Theoretically, say you have a mathematically perfect sphere. I know its impossible, so shut the fuck up. If you placed it on an impossibly perfect surface that is perfectly level, would the area of the sphere touching the flat base be infinitely small? Would the theoretical sphere be dented and made imperfect just by contact with the flat surface, regardless of weight, resilience or density?
What's the sphere made of?
>>8086050
>if there was a perfect sphere, would it be imperfect?
Sounds like no?
>>8086056
semen
>>8086056
Does it matter? Any material with a weight above floating level would weigh down on the sphere's infinitely small connecting area, and I would assume it would dent it on a very small scale.
>>8086063
How small are we talking?
>>8086057
That was very clearly not the question. I'm asking if it would be made imperfect by having it touch anything when affected by any force of motion.
>>8086066
The sphere or the point connecting the flat base and the sphere?
>>8086072
The dent.
>>8086076
Any dent would make it an imperfect sphere, no? I guess the size of it would depend on the size of the sphere.
>>8086076
are you retarded? OP asked would it cause any dent, as in anything as small as you can possibly imagine.
>>8086080
And more than that, as infinity implies.
>>8086050
> ignoring all material properties, does the material have this property?
Umm...no?
>>8086083
>you can not have theoretical problems in math
Metal spheres don't get dented on a microscopic level when in contact.
Now if we have a perfect sphere made of a material of finite stiffness we can figure out what happens to it when it contacts a flat surface using hertzian contact.
>>8086050
>what are the properties of this inpossible thing I made up
Whatever you want them to be, OP
>>8086087
Thank you. These were the words I was too dumb to think of.
>>8086089
Maybe it wouldn't be effected on a microscopic level, but it would probably be on a smaller degree than that. Also, good point.
>>8086091
That's fair i suppose, but its not like I didn't set guidelines.
Bump for theoretical curiosity.
>>8086050
I would imagine contact would displace some particle however small, and if the space occupied by this particle is measurable then it would factor into the measurements about the sphere and make it "mathematically imperfect."
OP here, any replies for my first question? The space touching the base to the sphere would be infinitely small right? Or am I retarded and missing something?
>>8086050
Every line is composed of an infinite amount of rational and irrational numbers. Pi is a definite amount, that is it has an "end", that is 3<π<4.
Lines are define in Euclid's Elements as breadthless lengths. I would say there exists a point of the plane, tangent to the sphere, which are coincident. On the surface of this sphere there exists and infinity amount of points.
>>8086050
pi is irrational we can't get a 'perfect sphere'.
>>8086123
>"I know it's impossible, so shut the fuck up"
>"hey btw this isnt possible lol"
I feel like you're looking for the word "infinitesimal", not "infinitely small", and yeah what you're describing is just a plane tangent to a surface. With regards to denting or anything like that, you can't really bring any type of physics into this if you want to talk about something mathematically perfect. There are no forces acting on it, so no nothing about it will change just by it contacting a plane.
>>8086128
Way to upload a thumbnail YOU STUPID FAGGOT!! I'M SOOO MAD!
>>8086131
What about gravity? That would be a force acting on it.
>>8086050
>would the area of the sphere touching the flat base be infinitely small?
Yes.
>Would the theoretical sphere be dented and made imperfect just by contact with the flat surface
Yes, unless it is also infinitely rigid.
>>8086059
I mean, could be. ¯\_(ツ)_/¯
>>8086050
But... why...?
>>8086113
This. Friction.
>>8086134
Yeah, but then we'd have to quantify it's mass, and measure it's gravitational constant to a certain margin of error.
See >>8086137
Parallel lines and perfect circles don't really exist in the outside world. Humans apply what is ideal to what is real constructively, from which, we strive to better insight to how to become more formally conscious of the world around us.
>>8086063
It would be made imperfect by it's own weight. Well, considering it was currently under the influence of a gravitational field.
>>8086154
Did not think of that. Thank you.
>>8086056
The sphere in OP >pic related
is silicon.
http://www.wired.com/2010/10/platinum-silicon-kilogram-standard/
>>8086050
would the touching area be the planck distance ^2?
>>8086087
>throw out every material property that would determine the answer to your arbitarily stupid question
>get called out on your stupidity
>"OMG IT'S ALL JUST THEORETICAL, BRO!"
stupid cunt
>>8086087
It's not a math problem. It's a material science problem as soon as you asked if it made a dent.
>>8086101
but you set guidelines that our current theories of physics cannot account, then asked what would happen according to our current theories of physics
you can ask this as a completely mathematical question, but that will require creating axioms about how things behave, which by all accounts will not be analogous to how things do behave in nature. you can argue that the axioms make "intuitive sense," which is fine, but then it's still just a maths problem. nature cares very little about what our intuition of it is.
>>8086050
Your question is:
>What would happen according to the laws if physics, if the laws of physics didn't apply?
Your question is incoherent.
>>8086063
What if we made it out of air??
The sphere will be touching the surface with area of point if both are made of hard material. i think so
In fact sphere will never touch surface because of force between atoms. (but if we aren't so precise it will be as i wrote up here^)
>>8086068
It would have to be on a theoretically perfectly flat surface, also a "no" and the weight of itself would have to not put any pressure on the bottom because that would molecularly disfigure the "perfectness" of the bottom of the sphere, also impossible since we have gravity.
So in effect the answer to your question is no, it wouldn't do that.
To your questions: nope.
When you start talking about density, weight and resilience you start to give it a physical sense, and that's not congruent with "the area of the sphere touching the flat base be infinitely small" (unless you don't mean that in a literal sense). So, due it's physically impossible for something to have an infinitely small base, well... then the other question doesn't work either.
See? This is one of many limits mathematics has for explaining physical phenomena.
You're asking about what would happen in "real life" (ofc, supposing a perfect sphere is somehow achievable) with a perfect sphere on a perfect surface. Well, we can't know what would happen between them because we can't know what's going on in the sphere's molecules that interact with the surface's molecules. So we can't know what happens at a macroscopic level.
This happens due the "area touching the flat base being infintely small". We cannot know how would it be if an object had a portion of it's surface being infintely small, because that'd be smaller than atoms and quarks, and any kind of particle we know... so, yeah, basically we can't imagine that scenario; it's almost illogical.
Of course, this is according to a more chemical and physical phenomena.
>>8086115
You're correct.
Think of the surface as the gradient of the sphere at that point.
Funny to see all these Math major autists facing the reality of their "science" not respecting the scientific method.
Get fucked undergraduates.
yes it would deform OP.
think of the sphere as a wire mesh made of trillions of triangles (3 atoms forming a face), so there would be so many triangles that only one would touch the perfectly smooth surface
1. being initially perfectly spherical (in that all of its surface atoms are initially equidistant to the center) does not mean they can change and deform due to applied stresses and surface interactions.
2. all materials behave differently at the surface than they do in the bulk - the surface can be thought of the 4th phase of matter (solid, liquid, vapor, surface), and there are many different ways in which surfaces interact
3. you'd never have just a single atom touching a surface because it would never be favorable to do so. gravity, QM shit, surface interactions would always prevent just 1 atom from touching at a time. it would be like trying to balance a pyramid on its tip
4. depending on the properties of the solid and the surface (rigidity, attractions, repulsions, etc), you could have 3 atoms, or much much more touching the surface as the solid deforms from its own weight.
and if the sphere was imperfect and had a "tip" )a single atom further away than the others), it would get squished back into the sphere if it did ever touch the surface.
in reality though we'd never achieve a perfect sphere due to the finite size of the atoms themselves, though we can come as close as possible with 3 atoms or more touching a surface.
assuming the sphere was absolutely perfect in every way (rigidity, smoothness, uniformity, etc) AND the surface was the same, you could maybe make the case that the sphere would touch the surface at only a single atom, but i doubt it. you'd see some pretty weird shit going on, probably spinning in place due to EM fields and all that interacting with nothing else to oppose them.
>>8087966
typo: doesnt mean they *can't* change and deform
>>8086050
It simply wouldn't touch. There's no reason to deform anything. Technically, nothing ever touches in the first place.
>>8086050
How is it im possible? Just 3D print a perfect sphere
>>8088343
Or blow bubbles
What would happen if I set a perfect sphere made of fire on a perfectly level surface made of ice? :^)
>>8086050
A perfect sphere would contact a perfect plane at a single point
However none of those things actually exists in real life
>>8086080
>as in anything as small as you can possibly imagine.
so a point.
OP is retarded btw, not that you can notice it, since you are an undergraduate.
>>8088350
>it wouldn't be perfect as soon as it's exposed to anything at all
It wouldn't be a perfect sphere if it were made of atoms.
Geometric shapes are ideals that only exist in the imaginary, Euclidean universe.
OP might as well ask "who would win in a fight, Spiderman or Han Solo?"
>>8088130
>Technically, nothing ever touches in the first place.
Virgin detected.
>>8086050
elasticity
>>8088560
The engineer knows things get close enough to matter though.
>>8087966
This is almost correct and the only decent answer in this thread. Are you an engineer sir?
I take issue with the deformity however, as soon as the sphere and plane get close enough to interact on a 'macro' scale there are a lot of interactions going on. Micro-gravitation, electrical, magnetic, chemical and atomic. All of these alter state at (and prior to) the action of bringing the two objects together. IMHO.
>>8086050
A singularity would touch. As for if it would be dented, that depends on the material that makes up the sphere and sheet, and the weight of the ball.
>>8088783
Any real physical object would deform to some degree, but since no real physical object can ever be a perfect sphere in the first place its irrelevant
>>8086050
Ignoring the limitations of space, like you ask:
For a sphere to be perfect, it can't be made out of particles. To put it simply, the shape of an object is determined by the distance between the particles that make it up. So to have a perfect sphere, you would need infinite vertices and therefore infinite particles. So your sphere is made out of some unknown continuous substance.
A continuous substance most likely cannot be moulded or changed. Changing the shape of an object is also something that relates to the particles making the object up. In this case moving them around. It would be have like a perfect compressible solid. Correct me if I'm wrong anyone.
I think if you put this sphere onto a flat surface, the surface may dent a little if it is made of particles. If the surface is made of the same stuff that the sphere is, I think nothing would distort and the area would be infinitesimally small, something that would be impossible for the same reason that the perfect sphere would be even if it was made out of a continuous substance.
>>8086050
The normal force would be infinitely great wouldnt it?
>>8089363
Normal force isn't dependent on area.
Pressure would be infinite/undefined though, I suppose
