Differentiability of a space consisting of arbitrary circles











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Consider a right circular cone of height h (measured along the z-axis) whose base is a circle on the x-y plane.



Five planes parallel to the x-y plane cut the right circular cone at arbitrary levels (we do not know the z-coordinate of their intersection with the z-axis). Projections of the intersection circles are drawn on a plane (call it D) parallel to but different from the x-y plane.



Is the space consisting of these five projected circles differentiable?



If the number of arbitrary planes is increased to infinity, is the space consisting of projected circles differentiable?










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  • Functions are what's typically described as differentiable (or not). What does it mean (to you) for a space to be differentiable?
    – John Hughes
    Nov 21 at 12:14










  • Perhaps I should ask whether the space consisting of the circles is a vector space. But I do not know enough mathematics to know whether that is the right question?
    – phil342
    Nov 21 at 14:01















up vote
0
down vote

favorite












Consider a right circular cone of height h (measured along the z-axis) whose base is a circle on the x-y plane.



Five planes parallel to the x-y plane cut the right circular cone at arbitrary levels (we do not know the z-coordinate of their intersection with the z-axis). Projections of the intersection circles are drawn on a plane (call it D) parallel to but different from the x-y plane.



Is the space consisting of these five projected circles differentiable?



If the number of arbitrary planes is increased to infinity, is the space consisting of projected circles differentiable?










share|cite|improve this question






















  • Functions are what's typically described as differentiable (or not). What does it mean (to you) for a space to be differentiable?
    – John Hughes
    Nov 21 at 12:14










  • Perhaps I should ask whether the space consisting of the circles is a vector space. But I do not know enough mathematics to know whether that is the right question?
    – phil342
    Nov 21 at 14:01













up vote
0
down vote

favorite









up vote
0
down vote

favorite











Consider a right circular cone of height h (measured along the z-axis) whose base is a circle on the x-y plane.



Five planes parallel to the x-y plane cut the right circular cone at arbitrary levels (we do not know the z-coordinate of their intersection with the z-axis). Projections of the intersection circles are drawn on a plane (call it D) parallel to but different from the x-y plane.



Is the space consisting of these five projected circles differentiable?



If the number of arbitrary planes is increased to infinity, is the space consisting of projected circles differentiable?










share|cite|improve this question













Consider a right circular cone of height h (measured along the z-axis) whose base is a circle on the x-y plane.



Five planes parallel to the x-y plane cut the right circular cone at arbitrary levels (we do not know the z-coordinate of their intersection with the z-axis). Projections of the intersection circles are drawn on a plane (call it D) parallel to but different from the x-y plane.



Is the space consisting of these five projected circles differentiable?



If the number of arbitrary planes is increased to infinity, is the space consisting of projected circles differentiable?







calculus derivatives






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share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Nov 21 at 4:23









phil342

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145












  • Functions are what's typically described as differentiable (or not). What does it mean (to you) for a space to be differentiable?
    – John Hughes
    Nov 21 at 12:14










  • Perhaps I should ask whether the space consisting of the circles is a vector space. But I do not know enough mathematics to know whether that is the right question?
    – phil342
    Nov 21 at 14:01


















  • Functions are what's typically described as differentiable (or not). What does it mean (to you) for a space to be differentiable?
    – John Hughes
    Nov 21 at 12:14










  • Perhaps I should ask whether the space consisting of the circles is a vector space. But I do not know enough mathematics to know whether that is the right question?
    – phil342
    Nov 21 at 14:01
















Functions are what's typically described as differentiable (or not). What does it mean (to you) for a space to be differentiable?
– John Hughes
Nov 21 at 12:14




Functions are what's typically described as differentiable (or not). What does it mean (to you) for a space to be differentiable?
– John Hughes
Nov 21 at 12:14












Perhaps I should ask whether the space consisting of the circles is a vector space. But I do not know enough mathematics to know whether that is the right question?
– phil342
Nov 21 at 14:01




Perhaps I should ask whether the space consisting of the circles is a vector space. But I do not know enough mathematics to know whether that is the right question?
– phil342
Nov 21 at 14:01















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