Geometric description of set
$begingroup$
What would be a geometric description of the following set:
$$D={u in mathbb{R}^n ,rleq |u-x/2| leq R , |(u,x)|leq C }$$ Where $xin mathbb{R}^n $ is a fixed point, $C>0$.
It looks like part of a spherical wedge if i am not mistaken . any thoughts ?
geometry multivariable-calculus
edited Jan 1 at 15:19
Bernard
121k740116
asked Jan 1 at 15:09
PmorphyPmorphy
1097
$endgroup$
add a comment |
$begingroup$
What would be a geometric description of the following set:
$$D={u in mathbb{R}^n ,rleq |u-x/2| leq R , |(u,x)|leq C }$$ Where $xin mathbb{R}^n $ is a fixed point, $C>0$.
It looks like part of a spherical wedge if i am not mistaken . any thoughts ?
geometry multivariable-calculus
edited Jan 1 at 15:19
Bernard
121k740116
asked Jan 1 at 15:09
PmorphyPmorphy
1097
$endgroup$
$begingroup$
yes inner product
$endgroup$
– Pmorphy
Jan 1 at 15:28
add a comment |
$begingroup$
What would be a geometric description of the following set:
$$D={u in mathbb{R}^n ,rleq |u-x/2| leq R , |(u,x)|leq C }$$ Where $xin mathbb{R}^n $ is a fixed point, $C>0$.
It looks like part of a spherical wedge if i am not mistaken . any thoughts ?
geometry multivariable-calculus
edited Jan 1 at 15:19
Bernard
121k740116
asked Jan 1 at 15:09
PmorphyPmorphy
1097
$endgroup$
What would be a geometric description of the following set:
$$D={u in mathbb{R}^n ,rleq |u-x/2| leq R , |(u,x)|leq C }$$ Where $xin mathbb{R}^n $ is a fixed point, $C>0$.
It looks like part of a spherical wedge if i am not mistaken . any thoughts ?
geometry multivariable-calculus
geometry multivariable-calculus
edited Jan 1 at 15:19
Bernard
121k740116
asked Jan 1 at 15:09
PmorphyPmorphy
1097
edited Jan 1 at 15:19
Bernard
121k740116
asked Jan 1 at 15:09
PmorphyPmorphy
1097
edited Jan 1 at 15:19
Bernard
121k740116
edited Jan 1 at 15:19
Bernard
121k740116
edited Jan 1 at 15:19
Bernard
121k740116
121k740116
asked Jan 1 at 15:09
PmorphyPmorphy
1097
asked Jan 1 at 15:09
PmorphyPmorphy
1097
asked Jan 1 at 15:09
PmorphyPmorphy
1097
1097
$begingroup$
yes inner product
$endgroup$
– Pmorphy
Jan 1 at 15:28
add a comment |
$begingroup$
yes inner product
$endgroup$
– Pmorphy
Jan 1 at 15:28
$begingroup$
yes inner product
$endgroup$
– Pmorphy
Jan 1 at 15:28
$begingroup$
yes inner product
$endgroup$
– Pmorphy
Jan 1 at 15:28
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Let $xinmathbb{R}^n$, and let $r,R,Cinmathbb{R}^+$. The set
$$
A={uinmathbb{R}^n : rleq|u-x/2|leq R}
$$
is an annulus centered at $x/2$, and the set
$$
S={uinmathbb{R}^n : |(u,x)|leq C}
$$
is a "strip" of "width" $frac{2C}{|x|^2}$ centered at the origin running in all directions orthogonal to $x$. The set $D$ in the OP is the intersection of these two sets. Depending on the choices of all parameters involved you will get many different kinds of shapes, so I think this is the most that can be said.
answered Jan 1 at 15:36
InequalitiesEverywhereInequalitiesEverywhere
1313
$endgroup$
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
$begingroup$
Let $xinmathbb{R}^n$, and let $r,R,Cinmathbb{R}^+$. The set
$$
A={uinmathbb{R}^n : rleq|u-x/2|leq R}
$$
is an annulus centered at $x/2$, and the set
$$
S={uinmathbb{R}^n : |(u,x)|leq C}
$$
is a "strip" of "width" $frac{2C}{|x|^2}$ centered at the origin running in all directions orthogonal to $x$. The set $D$ in the OP is the intersection of these two sets. Depending on the choices of all parameters involved you will get many different kinds of shapes, so I think this is the most that can be said.
answered Jan 1 at 15:36
InequalitiesEverywhereInequalitiesEverywhere
1313
$endgroup$
add a comment |
$begingroup$
Let $xinmathbb{R}^n$, and let $r,R,Cinmathbb{R}^+$. The set
$$
A={uinmathbb{R}^n : rleq|u-x/2|leq R}
$$
is an annulus centered at $x/2$, and the set
$$
S={uinmathbb{R}^n : |(u,x)|leq C}
$$
is a "strip" of "width" $frac{2C}{|x|^2}$ centered at the origin running in all directions orthogonal to $x$. The set $D$ in the OP is the intersection of these two sets. Depending on the choices of all parameters involved you will get many different kinds of shapes, so I think this is the most that can be said.
answered Jan 1 at 15:36
InequalitiesEverywhereInequalitiesEverywhere
1313
$endgroup$
add a comment |
$begingroup$
Let $xinmathbb{R}^n$, and let $r,R,Cinmathbb{R}^+$. The set
$$
A={uinmathbb{R}^n : rleq|u-x/2|leq R}
$$
is an annulus centered at $x/2$, and the set
$$
S={uinmathbb{R}^n : |(u,x)|leq C}
$$
is a "strip" of "width" $frac{2C}{|x|^2}$ centered at the origin running in all directions orthogonal to $x$. The set $D$ in the OP is the intersection of these two sets. Depending on the choices of all parameters involved you will get many different kinds of shapes, so I think this is the most that can be said.
answered Jan 1 at 15:36
InequalitiesEverywhereInequalitiesEverywhere
1313
$endgroup$
Let $xinmathbb{R}^n$, and let $r,R,Cinmathbb{R}^+$. The set
$$
A={uinmathbb{R}^n : rleq|u-x/2|leq R}
$$
is an annulus centered at $x/2$, and the set
$$
S={uinmathbb{R}^n : |(u,x)|leq C}
$$
is a "strip" of "width" $frac{2C}{|x|^2}$ centered at the origin running in all directions orthogonal to $x$. The set $D$ in the OP is the intersection of these two sets. Depending on the choices of all parameters involved you will get many different kinds of shapes, so I think this is the most that can be said.
answered Jan 1 at 15:36
InequalitiesEverywhereInequalitiesEverywhere
1313
answered Jan 1 at 15:36
InequalitiesEverywhereInequalitiesEverywhere
1313
answered Jan 1 at 15:36
InequalitiesEverywhereInequalitiesEverywhere
1313
answered Jan 1 at 15:36
InequalitiesEverywhereInequalitiesEverywhere
1313
1313
add a comment |
add a comment |
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$begingroup$
yes inner product
$endgroup$
– Pmorphy
Jan 1 at 15:28