Oddbean new post about login | logout Imagine a sphere. Is there any angle of approach from which a plane slicing the sphere in two can result in a flat surface on the two parts not being a circle? #asknostr #math
No.
If it's not a circle, it wasn't a sphere. But why are you asking?
Im curious what peoples response modes are and potential for explanation
You could have made it difficult if you had omitted 'in two', which implies symmetrical and identical halves.
Shoot, just read this and realised that it makes no difference for a sphere. https://primal.net/e/note1fgpdhma589puznxd3m462nd8v0kvph03nkfqzugn90rnd5mxs6hqul5s7l
P.S. You can still get a circle from a non-spherical object, but if it ain't a circle it ain't a sphere.
If you WANT an ellipse, those are conic sections.
Just imagining it while sitting alone and drinking a beer in an irish pub.. you would need to use an oblique plane that intersects the sphere at two different points on its axis and not passing vy the center to obtain an ellipse. But very likely when you say slicing a sphere you meant in two identical part passing the centre..
I like questions like this. I'm no math expert but I enjoy trying to think through stuff. I don't think you can get anything but a circle. Since the sphere is the same no matter how you rotate it, just forget about rotations and angles and imagine lowering the plane through the top of the sphere (or left side, or the right side, it doesn't matter which one you imagine because they are all the same). The plane is either tangent, outside, or inside. Those are the only 3 states the plane can be in. However "in" the plane is, the cut is always a circle.
Yes. I like these as well as a common person can imagine working with physical objects, or lacking that ability, find a suitable object to attempt. This experimentation, whether real, or as a thought process garners a greater understanding of the building blocks of the physical world.