Welcome to The Wide Screen! This is my first blog post and I'm not quite sure what exactly I'll be talking about, but once in awhile I'll just throw out some questions or ideas like this one:
This is a philosophical question I came up with on my own when I was about 9. If there is a perfectly round sphere and a perfectly flat surface, could either one of them touch the other?
We've all played with the spherical blocks in pre-k and hit them together against the flat blocks, trying to stack them into a tower, and of course they touched. This is my own answer to the question...
If they could touch, then the part of the sphere touching the flat surface would not be perfectly round. So they cannot touch if they are both perfect, even past the molecular level, as if there were no atoms or molecules.
Another question is if they cannot touch, then what would the distance be between them at which they could not move any closer?
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Connor McGowan
Connor McGowan
About Me
- Connor McGowan
- Atlanta, GA, United States
- I enjoy questions about life and the world and I like to play paintball. I live in Alpharetta Georgia and I like to think about things.
Feed the Hungry!
13 comments:
Hmmmm... If a circle has an infinite number of sides, I think that at some level, one of those sides (which by definition is not curved) could touch a flat surface.
Would the plane touching the sphere be similar to the tangent line to curve? A line based on one point of the curve?
Anyway, found you here through your dad. Welcome, and keep blogging!
Could they touch at a single point, infinitely small? And if so, does that mathematically count as touching?
What a way to start your blog, man!
I like the idea of questioning intuitions when dealing with purely mathematical constructs. I don't know what the mathematician's answer would be.
As a linguist, I'd say it depends on your definition of "touch", as your second question suggests.
Does anything ever actually touch anything else, or is there always a tiny bit of emptiness between them? After all, aren't seemingly solid surfaces mostly empty space anyway (at the atomic level)?
I'm sending my engineer husband over here as soon as he gets home; he can't get here from work.
I really enjoy your thought processes. ;)
Sorry, I can never get google to log me into my own account!
This is Betsy, a.k.a. ondfly123.
Welcome to the blogosphere! I look forward to reading your posts.
Hi! Thanks for all the comments. It's cool hearing from so many different people. =)
Mathematically speaking, this seems an awful lot like the tangent line to a curve that sarah mentioned (have you learned about tangents yet? it's pre-cal or calculus), except 3D instead of 2D. In 3D, it's a plane tangent to a sphere, which is exactly what you are mentioning. In a rendering program like matlab or mathematica, the sphere and plane would touch, and the amount they touched would decrease as you zoom in, always looking pretty much like a single point. In the abstract truth, where you truly do have an "perfect" sphere and plane, I believe it would be the infinitely small point that Michelle described.
From a chemistry standpoint, nothing ever truly touches, because as John says, the void space in an atom or molecule is much more than the real space occupied by its component parts (the electrons and nucleus). And when one atom gets close enough to another, their nuclei repel each other, keeping the atoms from actually "touching," although the electron clouds surrounding the nuclei might be able to overlap.
-an engineer scientist who read your father's book on parenting
I think I've said this several times on your Dad's blog, but you deserve to hear it firsthand. I have two sons, currently aged 3.5 and 7 months. If they turn out half as smart and awesome as you come across (and as I'm sure you ARE), I'll count myself one very lucky mother.
As to your question... I suck at math. :)
Good start, interesting question, not even gonna try to answer it ;)
Welcome to the world of blogging found you via your dad's blog.
Sir, in my brief browsing of your blog and your dad's, it occurs to me that you not only have a dad worth being proud of, but he has a son to be proud of as well. Congrats to both of you. I'm looking forward to reading more on both blogs.
Oops. I signed that comment with the right "name" but the wrong profile link. This one ought to lead you back to my blog if you have any interest.
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