Geometric description of set












0












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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







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  • $begingroup$
    yes inner product
    $endgroup$
    – Pmorphy
    Jan 1 at 15:28
















0












$begingroup$


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







share|cite|improve this question











$endgroup$












  • $begingroup$
    yes inner product
    $endgroup$
    – Pmorphy
    Jan 1 at 15:28














0












0








0


1



$begingroup$


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







share|cite|improve this question











$endgroup$




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






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edited Jan 1 at 15:19









Bernard

121k740116




121k740116










asked Jan 1 at 15:09









PmorphyPmorphy

1097




1097












  • $begingroup$
    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




$begingroup$
yes inner product
$endgroup$
– Pmorphy
Jan 1 at 15:28










1 Answer
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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.






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    $begingroup$

    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.






    share|cite|improve this answer









    $endgroup$


















      1












      $begingroup$

      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.






      share|cite|improve this answer









      $endgroup$
















        1












        1








        1





        $begingroup$

        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.






        share|cite|improve this answer









        $endgroup$



        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.







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Jan 1 at 15:36









        InequalitiesEverywhereInequalitiesEverywhere

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