[MWForum]RE:MIA, Ask an Expert: octagon diagonals
Dan Stone
mwforum@lists.mathcats.com
Wed, 2 Jun 2004 06:37:22 -0400
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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@lists.mathcats.com
[mailto:mwforum-admin@lists.mathcats.com] On Behalf Of Daniel Ajoy
Sent: Tuesday, June 01, 2004 12:15 AM
To: mwforum@lists.mathcats.com; orangetow@yahoo.com
Subject: [MWForum]RE:MIA, Ask an Expert: octagon diagonals
> > from: orangetow@yahoo.com
> > 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
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<DIV><SPAN class=3D860413310-02062004><FONT face=3DArial color=3D#0000ff =
size=3D2>Thank=20
you, Daniel.</FONT></SPAN></DIV>
<DIV><SPAN class=3D860413310-02062004><FONT face=3DArial color=3D#0000ff =
size=3D2></FONT></SPAN> </DIV>
<DIV><SPAN class=3D860413310-02062004><FONT face=3DArial color=3D#0000ff =
size=3D2></FONT></SPAN> </DIV>
<DIV><SPAN class=3D860413310-02062004><FONT face=3DArial color=3D#0000ff =
size=3D2>As=20
usual I focused too narrowly on the problem and missed most of it.=20
Sigh.</FONT></SPAN></DIV>
<DIV><SPAN class=3D860413310-02062004><FONT face=3DArial color=3D#0000ff =
size=3D2></FONT></SPAN> </DIV>
<DIV><SPAN class=3D860413310-02062004><FONT face=3DArial color=3D#0000ff =
size=3D2>I=20
haven't tried your code yet, but am looking forward to doing=20
so.</FONT></SPAN></DIV>
<DIV><SPAN class=3D860413310-02062004><FONT face=3DArial color=3D#0000ff =
size=3D2>I will=20
also be checking out the math site.</FONT></SPAN></DIV>
<DIV><SPAN class=3D860413310-02062004><FONT face=3DArial color=3D#0000ff =
size=3D2></FONT></SPAN> </DIV>
<DIV><SPAN class=3D860413310-02062004><FONT face=3DArial color=3D#0000ff =
size=3D2>Thans=20
again.</FONT></SPAN></DIV>
<DIV><SPAN class=3D860413310-02062004><FONT face=3DArial color=3D#0000ff =
size=3D2></FONT></SPAN> </DIV>
<DIV><SPAN class=3D860413310-02062004><FONT face=3DArial color=3D#0000ff =
size=3D2>Dan</FONT></SPAN></DIV>
<BLOCKQUOTE dir=3Dltr=20
style=3D"PADDING-LEFT: 5px; MARGIN-LEFT: 5px; BORDER-LEFT: #0000ff 2px =
solid; MARGIN-RIGHT: 0px">
<DIV></DIV>
<DIV class=3DOutlookMessageHeader lang=3Den-us dir=3Dltr =
align=3Dleft><FONT=20
face=3DTahoma size=3D2>-----Original Message-----<BR><B>From:</B>=20
mwforum-admin@lists.mathcats.com =
[mailto:mwforum-admin@lists.mathcats.com]=20
<B>On Behalf Of </B>Daniel Ajoy<BR><B>Sent:</B> Tuesday, June 01, 2004 =
12:15=20
AM<BR><B>To:</B> mwforum@lists.mathcats.com;=20
orangetow@yahoo.com<BR><B>Subject:</B> [MWForum]RE:MIA, Ask an Expert: =
octagon=20
diagonals<BR><BR></FONT></DIV>
<DIV align=3Dleft><FONT face=3D"Courier New"><SPAN style=3D"FONT-SIZE: =
10pt">>=20
> from: orangetow@yahoo.com</SPAN></FONT></DIV>
<DIV align=3Dleft><FONT face=3D"Courier New"><SPAN style=3D"FONT-SIZE: =
10pt">>=20
> date: Sun, 30 May 2004 7:54:02 -0600</SPAN></FONT></DIV>
<DIV align=3Dleft><FONT face=3D"Courier New"><SPAN style=3D"FONT-SIZE: =
10pt">>=20
></SPAN></FONT></DIV>
<DIV align=3Dleft><FONT face=3D"Courier New"><SPAN style=3D"FONT-SIZE: =
10pt">>=20
> if an octagon's diagnals are 139.25 inches, </SPAN></FONT></DIV>
<DIV align=3Dleft><FONT face=3D"Courier New"><SPAN style=3D"FONT-SIZE: =
10pt">>=20
> how long is each of its 8 sides</SPAN></FONT></DIV>
<DIV align=3Dleft><BR></DIV>
<DIV align=3Dleft><BR></DIV>
<DIV align=3Dleft><FONT face=3D"Courier New"><SPAN style=3D"FONT-SIZE: =
10pt">On 30=20
May 2004 at 17:52, Dan Stone wrote:</SPAN></FONT></DIV>
<DIV align=3Dleft><BR></DIV>
<DIV align=3Dleft><FONT face=3D"Courier New" color=3D#7f0000><SPAN=20
style=3D"FONT-SIZE: 10pt">> My quick and dirty procedure - I just =
changed the=20
side length until the</SPAN></FONT></DIV>
<DIV align=3Dleft><FONT face=3D"Courier New" color=3D#7f0000><SPAN=20
style=3D"FONT-SIZE: 10pt">> shape could 'hold' the=20
diagonals</SPAN></FONT></DIV>
<DIV align=3Dleft><FONT face=3D"Courier New" color=3D#7f0000><SPAN=20
style=3D"FONT-SIZE: 10pt">> that were drawn as 2=20
rectangles.</SPAN></FONT></DIV>
<DIV align=3Dleft><BR></DIV>
<DIV align=3Dleft><FONT face=3D"Courier New"><SPAN style=3D"FONT-SIZE: =
10pt">But=20
there are other diagonals (image attached)</SPAN></FONT></DIV>
<DIV align=3Dleft><BR></DIV>
<DIV align=3Dleft><IMG height=3D189 alt=3Dgraphic =
src=3D"cid:860413310@02062004-1D8F"=20
width=3D207 border=3D0></DIV>
<DIV align=3Dleft><BR></DIV>
<DIV align=3Dleft><FONT face=3D"Courier New"><SPAN style=3D"FONT-SIZE: =
10pt">I found=20
that out, here:</SPAN></FONT></DIV>
<DIV align=3Dleft><FONT face=3D"Courier New" color=3D#7f0000><SPAN=20
style=3D"FONT-SIZE: =
10pt">http://mathworld.wolfram.com/PolygonDiagonal.html</SPAN></FONT></DI=
V>
<DIV align=3Dleft><BR></DIV>
<DIV align=3Dleft><FONT face=3D"Courier New" color=3D#7f0000><SPAN=20
style=3D"FONT-SIZE: 10pt">> Okay, have I made a mountain out of a =
molehill?=20
<grin></SPAN></FONT></DIV>
<DIV align=3Dleft><FONT face=3D"Courier New" color=3D#7f0000><SPAN=20
style=3D"FONT-SIZE: 10pt">> What would be a better way to have done =
this?</SPAN></FONT></DIV>
<DIV align=3Dleft><BR></DIV>
<DIV align=3Dleft><FONT face=3D"Courier New"><SPAN style=3D"FONT-SIZE: =
10pt">I used=20
these procedures to find each possible length:</SPAN></FONT></DIV>
<DIV align=3Dleft><BR></DIV>
<DIV align=3Dleft><FONT face=3D"Courier New" color=3D#7f0000><SPAN=20
style=3D"FONT-SIZE: 10pt">to octagon :x</SPAN></FONT></DIV>
<DIV align=3Dleft><FONT face=3D"Courier New" color=3D#7f0000><SPAN=20
style=3D"FONT-SIZE: 10pt">cg</SPAN></FONT></DIV>
<DIV align=3Dleft><FONT face=3D"Courier New" color=3D#7f0000><SPAN=20
style=3D"FONT-SIZE: 10pt">t1,</SPAN></FONT></DIV>
<DIV align=3Dleft><FONT face=3D"Courier New" color=3D#7f0000><SPAN=20
style=3D"FONT-SIZE: 10pt">pu home pd repeat 8 [fd :x rt =
45]</SPAN></FONT></DIV>
<DIV align=3Dleft><FONT face=3D"Courier New" color=3D#7f0000><SPAN=20
style=3D"FONT-SIZE: 10pt">t2,</SPAN></FONT></DIV>
<DIV align=3Dleft><FONT face=3D"Courier New" color=3D#7f0000><SPAN=20
style=3D"FONT-SIZE: 10pt">pu home pd repeat </SPAN></FONT><FONT=20
face=3D"Courier New" color=3D#ff0000 size=3D5><SPAN=20
style=3D"FONT-SIZE: 18pt"><B>2</B></SPAN></FONT><FONT face=3D"Courier =
New"=20
color=3D#7f0000><SPAN style=3D"FONT-SIZE: 10pt"> [fd :x rt =
45]</SPAN></FONT></DIV>
<DIV align=3Dleft><FONT face=3D"Courier New" color=3D#7f0000><SPAN=20
style=3D"FONT-SIZE: 10pt">op distance "t1</SPAN></FONT></DIV>
<DIV align=3Dleft><FONT face=3D"Courier New" color=3D#7f0000><SPAN=20
style=3D"FONT-SIZE: 10pt">end</SPAN></FONT></DIV>
<DIV align=3Dleft><BR></DIV>
<DIV align=3Dleft><BR></DIV>
<DIV align=3Dleft><FONT face=3D"Courier New"><SPAN=20
style=3D"FONT-SIZE: 10pt">------------------</SPAN></FONT></DIV>
<DIV align=3Dleft><BR></DIV>
<DIV align=3Dleft><FONT face=3D"Courier New"><SPAN style=3D"FONT-SIZE: =
10pt">to=20
octagon :x</SPAN></FONT></DIV>
<DIV align=3Dleft><FONT face=3D"Courier New"><SPAN=20
style=3D"FONT-SIZE: 10pt">cg</SPAN></FONT></DIV>
<DIV align=3Dleft><FONT face=3D"Courier New"><SPAN=20
style=3D"FONT-SIZE: 10pt">t1,</SPAN></FONT></DIV>
<DIV align=3Dleft><FONT face=3D"Courier New"><SPAN style=3D"FONT-SIZE: =
10pt">pu home=20
pd repeat 8 [fd :x rt 45]</SPAN></FONT></DIV>
<DIV align=3Dleft><FONT face=3D"Courier New"><SPAN=20
style=3D"FONT-SIZE: 10pt">t2,</SPAN></FONT></DIV>
<DIV align=3Dleft><FONT face=3D"Courier New"><SPAN style=3D"FONT-SIZE: =
10pt">pu home=20
pd repeat </SPAN></FONT><FONT face=3D"Courier New" color=3D#0000ff =
size=3D5><SPAN=20
style=3D"FONT-SIZE: 18pt"><B>3</B></SPAN></FONT><FONT face=3D"Courier =
New"><SPAN=20
style=3D"FONT-SIZE: 10pt"> [fd :x rt 45]</SPAN></FONT></DIV>
<DIV align=3Dleft><FONT face=3D"Courier New"><SPAN style=3D"FONT-SIZE: =
10pt">op=20
distance "t1</SPAN></FONT></DIV>
<DIV align=3Dleft><FONT face=3D"Courier New"><SPAN=20
style=3D"FONT-SIZE: 10pt">end</SPAN></FONT></DIV>
<DIV align=3Dleft><BR></DIV>
<DIV align=3Dleft><FONT face=3D"Courier New"><SPAN=20
style=3D"FONT-SIZE: 10pt">------------------</SPAN></FONT></DIV>
<DIV align=3Dleft><BR></DIV>
<DIV align=3Dleft><BR></DIV>
<DIV align=3Dleft><FONT face=3D"Courier New"><SPAN style=3D"FONT-SIZE: =
10pt">to=20
octagon :x</SPAN></FONT></DIV>
<DIV align=3Dleft><FONT face=3D"Courier New"><SPAN=20
style=3D"FONT-SIZE: 10pt">cg</SPAN></FONT></DIV>
<DIV align=3Dleft><FONT face=3D"Courier New"><SPAN=20
style=3D"FONT-SIZE: 10pt">t1,</SPAN></FONT></DIV>
<DIV align=3Dleft><FONT face=3D"Courier New"><SPAN style=3D"FONT-SIZE: =
10pt">pu home=20
pd repeat 8 [fd :x rt 45]</SPAN></FONT></DIV>
<DIV align=3Dleft><FONT face=3D"Courier New"><SPAN=20
style=3D"FONT-SIZE: 10pt">t2,</SPAN></FONT></DIV>
<DIV align=3Dleft><FONT face=3D"Courier New"><SPAN style=3D"FONT-SIZE: =
10pt">pu home=20
pd repeat </SPAN></FONT><FONT face=3D"Courier New" color=3D#ff00ff =
size=3D5><SPAN=20
style=3D"FONT-SIZE: 18pt"><B>4</B></SPAN></FONT><FONT face=3D"Courier =
New"><SPAN=20
style=3D"FONT-SIZE: 10pt"> [fd :x rt 45]</SPAN></FONT></DIV>
<DIV align=3Dleft><FONT face=3D"Courier New"><SPAN style=3D"FONT-SIZE: =
10pt">op=20
distance "t1</SPAN></FONT></DIV>
<DIV align=3Dleft><FONT face=3D"Courier New"><SPAN=20
style=3D"FONT-SIZE: 10pt">end</SPAN></FONT></DIV>
<DIV align=3Dleft><BR></DIV>
<DIV align=3Dleft><FONT face=3D"Courier New"><SPAN=20
style=3D"FONT-SIZE: 10pt">------------------</SPAN></FONT></DIV>
<DIV align=3Dleft><BR></DIV>
<DIV align=3Dleft><FONT face=3D"Courier New"><SPAN style=3D"FONT-SIZE: =
10pt">Since=20
we want the distance that is the output of octagon</SPAN></FONT></DIV>
<DIV align=3Dleft><FONT face=3D"Courier New"><SPAN style=3D"FONT-SIZE: =
10pt">to be=20
139.25 in each case we could use trial and error</SPAN></FONT></DIV>
<DIV align=3Dleft><FONT face=3D"Courier New"><SPAN style=3D"FONT-SIZE: =
10pt">for=20
each of the three possible lengths. But we can also =
use</SPAN></FONT></DIV>
<DIV align=3Dleft><FONT face=3D"Courier New"><SPAN style=3D"FONT-SIZE: =
10pt">this=20
"find" procedure. It is fun to see it working.</SPAN></FONT></DIV>
<DIV align=3Dleft><BR></DIV>
<DIV align=3Dleft><FONT face=3D"Courier New"><SPAN style=3D"FONT-SIZE: =
10pt">to find=20
:func :ini :fin</SPAN></FONT></DIV>
<DIV align=3Dleft><FONT face=3D"Courier New"><SPAN style=3D"FONT-SIZE: =
10pt">if=20
0.001 > abs :ini - :fin [op :ini]</SPAN></FONT></DIV>
<DIV align=3Dleft><FONT face=3D"Courier New"><SPAN style=3D"FONT-SIZE: =
10pt">let=20
[mid (:ini + :fin) / 2]</SPAN></FONT></DIV>
<DIV align=3Dleft><FONT face=3D"Courier New"><SPAN style=3D"FONT-SIZE: =
10pt">let=20
[fini run se :func :ini]</SPAN></FONT></DIV>
<DIV align=3Dleft><FONT face=3D"Courier New"><SPAN style=3D"FONT-SIZE: =
10pt">let=20
[ffin run se :func :fin]</SPAN></FONT></DIV>
<DIV align=3Dleft><FONT face=3D"Courier New"><SPAN style=3D"FONT-SIZE: =
10pt">let=20
[fmid run se :func :mid]</SPAN></FONT></DIV>
<DIV align=3Dleft><FONT face=3D"Courier New"><SPAN style=3D"FONT-SIZE: =
10pt">if=20
:fini * :fmid < 0 [op find :func :ini :mid]</SPAN></FONT></DIV>
<DIV align=3Dleft><FONT face=3D"Courier New"><SPAN style=3D"FONT-SIZE: =
10pt">if=20
:fmid * :ffin < 0 [op find :func :mid :fin]</SPAN></FONT></DIV>
<DIV align=3Dleft><FONT face=3D"Courier New"><SPAN=20
style=3D"FONT-SIZE: 10pt">end</SPAN></FONT></DIV>
<DIV align=3Dleft><BR></DIV>
<DIV align=3Dleft><BR></DIV>
<DIV align=3Dleft><FONT face=3D"Courier New"><SPAN style=3D"FONT-SIZE: =
10pt">; with=20
repeat 2</SPAN></FONT></DIV>
<DIV align=3Dleft><FONT face=3D"Courier New"><SPAN style=3D"FONT-SIZE: =
10pt">show=20
find [139.25 - octagon] 50 100</SPAN></FONT></DIV>
<DIV align=3Dleft><FONT face=3D"Courier New"><SPAN=20
style=3D"FONT-SIZE: 10pt">75.3608703613</SPAN></FONT></DIV>
<DIV align=3Dleft><BR></DIV>
<DIV align=3Dleft><FONT face=3D"Courier New"><SPAN style=3D"FONT-SIZE: =
10pt">; with=20
repeat 3</SPAN></FONT></DIV>
<DIV align=3Dleft><FONT face=3D"Courier New"><SPAN style=3D"FONT-SIZE: =
10pt">show=20
find [139.25 - octagon] 50 100</SPAN></FONT></DIV>
<DIV align=3Dleft><FONT face=3D"Courier New"><SPAN=20
style=3D"FONT-SIZE: 10pt">57.6789855957</SPAN></FONT></DIV>
<DIV align=3Dleft><BR></DIV>
<DIV align=3Dleft><FONT face=3D"Courier New"><SPAN style=3D"FONT-SIZE: =
10pt">; with=20
repeat 4</SPAN></FONT></DIV>
<DIV align=3Dleft><FONT face=3D"Courier New"><SPAN style=3D"FONT-SIZE: =
10pt">show=20
find [139.25 - octagon] 50 100</SPAN></FONT></DIV>
<DIV align=3Dleft><FONT face=3D"Courier New"><SPAN=20
style=3D"FONT-SIZE: 10pt">53.288269043</SPAN></FONT></DIV>
<DIV align=3Dleft><BR></DIV>
<DIV align=3Dleft><BR></DIV>
<DIV align=3Dleft><FONT face=3D"Courier New"><SPAN style=3D"FONT-SIZE: =
10pt">Project=20
attached.</SPAN></FONT></DIV>
<DIV align=3Dleft><BR></DIV>
<DIV align=3Dleft><FONT face=3D"Courier New"><SPAN=20
style=3D"FONT-SIZE: 10pt">Daniel</SPAN></FONT></DIV>
<DIV align=3Dleft><FONT face=3D"Courier New"><SPAN=20
style=3D"FONT-SIZE: 10pt">OpenWorld Learning</SPAN></FONT></DIV>
<DIV align=3Dleft></DIV></BLOCKQUOTE></BODY></HTML>
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