octagon size in circle
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I am using yED to draw a schematic for a sound installation. It involves a circle with a diameter of 7 metres. I need to have 8 speakers at a regular distance so I am a drawing an octagon inside the circle. Now: how can I calculate the width and height of the octagon so that it fits within that circle of 7 metres?
Pretty basic question, I know, but it has been a long time ago since I did maths.
geometric-measure-theory
asked Nov 18 at 10:58
Samuel Van Ransbeeck
11
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up vote
-2
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I am using yED to draw a schematic for a sound installation. It involves a circle with a diameter of 7 metres. I need to have 8 speakers at a regular distance so I am a drawing an octagon inside the circle. Now: how can I calculate the width and height of the octagon so that it fits within that circle of 7 metres?
Pretty basic question, I know, but it has been a long time ago since I did maths.
geometric-measure-theory
asked Nov 18 at 10:58
Samuel Van Ransbeeck
11
add a comment |
up vote
-2
down vote
favorite
up vote
-2
down vote
favorite
I am using yED to draw a schematic for a sound installation. It involves a circle with a diameter of 7 metres. I need to have 8 speakers at a regular distance so I am a drawing an octagon inside the circle. Now: how can I calculate the width and height of the octagon so that it fits within that circle of 7 metres?
Pretty basic question, I know, but it has been a long time ago since I did maths.
geometric-measure-theory
asked Nov 18 at 10:58
Samuel Van Ransbeeck
11
I am using yED to draw a schematic for a sound installation. It involves a circle with a diameter of 7 metres. I need to have 8 speakers at a regular distance so I am a drawing an octagon inside the circle. Now: how can I calculate the width and height of the octagon so that it fits within that circle of 7 metres?
Pretty basic question, I know, but it has been a long time ago since I did maths.
geometric-measure-theory
geometric-measure-theory
asked Nov 18 at 10:58
Samuel Van Ransbeeck
11
asked Nov 18 at 10:58
Samuel Van Ransbeeck
11
asked Nov 18 at 10:58
Samuel Van Ransbeeck
11
asked Nov 18 at 10:58
Samuel Van Ransbeeck
11
asked Nov 18 at 10:58
Samuel Van Ransbeeck
11
11
add a comment |
add a comment |
1 Answer
1
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oldest
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0
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Such an octagon is formed of 8 isosceles triangles, each having an angle of 45 degrees at the centre, and the two adjacent sides being 7m long. That gives the third side (which is the side-length of the octagon) at $7sqrt{2-sqrt{2}}$, or around 5.358m.
However, you don't need any of that information to construct such an octagon: instead, first find the centre of the circle (if you don't know already, pick any point, tie a string to it, pull the string tight to any other point on the circle, and move around, keeping the string tight, until you reach the point where it is longest. Repeat for a different starting point, and the centre is where the strings cross.
Place your first speaker anywhere you like (if you used the two-string method to find the centre, use one end of one of your pieces of string: it'll make life easier). Place the other exactly opposite the centre from there (that's at the other end of your piece of string, if you used it).
Now, take two pieces of string (say 5m long, but it doesn't matter as long as it's significantly over 3.5m and both the same). Tie one to each of your placed speakers. There are exactly two places where you can stand and hold the ends of the strings touching each other with both tight. Find them and mark them. Take a straight line between them (if you didn't mess up, this line will go exactly through the centre of your circle). Put a speaker at either end of that line.
Now, tie those two pieces of string to two adjacent speakers. Find one of the places that they cross (the other one is outside the circle). Draw a line through that and the centre. Place a speaker at either end of it. Finally, move your string to two speakers that are 90 degrees apart and don't have a speaker between them. Repeat the process to construct your last line, and place a speaker at opposite ends of that.
answered Nov 18 at 11:13
user3482749
1,931411
Thank you for such a detailed answer. However, I will need it for a drawing that I will make inside that circle on the floor. Having the right size of the octagon is important as it will influence how big the drawing will be (luckily the drawing are just straight lines o no heavy mathematics involved). I tried your formula but the octagon comes up way smaller than the circle. If I crudely draw the octagon, the width and height should be around 645 cm.
– Samuel Van Ransbeeck
Nov 18 at 11:33
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
Such an octagon is formed of 8 isosceles triangles, each having an angle of 45 degrees at the centre, and the two adjacent sides being 7m long. That gives the third side (which is the side-length of the octagon) at $7sqrt{2-sqrt{2}}$, or around 5.358m.
However, you don't need any of that information to construct such an octagon: instead, first find the centre of the circle (if you don't know already, pick any point, tie a string to it, pull the string tight to any other point on the circle, and move around, keeping the string tight, until you reach the point where it is longest. Repeat for a different starting point, and the centre is where the strings cross.
Place your first speaker anywhere you like (if you used the two-string method to find the centre, use one end of one of your pieces of string: it'll make life easier). Place the other exactly opposite the centre from there (that's at the other end of your piece of string, if you used it).
Now, take two pieces of string (say 5m long, but it doesn't matter as long as it's significantly over 3.5m and both the same). Tie one to each of your placed speakers. There are exactly two places where you can stand and hold the ends of the strings touching each other with both tight. Find them and mark them. Take a straight line between them (if you didn't mess up, this line will go exactly through the centre of your circle). Put a speaker at either end of that line.
Now, tie those two pieces of string to two adjacent speakers. Find one of the places that they cross (the other one is outside the circle). Draw a line through that and the centre. Place a speaker at either end of it. Finally, move your string to two speakers that are 90 degrees apart and don't have a speaker between them. Repeat the process to construct your last line, and place a speaker at opposite ends of that.
answered Nov 18 at 11:13
user3482749
1,931411
Thank you for such a detailed answer. However, I will need it for a drawing that I will make inside that circle on the floor. Having the right size of the octagon is important as it will influence how big the drawing will be (luckily the drawing are just straight lines o no heavy mathematics involved). I tried your formula but the octagon comes up way smaller than the circle. If I crudely draw the octagon, the width and height should be around 645 cm.
– Samuel Van Ransbeeck
Nov 18 at 11:33
add a comment |
up vote
0
down vote
Such an octagon is formed of 8 isosceles triangles, each having an angle of 45 degrees at the centre, and the two adjacent sides being 7m long. That gives the third side (which is the side-length of the octagon) at $7sqrt{2-sqrt{2}}$, or around 5.358m.
However, you don't need any of that information to construct such an octagon: instead, first find the centre of the circle (if you don't know already, pick any point, tie a string to it, pull the string tight to any other point on the circle, and move around, keeping the string tight, until you reach the point where it is longest. Repeat for a different starting point, and the centre is where the strings cross.
Place your first speaker anywhere you like (if you used the two-string method to find the centre, use one end of one of your pieces of string: it'll make life easier). Place the other exactly opposite the centre from there (that's at the other end of your piece of string, if you used it).
Now, take two pieces of string (say 5m long, but it doesn't matter as long as it's significantly over 3.5m and both the same). Tie one to each of your placed speakers. There are exactly two places where you can stand and hold the ends of the strings touching each other with both tight. Find them and mark them. Take a straight line between them (if you didn't mess up, this line will go exactly through the centre of your circle). Put a speaker at either end of that line.
Now, tie those two pieces of string to two adjacent speakers. Find one of the places that they cross (the other one is outside the circle). Draw a line through that and the centre. Place a speaker at either end of it. Finally, move your string to two speakers that are 90 degrees apart and don't have a speaker between them. Repeat the process to construct your last line, and place a speaker at opposite ends of that.
answered Nov 18 at 11:13
user3482749
1,931411
Thank you for such a detailed answer. However, I will need it for a drawing that I will make inside that circle on the floor. Having the right size of the octagon is important as it will influence how big the drawing will be (luckily the drawing are just straight lines o no heavy mathematics involved). I tried your formula but the octagon comes up way smaller than the circle. If I crudely draw the octagon, the width and height should be around 645 cm.
– Samuel Van Ransbeeck
Nov 18 at 11:33
add a comment |
up vote
0
down vote
up vote
0
down vote
Such an octagon is formed of 8 isosceles triangles, each having an angle of 45 degrees at the centre, and the two adjacent sides being 7m long. That gives the third side (which is the side-length of the octagon) at $7sqrt{2-sqrt{2}}$, or around 5.358m.
However, you don't need any of that information to construct such an octagon: instead, first find the centre of the circle (if you don't know already, pick any point, tie a string to it, pull the string tight to any other point on the circle, and move around, keeping the string tight, until you reach the point where it is longest. Repeat for a different starting point, and the centre is where the strings cross.
Place your first speaker anywhere you like (if you used the two-string method to find the centre, use one end of one of your pieces of string: it'll make life easier). Place the other exactly opposite the centre from there (that's at the other end of your piece of string, if you used it).
Now, take two pieces of string (say 5m long, but it doesn't matter as long as it's significantly over 3.5m and both the same). Tie one to each of your placed speakers. There are exactly two places where you can stand and hold the ends of the strings touching each other with both tight. Find them and mark them. Take a straight line between them (if you didn't mess up, this line will go exactly through the centre of your circle). Put a speaker at either end of that line.
Now, tie those two pieces of string to two adjacent speakers. Find one of the places that they cross (the other one is outside the circle). Draw a line through that and the centre. Place a speaker at either end of it. Finally, move your string to two speakers that are 90 degrees apart and don't have a speaker between them. Repeat the process to construct your last line, and place a speaker at opposite ends of that.
answered Nov 18 at 11:13
user3482749
1,931411
Such an octagon is formed of 8 isosceles triangles, each having an angle of 45 degrees at the centre, and the two adjacent sides being 7m long. That gives the third side (which is the side-length of the octagon) at $7sqrt{2-sqrt{2}}$, or around 5.358m.
However, you don't need any of that information to construct such an octagon: instead, first find the centre of the circle (if you don't know already, pick any point, tie a string to it, pull the string tight to any other point on the circle, and move around, keeping the string tight, until you reach the point where it is longest. Repeat for a different starting point, and the centre is where the strings cross.
Place your first speaker anywhere you like (if you used the two-string method to find the centre, use one end of one of your pieces of string: it'll make life easier). Place the other exactly opposite the centre from there (that's at the other end of your piece of string, if you used it).
Now, take two pieces of string (say 5m long, but it doesn't matter as long as it's significantly over 3.5m and both the same). Tie one to each of your placed speakers. There are exactly two places where you can stand and hold the ends of the strings touching each other with both tight. Find them and mark them. Take a straight line between them (if you didn't mess up, this line will go exactly through the centre of your circle). Put a speaker at either end of that line.
Now, tie those two pieces of string to two adjacent speakers. Find one of the places that they cross (the other one is outside the circle). Draw a line through that and the centre. Place a speaker at either end of it. Finally, move your string to two speakers that are 90 degrees apart and don't have a speaker between them. Repeat the process to construct your last line, and place a speaker at opposite ends of that.
answered Nov 18 at 11:13
user3482749
1,931411
answered Nov 18 at 11:13
user3482749
1,931411
answered Nov 18 at 11:13
user3482749
1,931411
answered Nov 18 at 11:13
user3482749
1,931411
1,931411
Thank you for such a detailed answer. However, I will need it for a drawing that I will make inside that circle on the floor. Having the right size of the octagon is important as it will influence how big the drawing will be (luckily the drawing are just straight lines o no heavy mathematics involved). I tried your formula but the octagon comes up way smaller than the circle. If I crudely draw the octagon, the width and height should be around 645 cm.
– Samuel Van Ransbeeck
Nov 18 at 11:33
add a comment |
Thank you for such a detailed answer. However, I will need it for a drawing that I will make inside that circle on the floor. Having the right size of the octagon is important as it will influence how big the drawing will be (luckily the drawing are just straight lines o no heavy mathematics involved). I tried your formula but the octagon comes up way smaller than the circle. If I crudely draw the octagon, the width and height should be around 645 cm.
– Samuel Van Ransbeeck
Nov 18 at 11:33
Thank you for such a detailed answer. However, I will need it for a drawing that I will make inside that circle on the floor. Having the right size of the octagon is important as it will influence how big the drawing will be (luckily the drawing are just straight lines o no heavy mathematics involved). I tried your formula but the octagon comes up way smaller than the circle. If I crudely draw the octagon, the width and height should be around 645 cm.
– Samuel Van Ransbeeck
Nov 18 at 11:33
Thank you for such a detailed answer. However, I will need it for a drawing that I will make inside that circle on the floor. Having the right size of the octagon is important as it will influence how big the drawing will be (luckily the drawing are just straight lines o no heavy mathematics involved). I tried your formula but the octagon comes up way smaller than the circle. If I crudely draw the octagon, the width and height should be around 645 cm.
– Samuel Van Ransbeeck
Nov 18 at 11:33
add a comment |
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