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Atlas3
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Can it be defined a disfigured sphere to approximate a cube mathematically? 8 corners equilateral to some extent. Not exact.
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.robphy said:Do you mean something analogous to say
##x^8+y^8=(1/8)## ?
https://www.desmos.com/calculator/k30qaemomp
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.HallsofIvy said: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?
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.Atlas3 said: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 said:Yes it is. The effort by Rohphy graphically showed that.
What type of geometry would allow that rounding..
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.micromass said: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.
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 said: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.
A sphere in a cube is a geometric shape that consists of a sphere inscribed within a cube, meaning that the sphere touches all six faces of the cube.
A sphere in a cube is defined as a subset of points within a cube that are equidistant from a central point, which is the center of the inscribed sphere.
Yes, a sphere in a cube can be created in real life with the use of certain materials and techniques such as 3D printing or carving. However, it may not be a perfect sphere due to limitations of materials and precision.
A sphere in a cube has the same properties as a regular sphere, such as being a three-dimensional shape with a curved surface and having a constant radius. However, it also has the added property of being inscribed within a cube, which gives it a unique geometric relationship with the cube's faces and edges.
Yes, a sphere in a cube has practical applications in fields such as architecture, mathematics, and engineering. It can be used in the design of structures, as a model for studying geometric relationships, and in the creation of new technologies.