How can I plot a set of points in 3d?
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durnig exams I often have the problem to visualize the sets I should work with, especially in 3D. So I wanted to ask if there is a trick on how to sketch the following set for example
$ G:={(x,y,z)^T in mathbb{R}^3: x^2+y^2<4,~0<z<4-x^2-y^2} $
I would also really like to know how I could plot this by using WolframAlpha?
functional-analysis
asked Dec 20 '18 at 18:58
JaneJane
31
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add a comment |
$begingroup$
durnig exams I often have the problem to visualize the sets I should work with, especially in 3D. So I wanted to ask if there is a trick on how to sketch the following set for example
$ G:={(x,y,z)^T in mathbb{R}^3: x^2+y^2<4,~0<z<4-x^2-y^2} $
I would also really like to know how I could plot this by using WolframAlpha?
functional-analysis
asked Dec 20 '18 at 18:58
JaneJane
31
$endgroup$
$begingroup$
It seems off-topic to ask about 3D plotting using WolframAlpha, though I can imagine having access to it during exams would simplify a large number of tasks. In general there is no trick to visualizing 3D sets using pencil and paper, or rather the approaches (isometric drawing and orthographic projection) are reasonably well-known but not taught specifically in math courses.
$endgroup$
– hardmath
Dec 20 '18 at 19:05
add a comment |
$begingroup$
durnig exams I often have the problem to visualize the sets I should work with, especially in 3D. So I wanted to ask if there is a trick on how to sketch the following set for example
$ G:={(x,y,z)^T in mathbb{R}^3: x^2+y^2<4,~0<z<4-x^2-y^2} $
I would also really like to know how I could plot this by using WolframAlpha?
functional-analysis
asked Dec 20 '18 at 18:58
JaneJane
31
$endgroup$
durnig exams I often have the problem to visualize the sets I should work with, especially in 3D. So I wanted to ask if there is a trick on how to sketch the following set for example
$ G:={(x,y,z)^T in mathbb{R}^3: x^2+y^2<4,~0<z<4-x^2-y^2} $
I would also really like to know how I could plot this by using WolframAlpha?
functional-analysis
functional-analysis
asked Dec 20 '18 at 18:58
JaneJane
31
asked Dec 20 '18 at 18:58
JaneJane
31
asked Dec 20 '18 at 18:58
JaneJane
31
asked Dec 20 '18 at 18:58
JaneJane
31
asked Dec 20 '18 at 18:58
JaneJane
31
31
$begingroup$
It seems off-topic to ask about 3D plotting using WolframAlpha, though I can imagine having access to it during exams would simplify a large number of tasks. In general there is no trick to visualizing 3D sets using pencil and paper, or rather the approaches (isometric drawing and orthographic projection) are reasonably well-known but not taught specifically in math courses.
$endgroup$
– hardmath
Dec 20 '18 at 19:05
add a comment |
$begingroup$
It seems off-topic to ask about 3D plotting using WolframAlpha, though I can imagine having access to it during exams would simplify a large number of tasks. In general there is no trick to visualizing 3D sets using pencil and paper, or rather the approaches (isometric drawing and orthographic projection) are reasonably well-known but not taught specifically in math courses.
$endgroup$
– hardmath
Dec 20 '18 at 19:05
$begingroup$
It seems off-topic to ask about 3D plotting using WolframAlpha, though I can imagine having access to it during exams would simplify a large number of tasks. In general there is no trick to visualizing 3D sets using pencil and paper, or rather the approaches (isometric drawing and orthographic projection) are reasonably well-known but not taught specifically in math courses.
$endgroup$
– hardmath
Dec 20 '18 at 19:05
$begingroup$
It seems off-topic to ask about 3D plotting using WolframAlpha, though I can imagine having access to it during exams would simplify a large number of tasks. In general there is no trick to visualizing 3D sets using pencil and paper, or rather the approaches (isometric drawing and orthographic projection) are reasonably well-known but not taught specifically in math courses.
$endgroup$
– hardmath
Dec 20 '18 at 19:05
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
HINT
Do you recognize the surface $z = x^{2} + y^{2}$? It is a paraboloid! The same applies to $z = -x^{2} - y^{2}$, which is the reflection of $z = x^{2} + y^{2}$ as to the plane $xy$. If you translate its vertice to $(0,0,4)$, you obtain the given surface when you restrict its domain to the circle $x^{2} + y^{2} < 4$.
answered Dec 20 '18 at 19:03
APC89APC89
2,371720
$endgroup$
$begingroup$
This might help with visualization (and the general technique might be called finding cross-sections), but it avoids the issue of plotting. I'll let the OP be the judge whether it helps.
$endgroup$
– hardmath
Dec 20 '18 at 19:07
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
HINT
Do you recognize the surface $z = x^{2} + y^{2}$? It is a paraboloid! The same applies to $z = -x^{2} - y^{2}$, which is the reflection of $z = x^{2} + y^{2}$ as to the plane $xy$. If you translate its vertice to $(0,0,4)$, you obtain the given surface when you restrict its domain to the circle $x^{2} + y^{2} < 4$.
answered Dec 20 '18 at 19:03
APC89APC89
2,371720
$endgroup$
$begingroup$
This might help with visualization (and the general technique might be called finding cross-sections), but it avoids the issue of plotting. I'll let the OP be the judge whether it helps.
$endgroup$
– hardmath
Dec 20 '18 at 19:07
add a comment |
$begingroup$
HINT
Do you recognize the surface $z = x^{2} + y^{2}$? It is a paraboloid! The same applies to $z = -x^{2} - y^{2}$, which is the reflection of $z = x^{2} + y^{2}$ as to the plane $xy$. If you translate its vertice to $(0,0,4)$, you obtain the given surface when you restrict its domain to the circle $x^{2} + y^{2} < 4$.
answered Dec 20 '18 at 19:03
APC89APC89
2,371720
$endgroup$
$begingroup$
This might help with visualization (and the general technique might be called finding cross-sections), but it avoids the issue of plotting. I'll let the OP be the judge whether it helps.
$endgroup$
– hardmath
Dec 20 '18 at 19:07
add a comment |
$begingroup$
HINT
Do you recognize the surface $z = x^{2} + y^{2}$? It is a paraboloid! The same applies to $z = -x^{2} - y^{2}$, which is the reflection of $z = x^{2} + y^{2}$ as to the plane $xy$. If you translate its vertice to $(0,0,4)$, you obtain the given surface when you restrict its domain to the circle $x^{2} + y^{2} < 4$.
answered Dec 20 '18 at 19:03
APC89APC89
2,371720
$endgroup$
HINT
Do you recognize the surface $z = x^{2} + y^{2}$? It is a paraboloid! The same applies to $z = -x^{2} - y^{2}$, which is the reflection of $z = x^{2} + y^{2}$ as to the plane $xy$. If you translate its vertice to $(0,0,4)$, you obtain the given surface when you restrict its domain to the circle $x^{2} + y^{2} < 4$.
answered Dec 20 '18 at 19:03
APC89APC89
2,371720
answered Dec 20 '18 at 19:03
APC89APC89
2,371720
answered Dec 20 '18 at 19:03
APC89APC89
2,371720
answered Dec 20 '18 at 19:03
APC89APC89
2,371720
2,371720
$begingroup$
This might help with visualization (and the general technique might be called finding cross-sections), but it avoids the issue of plotting. I'll let the OP be the judge whether it helps.
$endgroup$
– hardmath
Dec 20 '18 at 19:07
add a comment |
$begingroup$
This might help with visualization (and the general technique might be called finding cross-sections), but it avoids the issue of plotting. I'll let the OP be the judge whether it helps.
$endgroup$
– hardmath
Dec 20 '18 at 19:07
$begingroup$
This might help with visualization (and the general technique might be called finding cross-sections), but it avoids the issue of plotting. I'll let the OP be the judge whether it helps.
$endgroup$
– hardmath
Dec 20 '18 at 19:07
$begingroup$
This might help with visualization (and the general technique might be called finding cross-sections), but it avoids the issue of plotting. I'll let the OP be the judge whether it helps.
$endgroup$
– hardmath
Dec 20 '18 at 19:07
add a comment |
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$begingroup$
It seems off-topic to ask about 3D plotting using WolframAlpha, though I can imagine having access to it during exams would simplify a large number of tasks. In general there is no trick to visualizing 3D sets using pencil and paper, or rather the approaches (isometric drawing and orthographic projection) are reasonably well-known but not taught specifically in math courses.
$endgroup$
– hardmath
Dec 20 '18 at 19:05