Software or advice on calculating sides of an octagon

<snip>

Hi John,

basic math time (I hope) (bet someone shoots me down)

ok, lets imagine the octagon.

We know that the radius is 2.25 m (cos you told us you have a 4.5m square
base.

we also know that the octagon is made of 16 right angle triangles. we know
the length of one of the sides, and we know all the internal angles, so we
can use trigonometry to give us all the lengths.

In effect 1/2 s (s being side length) is:

2.25 * tan 22.5 = 0.931m

therefore the length of each side, for a perfect octagon is 0.931*2 =
1.863m (using the scientific calc)

Does this help?

Si

"alexy" <[email protected]> wrote in message
news:[email protected]...
: "GrnOval" <[email protected]> wrote:
:
: ><snip>
: >
: >Hi John,
: >
: >basic math time (I hope) (bet someone shoots me down)
: >
: >ok, lets imagine the octagon.
: >
: >We know that the radius is 2.25 m (cos you told us you have a 4.5m square
: >base.
: >
: >we also know that the octagon is made of 16 right angle triangles. we
know
: >the length of one of the sides, and we know all the internal angles, so
we
: >can use trigonometry to give us all the lengths.
: >
: >In effect 1/2 s (s being side length) is:
: >
: >2.25 * tan 22.5 = 0.931m
: >
: >therefore the length of each side, for a perfect octagon is 0.931*2 =
: >1.863m (using the scientific calc)
:
: I got to the same side measure via a different route. But couldn't
: make sense of how it fit with the rest of his description. Look at
: your 16 right triangles. They each have an area of
: .931*2.25/2=1.04m^2, so the total area is 16.8m^2. The original
: description says 4 m^2, which sounds pretty tiny for the stated
: purpose. Wonder if it was described as "the same area as a square
: building 4 meters on a side", and that was misinterpreted as 4 m^2.
: >
: >Si

i couldnt decide if 4m square for the interior of the octagon was required,
or an octagon that would fir the 4.5 sq m base - so i went for one that
would fill the base as much as poss

Si

"bob" <[email protected]> wrote in message
news:[email protected]...
:
: D-oh! 4.5m square, not 4.

i think like me you read the original request in many ways -

4.5 sq m base or
internal of a 4 m sq
or 4 sq m octagon

John - I reckon we've covered all the bases here for you - which one is it?

Si

I'm so used to drawing odd-shaped mechaincal enclosures, I completely forgot
about the polygon tool!


--
Bob

Travel and Astronomy Photos
http://www3.sympatico.ca/bomo




"CW" <[email protected]> wrote in message
news:[email protected]...
> If you are going to use Autocad, why the extra steps? Just use the polygon
> tool.
>
> "bob" <[email protected]> wrote in message
> news:[email protected]...
> > I dunno man....
> >
> > You can do it graphically by drawing a square in AutoCad, 4 units to a
> side.
> > Copy the square, rotate by 45 degrees, and drop it back onto the first
> > square. If you measure the sides of the resulting octagon, you get
> > 1.657/side, and a 4m square footprint. Maybe I misread the original
> > question.
> >
>
>

It does if you ignore the corners. I omitted that bit.


--
Bob

Travel and Astronomy Photos
http://www3.sympatico.ca/bomo




"Doug Miller" <[email protected]> wrote in message
news:[email protected]...
> In article <[email protected]>, "bob"
<[email protected]> wrote:
> >I dunno man....
> >
> >You can do it graphically by drawing a square in AutoCad, 4 units to a
side.
> >Copy the square, rotate by 45 degrees, and drop it back onto the first
> >square. If you measure the sides of the resulting octagon,
>
> Ummmmm.... how does that make an octagon?
>
> --
> Regards,
> Doug Miller (alphageek at milmac dot com)
>
> It's time to throw all their damned tea in the harbor again.

If you are going to use Autocad, why the extra steps? Just use the polygon
tool.

"bob" <[email protected]> wrote in message
news:[email protected]...
> I dunno man....
>
> You can do it graphically by drawing a square in AutoCad, 4 units to a
side.
> Copy the square, rotate by 45 degrees, and drop it back onto the first
> square. If you measure the sides of the resulting octagon, you get
> 1.657/side, and a 4m square footprint. Maybe I misread the original
> question.
>

"John (aka wheelzuk)" <[email protected]> wrote in message
news:[email protected]...
Hi fellow woodies,

My latest project involves the planning and construction, of an octagonal (8
sided) summerhouse/workshop on a base measuring 4.5 metres square, with a
floor capacity of 4 metres² - 43.056 feet² - 6200.12 inches², and a wall
height of (2.14 metres - 7 feet and 0.25 inch - 84.25inches). Try as hard
as I can, I've been unable to get my head around the calculations necessary
to work out how wide each of the individual 8 sides should be. I visited a
book called 'The Woodworker's Complete Shop Reference' by J Churchill.
However, my insufficient brain capacity cannot cope with the math, which
seems to read as :- Radius=(Length / 2)² / height² / 2 x Height ( / =
divided by). I've most likely misinterpreted the math calculation, as this
is a weak point with me.

Simple checks using a graphics program seem to suggest a length in the
region of 1.57 metres, however, I'm not sure if the prog has also measured
the effects of certain viual effects used to make the plans look good when
printed (thick outer lines of 5 points and rendering/bevelling and shading
***********************


The answer is 1.657 m per side for a perfect octagon. Given that the angled
sides are at 45 degrees, and a side is x, that means that a 4 m edge will
"see" x + .707x + .707x. So that means 4m = 2.414x, or x = 1.657


--
Bob

Travel and Astronomy Photos
http://www3.sympatico.ca/bomo

D-oh! 4.5m square, not 4.

I dunno man....

You can do it graphically by drawing a square in AutoCad, 4 units to a side.
Copy the square, rotate by 45 degrees, and drop it back onto the first
square. If you measure the sides of the resulting octagon, you get
1.657/side, and a 4m square footprint. Maybe I misread the original
question.


--
Bob

Travel and Astronomy Photos
http://www3.sympatico.ca/bomo




"DJ Delorie" <[email protected]> wrote in message
news:[email protected]...
>
> I illustrate and describe the math here:
>
> http://www.delorie.com/quake3/octatrap/
>
> (you only need the small section on calculating the octagon, not all
> the other game-editing steps ;)
>
> I get 1.864 meters too.

In article <[email protected]>, "bob" <[email protected]> wrote:
>I dunno man....
>
>You can do it graphically by drawing a square in AutoCad, 4 units to a side.
>Copy the square, rotate by 45 degrees, and drop it back onto the first
>square. If you measure the sides of the resulting octagon,

Ummmmm.... how does that make an octagon?

--
Regards,
Doug Miller (alphageek at milmac dot com)

It's time to throw all their damned tea in the harbor again.

[email protected] (Doug Miller) wrote:

>In article <[email protected]>, "bob" <[email protected]> wrote:
>>I dunno man....
>>
>>You can do it graphically by drawing a square in AutoCad, 4 units to a side.
>>Copy the square, rotate by 45 degrees, and drop it back onto the first
>>square. If you measure the sides of the resulting octagon,
>
>Ummmmm.... how does that make an octagon?

This is a case where you need to think INSIDE the box!
--
Alex -- Replace "nospam" with "mail" to reply by email. Checked infrequently.

"GrnOval" <[email protected]> wrote:

><snip>
>
>Hi John,
>
>basic math time (I hope) (bet someone shoots me down)
>
>ok, lets imagine the octagon.
>
>We know that the radius is 2.25 m (cos you told us you have a 4.5m square
>base.
>
>we also know that the octagon is made of 16 right angle triangles. we know
>the length of one of the sides, and we know all the internal angles, so we
>can use trigonometry to give us all the lengths.
>
>In effect 1/2 s (s being side length) is:
>
>2.25 * tan 22.5 = 0.931m
>
>therefore the length of each side, for a perfect octagon is 0.931*2 =
>1.863m (using the scientific calc)

I got to the same side measure via a different route. But couldn't
make sense of how it fit with the rest of his description. Look at
your 16 right triangles. They each have an area of
.931*2.25/2=1.04m^2, so the total area is 16.8m^2. The original
description says 4 m^2, which sounds pretty tiny for the stated
purpose. Wonder if it was described as "the same area as a square
building 4 meters on a side", and that was misinterpreted as 4 m^2.
>
>Si

--
Alex -- Replace "nospam" with "mail" to reply by email. Checked infrequently.

"GrnOval" <[email protected]> wrote in message
news:[email protected]...
>
> "bob" <[email protected]> wrote in message
> news:[email protected]...
> :
> : D-oh! 4.5m square, not 4.
>
> i think like me you read the original request in many ways -
>
> 4.5 sq m base or
> internal of a 4 m sq
> or 4 sq m octagon
>
> John - I reckon we've covered all the bases here for you - which one is
it?
>
> Si
>

Just goes ta show ya, there are at least 3 sides to every octagon...


--
Bob

Travel and Astronomy Photos
http://www3.sympatico.ca/bomo

I illustrate and describe the math here:

http://www.delorie.com/quake3/octatrap/

(you only need the small section on calculating the octagon, not all
the other game-editing steps ;)

I get 1.864 meters too.