, 03:45 PM
This thread is completely nonsense. Anyway I'll try to reply. A sphere resting on a plane touches the plane in a single point. The point has an area, and this area is 0. This is the mathematical reply.

Now, if you actually put a sphere on the floor in the real world, both the sphere and the floor will deform, due to the weight of the sphere. Being deformed, their surface of contact will be something of nonzero area, not necessarily a circle. This area depends on the weight of the sphere, the material which composes the sphere and the pane and so on. So you can't readily calculate it.

Also keep in mind that in the real wolrd the sphere won't be a perfect sphere and the floor won't be perfectly plane. So you won't get an answer from your math teacher, because the answer is: it depends. And it depends really on a lot of variables.

By the way, the correct english word for "integer" is "integral" (integer is an english word, but has a different meaning from what you're trying to convey) and for "derivate" is "derivative".

ReiKn
January 2nd, 2007, 04:30 PM
Now, if you actually put a sphere on the floor in the real world, both the sphere and the floor will deform, due to the weight of the sphere. Being deformed, their surface of contact will be something of nonzero area, not necessarily a circle. This area depends on the weight of the sphere, the material which composes the sphere and the pane and so on. So you can't readily calculate it.


In a real world we'd have to start by defining 'touching'. I can't come up with any other definition than that two objects touching each other interact via a force. Then the area in connection would be the area of the plane which is interaction with the sphere with some force - which again is infinite unless we decide that the interaction should be over some threshold limit until we call it 'touching'. (the forces keeping the two apart might be modeled with some hard sphere model with infinite force fields) So I wouldn't try to give it an exact definition in the real world either :)

Nonno Bassotto
January 2nd, 2007, 09:49 PM
I wasn't trying to give a definition of touching in the real world. In any case your definition is quite strange: according to it two electric charges put one meter apart are touching each other.

ReiKn
January 2nd, 2007, 10:03 PM
I wasn't trying to give a definition of touching in the real world. In any case your definition is quite strange: according to it two electric charges put one meter apart are touching each other.

Well that's why I said one has to have some threshold level to call an interaction 'touching' but still there isn't a state where two objects are in contact but if moved just a tiniest bit further from each other they wouldn't be anymore. But anyways, I wasn't criticizing your message or saying you were defining touching, I just took the quote to have something to begin from.

in_flu_ence
January 3rd, 2007, 01:49 AM
Let's make this question more to the computer-related.

Does it mean that having a perfect sphere touching my touchscreen, i will have a very precise point hitting on the screen?

WiseElben
January 3rd, 2007, 05:09 AM
speaking of math, i have a question of my own.

let's say that you have a sphere resting on a plane. how much of that sphere's surface area actually "touches" the plane ? what about a circle and a line ?

Literary? None. The electrons on the sphere will repel the electrons on the plane. They are actually floating.

Thus begin modern physics.

bobbybobington
January 3rd, 2007, 05:33 AM
You cant measure a point, because it is in the 1st dimention, and you must be in the 2nd or higher to measure anything.

Edit: ok im totally stupid so disregard whatever i just said, yeah a point has no dimentions so good luck trying to measure its area.

dbbolton
January 3rd, 2007, 06:33 AM
Literary? None. The electrons on the sphere will repel the electrons on the plane. They are actually floating.

Thus begin modern physics.
hence
so it depends on whether the sphere in question is geometrical, or physical.

or real.