Proof that a regular octagon has a centre [closed]
0
$begingroup$
How do I proove that a regular octagon has a centre?
By centre i mean a point equidistant from all the vertices?
geometry proof-writing
asked Dec 22 '18 at 11:43
Rasmus LarsenRasmus Larsen
1034
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closed as off-topic by Saad, José Carlos Santos, Paul Frost, Alex Provost, Rebellos Dec 22 '18 at 16:05
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Saad, José Carlos Santos, Paul Frost, Alex Provost, Rebellos
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
0
$begingroup$
How do I proove that a regular octagon has a centre?
By centre i mean a point equidistant from all the vertices?
geometry proof-writing
asked Dec 22 '18 at 11:43
Rasmus LarsenRasmus Larsen
1034
$endgroup$
closed as off-topic by Saad, José Carlos Santos, Paul Frost, Alex Provost, Rebellos Dec 22 '18 at 16:05
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Saad, José Carlos Santos, Paul Frost, Alex Provost, Rebellos
If this question can be reworded to fit the rules in the help center, please edit the question.
$begingroup$
What's your definition of a regular octagon?
$endgroup$
– Jyrki Lahtonen
Dec 22 '18 at 12:38
$begingroup$
I think the definition is given in drawing: all sides and all angles are equal.
$endgroup$
– user
Dec 22 '18 at 12:44
$begingroup$
How do you know the octagon constructed in this way closes up?
$endgroup$
– Christian Blatter
Dec 22 '18 at 18:48
$begingroup$
@christianblatter thanks, that is a very good question, I did not think of this.
$endgroup$
– Rasmus Larsen
Dec 23 '18 at 6:34
add a comment |
0
0
0
$begingroup$
How do I proove that a regular octagon has a centre?
By centre i mean a point equidistant from all the vertices?
geometry proof-writing
asked Dec 22 '18 at 11:43
Rasmus LarsenRasmus Larsen
1034
$endgroup$
How do I proove that a regular octagon has a centre?
By centre i mean a point equidistant from all the vertices?
geometry proof-writing
geometry proof-writing
asked Dec 22 '18 at 11:43
Rasmus LarsenRasmus Larsen
1034
asked Dec 22 '18 at 11:43
Rasmus LarsenRasmus Larsen
1034
asked Dec 22 '18 at 11:43
Rasmus LarsenRasmus Larsen
1034
asked Dec 22 '18 at 11:43
Rasmus LarsenRasmus Larsen
1034
asked Dec 22 '18 at 11:43
Rasmus LarsenRasmus Larsen
1034
1034
closed as off-topic by Saad, José Carlos Santos, Paul Frost, Alex Provost, Rebellos Dec 22 '18 at 16:05
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Saad, José Carlos Santos, Paul Frost, Alex Provost, Rebellos
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by Saad, José Carlos Santos, Paul Frost, Alex Provost, Rebellos Dec 22 '18 at 16:05
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Saad, José Carlos Santos, Paul Frost, Alex Provost, Rebellos
If this question can be reworded to fit the rules in the help center, please edit the question.
$begingroup$
What's your definition of a regular octagon?
$endgroup$
– Jyrki Lahtonen
Dec 22 '18 at 12:38
$begingroup$
I think the definition is given in drawing: all sides and all angles are equal.
$endgroup$
– user
Dec 22 '18 at 12:44
$begingroup$
How do you know the octagon constructed in this way closes up?
$endgroup$
– Christian Blatter
Dec 22 '18 at 18:48
$begingroup$
@christianblatter thanks, that is a very good question, I did not think of this.
$endgroup$
– Rasmus Larsen
Dec 23 '18 at 6:34
add a comment |
$begingroup$
What's your definition of a regular octagon?
$endgroup$
– Jyrki Lahtonen
Dec 22 '18 at 12:38
$begingroup$
I think the definition is given in drawing: all sides and all angles are equal.
$endgroup$
– user
Dec 22 '18 at 12:44
$begingroup$
How do you know the octagon constructed in this way closes up?
$endgroup$
– Christian Blatter
Dec 22 '18 at 18:48
$begingroup$
@christianblatter thanks, that is a very good question, I did not think of this.
$endgroup$
– Rasmus Larsen
Dec 23 '18 at 6:34
$begingroup$
What's your definition of a regular octagon?
$endgroup$
– Jyrki Lahtonen
Dec 22 '18 at 12:38
$begingroup$
What's your definition of a regular octagon?
$endgroup$
– Jyrki Lahtonen
Dec 22 '18 at 12:38
$begingroup$
I think the definition is given in drawing: all sides and all angles are equal.
$endgroup$
– user
Dec 22 '18 at 12:44
$begingroup$
I think the definition is given in drawing: all sides and all angles are equal.
$endgroup$
– user
Dec 22 '18 at 12:44
$begingroup$
How do you know the octagon constructed in this way closes up?
$endgroup$
– Christian Blatter
Dec 22 '18 at 18:48
$begingroup$
How do you know the octagon constructed in this way closes up?
$endgroup$
– Christian Blatter
Dec 22 '18 at 18:48
$begingroup$
@christianblatter thanks, that is a very good question, I did not think of this.
$endgroup$
– Rasmus Larsen
Dec 23 '18 at 6:34
$begingroup$
@christianblatter thanks, that is a very good question, I did not think of this.
$endgroup$
– Rasmus Larsen
Dec 23 '18 at 6:34
add a comment |
1 Answer
1
active
oldest
votes
3
$begingroup$
Take a line segment from one vertex to its opposite vertex. Bisect that segment. Clearly this point is equidistant from those two vertices.
Now rotate the octagon about that point, placing two new vertices onto the ends of the line segment. Rotations don't change distance; so those two vertices must be equidistant from the centre too.
Repeat.
answered Dec 22 '18 at 11:48
Patrick StevensPatrick Stevens
28.9k52874
$endgroup$
$begingroup$
I'm a bit uncomfortable with your argument. You seem to assume that the prescribed rotation exists. I rather think that you are to prove its existence! Of course, the OP should specify their definition of a regular octagon.
$endgroup$
– Jyrki Lahtonen
Dec 22 '18 at 12:37
$begingroup$
I was really internally assuming that $D_{16}$ can act on the thing, yes.
$endgroup$
– Patrick Stevens
Dec 22 '18 at 12:41
$begingroup$
@PatrickStevens Thanks. What does D_{16} refer to? Some kind classification of geometric functions?
$endgroup$
– Rasmus Larsen
Jan 3 at 9:33
1
$begingroup$
@RasmusLarsen The dihedral group of order $16$.
$endgroup$
– Patrick Stevens
Jan 3 at 18:47
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
3
$begingroup$
Take a line segment from one vertex to its opposite vertex. Bisect that segment. Clearly this point is equidistant from those two vertices.
Now rotate the octagon about that point, placing two new vertices onto the ends of the line segment. Rotations don't change distance; so those two vertices must be equidistant from the centre too.
Repeat.
answered Dec 22 '18 at 11:48
Patrick StevensPatrick Stevens
28.9k52874
$endgroup$
$begingroup$
I'm a bit uncomfortable with your argument. You seem to assume that the prescribed rotation exists. I rather think that you are to prove its existence! Of course, the OP should specify their definition of a regular octagon.
$endgroup$
– Jyrki Lahtonen
Dec 22 '18 at 12:37
$begingroup$
I was really internally assuming that $D_{16}$ can act on the thing, yes.
$endgroup$
– Patrick Stevens
Dec 22 '18 at 12:41
$begingroup$
@PatrickStevens Thanks. What does D_{16} refer to? Some kind classification of geometric functions?
$endgroup$
– Rasmus Larsen
Jan 3 at 9:33
1
$begingroup$
@RasmusLarsen The dihedral group of order $16$.
$endgroup$
– Patrick Stevens
Jan 3 at 18:47
add a comment |
3
$begingroup$
Take a line segment from one vertex to its opposite vertex. Bisect that segment. Clearly this point is equidistant from those two vertices.
Now rotate the octagon about that point, placing two new vertices onto the ends of the line segment. Rotations don't change distance; so those two vertices must be equidistant from the centre too.
Repeat.
answered Dec 22 '18 at 11:48
Patrick StevensPatrick Stevens
28.9k52874
$endgroup$
$begingroup$
I'm a bit uncomfortable with your argument. You seem to assume that the prescribed rotation exists. I rather think that you are to prove its existence! Of course, the OP should specify their definition of a regular octagon.
$endgroup$
– Jyrki Lahtonen
Dec 22 '18 at 12:37
$begingroup$
I was really internally assuming that $D_{16}$ can act on the thing, yes.
$endgroup$
– Patrick Stevens
Dec 22 '18 at 12:41
$begingroup$
@PatrickStevens Thanks. What does D_{16} refer to? Some kind classification of geometric functions?
$endgroup$
– Rasmus Larsen
Jan 3 at 9:33
1
$begingroup$
@RasmusLarsen The dihedral group of order $16$.
$endgroup$
– Patrick Stevens
Jan 3 at 18:47
add a comment |
3
3
3
$begingroup$
Take a line segment from one vertex to its opposite vertex. Bisect that segment. Clearly this point is equidistant from those two vertices.
Now rotate the octagon about that point, placing two new vertices onto the ends of the line segment. Rotations don't change distance; so those two vertices must be equidistant from the centre too.
Repeat.
answered Dec 22 '18 at 11:48
Patrick StevensPatrick Stevens
28.9k52874
$endgroup$
Take a line segment from one vertex to its opposite vertex. Bisect that segment. Clearly this point is equidistant from those two vertices.
Now rotate the octagon about that point, placing two new vertices onto the ends of the line segment. Rotations don't change distance; so those two vertices must be equidistant from the centre too.
Repeat.
answered Dec 22 '18 at 11:48
Patrick StevensPatrick Stevens
28.9k52874
edited Dec 22 '18 at 12:10
answered Dec 22 '18 at 11:48
Patrick StevensPatrick Stevens
28.9k52874
answered Dec 22 '18 at 11:48
Patrick StevensPatrick Stevens
28.9k52874
answered Dec 22 '18 at 11:48
Patrick StevensPatrick Stevens
28.9k52874
28.9k52874
$begingroup$
I'm a bit uncomfortable with your argument. You seem to assume that the prescribed rotation exists. I rather think that you are to prove its existence! Of course, the OP should specify their definition of a regular octagon.
$endgroup$
– Jyrki Lahtonen
Dec 22 '18 at 12:37
$begingroup$
I was really internally assuming that $D_{16}$ can act on the thing, yes.
$endgroup$
– Patrick Stevens
Dec 22 '18 at 12:41
$begingroup$
@PatrickStevens Thanks. What does D_{16} refer to? Some kind classification of geometric functions?
$endgroup$
– Rasmus Larsen
Jan 3 at 9:33
1
$begingroup$
@RasmusLarsen The dihedral group of order $16$.
$endgroup$
– Patrick Stevens
Jan 3 at 18:47
add a comment |
$begingroup$
I'm a bit uncomfortable with your argument. You seem to assume that the prescribed rotation exists. I rather think that you are to prove its existence! Of course, the OP should specify their definition of a regular octagon.
$endgroup$
– Jyrki Lahtonen
Dec 22 '18 at 12:37
$begingroup$
I was really internally assuming that $D_{16}$ can act on the thing, yes.
$endgroup$
– Patrick Stevens
Dec 22 '18 at 12:41
$begingroup$
@PatrickStevens Thanks. What does D_{16} refer to? Some kind classification of geometric functions?
$endgroup$
– Rasmus Larsen
Jan 3 at 9:33
1
$begingroup$
@RasmusLarsen The dihedral group of order $16$.
$endgroup$
– Patrick Stevens
Jan 3 at 18:47
$begingroup$
I'm a bit uncomfortable with your argument. You seem to assume that the prescribed rotation exists. I rather think that you are to prove its existence! Of course, the OP should specify their definition of a regular octagon.
$endgroup$
– Jyrki Lahtonen
Dec 22 '18 at 12:37
$begingroup$
I'm a bit uncomfortable with your argument. You seem to assume that the prescribed rotation exists. I rather think that you are to prove its existence! Of course, the OP should specify their definition of a regular octagon.
$endgroup$
– Jyrki Lahtonen
Dec 22 '18 at 12:37
$begingroup$
I was really internally assuming that $D_{16}$ can act on the thing, yes.
$endgroup$
– Patrick Stevens
Dec 22 '18 at 12:41
$begingroup$
I was really internally assuming that $D_{16}$ can act on the thing, yes.
$endgroup$
– Patrick Stevens
Dec 22 '18 at 12:41
$begingroup$
@PatrickStevens Thanks. What does D_{16} refer to? Some kind classification of geometric functions?
$endgroup$
– Rasmus Larsen
Jan 3 at 9:33
$begingroup$
@PatrickStevens Thanks. What does D_{16} refer to? Some kind classification of geometric functions?
$endgroup$
– Rasmus Larsen
Jan 3 at 9:33
1
1
$begingroup$
@RasmusLarsen The dihedral group of order $16$.
$endgroup$
– Patrick Stevens
Jan 3 at 18:47
$begingroup$
@RasmusLarsen The dihedral group of order $16$.
$endgroup$
– Patrick Stevens
Jan 3 at 18:47
add a comment |
$begingroup$
What's your definition of a regular octagon?
$endgroup$
– Jyrki Lahtonen
Dec 22 '18 at 12:38
$begingroup$
I think the definition is given in drawing: all sides and all angles are equal.
$endgroup$
– user
Dec 22 '18 at 12:44
$begingroup$
How do you know the octagon constructed in this way closes up?
$endgroup$
– Christian Blatter
Dec 22 '18 at 18:48
$begingroup$
@christianblatter thanks, that is a very good question, I did not think of this.
$endgroup$
– Rasmus Larsen
Dec 23 '18 at 6:34