How to calculate the center of a regular polygon?
Clash Royale CLAN TAG#URR8PPP
up vote
0
down vote
favorite
What is the formula for the center of an n
-edge regular polygon that has the given segment as its edge?
So, given a segment AB
, with endpoints A=(a1,a2)
and B=(b1,b2)
, I need to find out the two points X=(x1,x2)
and Y=(y1,y2)
, such that the n
-edge regular polygon with center at X
, and the one with center at Y
have AB
as their edge.
metric-geometry polygons
migrated from mathoverflow.net Dec 25 '14 at 17:27
This question came from our site for professional mathematicians.
add a comment |Â
up vote
0
down vote
favorite
What is the formula for the center of an n
-edge regular polygon that has the given segment as its edge?
So, given a segment AB
, with endpoints A=(a1,a2)
and B=(b1,b2)
, I need to find out the two points X=(x1,x2)
and Y=(y1,y2)
, such that the n
-edge regular polygon with center at X
, and the one with center at Y
have AB
as their edge.
metric-geometry polygons
migrated from mathoverflow.net Dec 25 '14 at 17:27
This question came from our site for professional mathematicians.
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
What is the formula for the center of an n
-edge regular polygon that has the given segment as its edge?
So, given a segment AB
, with endpoints A=(a1,a2)
and B=(b1,b2)
, I need to find out the two points X=(x1,x2)
and Y=(y1,y2)
, such that the n
-edge regular polygon with center at X
, and the one with center at Y
have AB
as their edge.
metric-geometry polygons
What is the formula for the center of an n
-edge regular polygon that has the given segment as its edge?
So, given a segment AB
, with endpoints A=(a1,a2)
and B=(b1,b2)
, I need to find out the two points X=(x1,x2)
and Y=(y1,y2)
, such that the n
-edge regular polygon with center at X
, and the one with center at Y
have AB
as their edge.
metric-geometry polygons
asked Dec 25 '14 at 15:12
Vahagn
migrated from mathoverflow.net Dec 25 '14 at 17:27
This question came from our site for professional mathematicians.
migrated from mathoverflow.net Dec 25 '14 at 17:27
This question came from our site for professional mathematicians.
add a comment |Â
add a comment |Â
1 Answer
1
active
oldest
votes
up vote
0
down vote
Let $T=tan(180^circ/n)$. The midpoint of $AB$ is $((a1+b1)/2,(a2+b2)/2)$, the centres would be
$$((a1+b1)/2+(a2-b2)/2T,(a2+b2)/2+(b1-a1)/2T)\
((a1+b1)/2+(b2-a2)/2T,(a2+b2)/2+(a1-b1)/2T)$$
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
Let $T=tan(180^circ/n)$. The midpoint of $AB$ is $((a1+b1)/2,(a2+b2)/2)$, the centres would be
$$((a1+b1)/2+(a2-b2)/2T,(a2+b2)/2+(b1-a1)/2T)\
((a1+b1)/2+(b2-a2)/2T,(a2+b2)/2+(a1-b1)/2T)$$
add a comment |Â
up vote
0
down vote
Let $T=tan(180^circ/n)$. The midpoint of $AB$ is $((a1+b1)/2,(a2+b2)/2)$, the centres would be
$$((a1+b1)/2+(a2-b2)/2T,(a2+b2)/2+(b1-a1)/2T)\
((a1+b1)/2+(b2-a2)/2T,(a2+b2)/2+(a1-b1)/2T)$$
add a comment |Â
up vote
0
down vote
up vote
0
down vote
Let $T=tan(180^circ/n)$. The midpoint of $AB$ is $((a1+b1)/2,(a2+b2)/2)$, the centres would be
$$((a1+b1)/2+(a2-b2)/2T,(a2+b2)/2+(b1-a1)/2T)\
((a1+b1)/2+(b2-a2)/2T,(a2+b2)/2+(a1-b1)/2T)$$
Let $T=tan(180^circ/n)$. The midpoint of $AB$ is $((a1+b1)/2,(a2+b2)/2)$, the centres would be
$$((a1+b1)/2+(a2-b2)/2T,(a2+b2)/2+(b1-a1)/2T)\
((a1+b1)/2+(b2-a2)/2T,(a2+b2)/2+(a1-b1)/2T)$$
answered Dec 25 '14 at 17:40
Empy2
31.9k12059
31.9k12059
add a comment |Â
add a comment |Â
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f1080751%2fhow-to-calculate-the-center-of-a-regular-polygon%23new-answer', 'question_page');
);
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password