Sphere in a cube

1. May 7, 2015

Atlas3

Can it be defined a disfigured sphere to approximate a cube mathematically? 8 corners equilateral to some extent. Not exact.

2. May 7, 2015

3. May 7, 2015

Atlas3

This is interesting. But fit the sphere in the cube in 3 dimensions. Might be a space with limits bounding a unit cube with a sphere in an equivalent space is what I'm trying to resolve possibly. Thanks this was news to me.

4. May 8, 2015

HallsofIvy

You are repeatedly asking questions that are simply too vague to be answered. What exactly do you mean by a disfigured sphere? Certainly, you can round the corners of a cube as close to the cube itself as you wish. Is that a "disfigured" sphere?

5. May 8, 2015

Atlas3

Yes it is. The effort by Rohphy graphically showed that. What type of geometry would allow that rounding. What mathematics in the academic sense. The only thing I know of isn't solid. It's a nurbs.

6. May 8, 2015

Atlas3

I was asking about a disfigured sphere because a circle can be exact in nurbs spline. I thought possibly so could a sphere but control points allow a distortion of the figure.

Last edited: May 8, 2015
7. May 8, 2015

micromass

What Rohphy showed is not the rounding of the corners of a square. Although rounding of the corners of a square is certainly possible.

You can do it in Euclidean geometry. I have no idea what you want more.

8. May 8, 2015

Atlas3

I feel that is sufficient for me. More than I can do however. It wasn't vague just simple yet very complicated in practice. I feel good about asking such a question in this forum. There is great knowledge here. It may be vague to some but not to others. I realize such a question may have no practical purposes. But it's a valid question if there is an answer. I cannot expect everyone to take time to reply.

9. May 20, 2015

HallsofIvy

Choose a radius, "r" (the smaller r is, the closer the "rounded cube" is to the actual cube). From any corner of the cube, measure along one edge a distance r. From that point measure along either of the two faces that meet in that edge, perpendicular to the edge, a distance r. From that point, measure along a line perpendicular to the face, into the cube, a distance r. Using that point as center, construct a sphere with radius r. Those 8 spheres will "round" the 8 corners of the sphere.

10. May 20, 2015

Atlas3

For future study, I am going to gain understanding of Euclidean Geometry. It seems quite a necessary next step. It wasn't a part of my undergraduate studies. Thank you all for your replies. I like these different ideas. It seems as though the Euclidean Geometry is the technique I need to grasp.

11. May 22, 2015

HallsofIvy

"Euclidean Geometry" is usually taught in secondary school, not college!

12. May 22, 2015

Atlas3

I had Geometry in High School. But The mapping of one space to another was taught in Linear Algebra in college. I think what I need is an extension of that Mathematics of Spaces. I could be wrong.

13. Jun 10, 2015

Atlas3

I made a mistake above I think. It is non-Euclidean geometry I desire to know more about. Any thoughts?

14. Jun 10, 2015

micromass

Your question has nothing to do with non-Euclidean geometry.