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Subject: RE:MIA, Ask an Expert: octagon diagonals
From: mwforum@xxxxxxxxxxxxxxxxxx (Dan Stone)
Date: Wed, 2 Jun 2004 06:37:22 -0400

Thank you,  Daniel.
 
 
As usual I focused too narrowly on the problem and missed most of it.
Sigh.
 
I haven't tried your code yet, but am looking forward to doing so.
I will also be checking out the math site.
 
Thans again.
 
Dan

-----Original Message-----
From: mwforum-admin@xxxxxxxxxxxxxxxxxx
[mailto:mwforum-admin@xxxxxxxxxxxxxxxxxx] On Behalf Of Daniel Ajoy
Sent: Tuesday, June 01, 2004 12:15 AM
To: mwforum@xxxxxxxxxxxxxxxxxx; orangetow@xxxxxxxxx
Subject: [MWForum]RE:MIA, Ask an Expert: octagon diagonals


> > from: orangetow@xxxxxxxxx
> > date: Sun, 30 May 2004 7:54:02 -0600
> >
> > if an octagon's diagnals are 139.25 inches, 
> > how long is each of its 8 sides


On 30 May 2004 at 17:52, Dan Stone wrote:

> My quick and dirty procedure - I just changed the side length until
the
> shape could 'hold' the diagonals
> that were drawn as 2 rectangles.

But there are other diagonals (image attached)

graphic

I found that out, here:
http://mathworld.wolfram.com/PolygonDiagonal.html

> Okay, have I made a mountain out of a molehill? <grin>
> What would be a better way to have done this?

I used these procedures to find each possible length:

to octagon :x
cg
t1,
pu home pd repeat 8 [fd :x rt 45]
t2,
pu home pd repeat 2 [fd :x rt 45]
op distance "t1
end


------------------

to octagon :x
cg
t1,
pu home pd repeat 8 [fd :x rt 45]
t2,
pu home pd repeat 3 [fd :x rt 45]
op distance "t1
end

------------------


to octagon :x
cg
t1,
pu home pd repeat 8 [fd :x rt 45]
t2,
pu home pd repeat 4 [fd :x rt 45]
op distance "t1
end

------------------

Since we want the distance that is the output of octagon
to be 139.25 in each case we could use trial and error
for each of the three possible lengths. But we can also use
this "find" procedure. It is fun to see it working.

to find :func :ini :fin
if 0.001 > abs :ini - :fin [op :ini]
let [mid (:ini + :fin) / 2]
let [fini run se :func :ini]
let [ffin run se :func :fin]
let [fmid run se :func :mid]
if :fini * :fmid < 0 [op find :func :ini :mid]
if :fmid * :ffin < 0 [op find :func :mid :fin]
end


; with repeat 2
show find [139.25 - octagon] 50 100
75.3608703613

; with repeat 3
show find [139.25 - octagon] 50 100
57.6789855957

; with repeat 4
show find [139.25 - octagon] 50 100
53.288269043


Project attached.

Daniel
OpenWorld Learning

Attachment: OCTAGON.GIF
Description: Binary data


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