Hyperbolic Geometry (circle)
-3
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Consider in $H^2$ the hyperbolic circle centered at $a + ib$ with radius $r$; i.e., the set $C = left{zin H^2mid dH^2 (z, a + ib) = rright}$
- Show that $C$ is the Euclidean circle with center $a + ibdfrac{e^r + e^{−r}}{2}$ and radius $bdfrac{e^r − e^{−r}}{2}$. (You may want to reduce to the case where $a = 0$.)
- Deduce that any Euclidean circle is also a hyperbolic circle.
geometry hyperbolic-geometry
edited Jan 9 at 14:06
Blue
47.8k870152
asked Jan 9 at 13:19
Shay AdlerShay Adler
1
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add a comment |
-3
$begingroup$
Consider in $H^2$ the hyperbolic circle centered at $a + ib$ with radius $r$; i.e., the set $C = left{zin H^2mid dH^2 (z, a + ib) = rright}$
- Show that $C$ is the Euclidean circle with center $a + ibdfrac{e^r + e^{−r}}{2}$ and radius $bdfrac{e^r − e^{−r}}{2}$. (You may want to reduce to the case where $a = 0$.)
- Deduce that any Euclidean circle is also a hyperbolic circle.
geometry hyperbolic-geometry
edited Jan 9 at 14:06
Blue
47.8k870152
asked Jan 9 at 13:19
Shay AdlerShay Adler
1
$endgroup$
$begingroup$
Welcome to Math.SE! Your question is attracting down votes and close votes, most-likely because it's nothing more than a problem statement. The community here prefers/expects questions to include some idea of what you know about a problem and/or where you got stuck. Such information helps answerers target their responses to your skill level and specific need, while avoiding wasting everyone's time telling you things you already know. (Plus, it helps convince people that you're not simply trying to get them to do your homework for you..)
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– Blue
Jan 9 at 14:04
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I think you would attain more attention towards your question by adding more details of standard definitions and personal attempts....
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– Mostafa Ayaz
Jan 9 at 16:00
add a comment |
-3
-3
-3
$begingroup$
Consider in $H^2$ the hyperbolic circle centered at $a + ib$ with radius $r$; i.e., the set $C = left{zin H^2mid dH^2 (z, a + ib) = rright}$
- Show that $C$ is the Euclidean circle with center $a + ibdfrac{e^r + e^{−r}}{2}$ and radius $bdfrac{e^r − e^{−r}}{2}$. (You may want to reduce to the case where $a = 0$.)
- Deduce that any Euclidean circle is also a hyperbolic circle.
geometry hyperbolic-geometry
edited Jan 9 at 14:06
Blue
47.8k870152
asked Jan 9 at 13:19
Shay AdlerShay Adler
1
$endgroup$
Consider in $H^2$ the hyperbolic circle centered at $a + ib$ with radius $r$; i.e., the set $C = left{zin H^2mid dH^2 (z, a + ib) = rright}$
- Show that $C$ is the Euclidean circle with center $a + ibdfrac{e^r + e^{−r}}{2}$ and radius $bdfrac{e^r − e^{−r}}{2}$. (You may want to reduce to the case where $a = 0$.)
- Deduce that any Euclidean circle is also a hyperbolic circle.
geometry hyperbolic-geometry
geometry hyperbolic-geometry
edited Jan 9 at 14:06
Blue
47.8k870152
asked Jan 9 at 13:19
Shay AdlerShay Adler
1
edited Jan 9 at 14:06
Blue
47.8k870152
asked Jan 9 at 13:19
Shay AdlerShay Adler
1
edited Jan 9 at 14:06
Blue
47.8k870152
edited Jan 9 at 14:06
Blue
47.8k870152
edited Jan 9 at 14:06
Blue
47.8k870152
47.8k870152
asked Jan 9 at 13:19
Shay AdlerShay Adler
1
asked Jan 9 at 13:19
Shay AdlerShay Adler
1
asked Jan 9 at 13:19
Shay AdlerShay Adler
1
1
$begingroup$
Welcome to Math.SE! Your question is attracting down votes and close votes, most-likely because it's nothing more than a problem statement. The community here prefers/expects questions to include some idea of what you know about a problem and/or where you got stuck. Such information helps answerers target their responses to your skill level and specific need, while avoiding wasting everyone's time telling you things you already know. (Plus, it helps convince people that you're not simply trying to get them to do your homework for you..)
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– Blue
Jan 9 at 14:04
$begingroup$
I think you would attain more attention towards your question by adding more details of standard definitions and personal attempts....
$endgroup$
– Mostafa Ayaz
Jan 9 at 16:00
add a comment |
$begingroup$
Welcome to Math.SE! Your question is attracting down votes and close votes, most-likely because it's nothing more than a problem statement. The community here prefers/expects questions to include some idea of what you know about a problem and/or where you got stuck. Such information helps answerers target their responses to your skill level and specific need, while avoiding wasting everyone's time telling you things you already know. (Plus, it helps convince people that you're not simply trying to get them to do your homework for you..)
$endgroup$
– Blue
Jan 9 at 14:04
$begingroup$
I think you would attain more attention towards your question by adding more details of standard definitions and personal attempts....
$endgroup$
– Mostafa Ayaz
Jan 9 at 16:00
$begingroup$
Welcome to Math.SE! Your question is attracting down votes and close votes, most-likely because it's nothing more than a problem statement. The community here prefers/expects questions to include some idea of what you know about a problem and/or where you got stuck. Such information helps answerers target their responses to your skill level and specific need, while avoiding wasting everyone's time telling you things you already know. (Plus, it helps convince people that you're not simply trying to get them to do your homework for you..)
$endgroup$
– Blue
Jan 9 at 14:04
$begingroup$
Welcome to Math.SE! Your question is attracting down votes and close votes, most-likely because it's nothing more than a problem statement. The community here prefers/expects questions to include some idea of what you know about a problem and/or where you got stuck. Such information helps answerers target their responses to your skill level and specific need, while avoiding wasting everyone's time telling you things you already know. (Plus, it helps convince people that you're not simply trying to get them to do your homework for you..)
$endgroup$
– Blue
Jan 9 at 14:04
$begingroup$
I think you would attain more attention towards your question by adding more details of standard definitions and personal attempts....
$endgroup$
– Mostafa Ayaz
Jan 9 at 16:00
$begingroup$
I think you would attain more attention towards your question by adding more details of standard definitions and personal attempts....
$endgroup$
– Mostafa Ayaz
Jan 9 at 16:00
add a comment |
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$begingroup$
Welcome to Math.SE! Your question is attracting down votes and close votes, most-likely because it's nothing more than a problem statement. The community here prefers/expects questions to include some idea of what you know about a problem and/or where you got stuck. Such information helps answerers target their responses to your skill level and specific need, while avoiding wasting everyone's time telling you things you already know. (Plus, it helps convince people that you're not simply trying to get them to do your homework for you..)
$endgroup$
– Blue
Jan 9 at 14:04
$begingroup$
I think you would attain more attention towards your question by adding more details of standard definitions and personal attempts....
$endgroup$
– Mostafa Ayaz
Jan 9 at 16:00