Sphere in Cube: Can it be Defined?

[Atlas3]

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

 

[robphy]

Do you mean something analogous to say
##x^8+y^8=(1/8)## ?
https://www.desmos.com/calculator/k30qaemomp

 

[Atlas3]

Do you mean something analogous to say
##x^8+y^8=(1/8)## ?
https://www.desmos.com/calculator/k30qaemomp

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.

 

[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?

 

[Atlas3]

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?

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.

 

[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.

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.

 

[micromass]

Yes it is. The effort by Rohphy graphically showed that.

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

What type of geometry would allow that rounding..

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

 

[Atlas3]

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.

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.

 

[HallsofIvy]

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.

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.

 

[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.

 

[HallsofIvy]

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

 

[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.

 

[Atlas3]

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

 

[micromass]

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