Mixing
Differentiability of a space consisting of arbitrary circles
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
asked Nov 21 '18 at 4:23
phil342
145
add a comment |
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
asked Nov 21 '18 at 4:23
phil342
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 '18 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 '18 at 14:01
add a comment |
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
asked Nov 21 '18 at 4:23
phil342
145
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
calculus derivatives
asked Nov 21 '18 at 4:23
phil342
145
asked Nov 21 '18 at 4:23
phil342
145
asked Nov 21 '18 at 4:23
phil342
145
asked Nov 21 '18 at 4:23
phil342
145
asked Nov 21 '18 at 4:23
phil342
145
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 '18 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 '18 at 14:01
add a comment |
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 '18 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 '18 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 '18 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 '18 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 '18 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 '18 at 14:01
add a comment |
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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 '18 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 '18 at 14:01