[MWForum]RE:MIA, Ask an Expert: octagon diagonals
Daniel Ajoy
mwforum@lists.mathcats.com
Mon, 31 May 2004 23:14:55 -0500
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<div align="left"><font face="Courier New"><span style="font-size:10pt">> > from: orangetow@yahoo.com</span></font></div>
<div align="left"><font face="Courier New"><span style="font-size:10pt">> > date: Sun, 30 May 2004 7:54:02 -0600</span></font></div>
<div align="left"><font face="Courier New"><span style="font-size:10pt">> ></span></font></div>
<div align="left"><font face="Courier New"><span style="font-size:10pt">> > if an octagon's diagnals are 139.25 inches, </span></font></div>
<div align="left"><font face="Courier New"><span style="font-size:10pt">> > how long is each of its 8 sides</span></font></div>
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<div align="left"><font face="Courier New"><span style="font-size:10pt">On 30 May 2004 at 17:52, Dan Stone wrote:</span></font></div>
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<div align="left"><font face="Courier New" color="#7f0000"><span style="font-size:10pt">> My quick and dirty procedure - I just changed the side length until the</span></font></div>
<div align="left"><font face="Courier New" color="#7f0000"><span style="font-size:10pt">> shape could 'hold' the diagonals</span></font></div>
<div align="left"><font face="Courier New" color="#7f0000"><span style="font-size:10pt">> that were drawn as 2 rectangles.</span></font></div>
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<div align="left"><font face="Courier New"><span style="font-size:10pt">But there are other diagonals (image attached)</span></font></div>
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<div align="left"><img src="cid:13526869.1086045296.12428" width="207" height="189" border="0" alt="graphic"/></div>
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<div align="left"><font face="Courier New"><span style="font-size:10pt">I found that out, here:</span></font></div>
<div align="left"><font face="Courier New" color="#7f0000"><span style="font-size:10pt">http://mathworld.wolfram.com/PolygonDiagonal.html</span></font></div>
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<div align="left"><font face="Courier New" color="#7f0000"><span style="font-size:10pt">> Okay, have I made a mountain out of a molehill? <grin></span></font></div>
<div align="left"><font face="Courier New" color="#7f0000"><span style="font-size:10pt">> What would be a better way to have done this?</span></font></div>
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<div align="left"><font face="Courier New"><span style="font-size:10pt">I used these procedures to find each possible length:</span></font></div>
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<div align="left"><font face="Courier New" color="#7f0000"><span style="font-size:10pt">to octagon :x</span></font></div>
<div align="left"><font face="Courier New" color="#7f0000"><span style="font-size:10pt">cg</span></font></div>
<div align="left"><font face="Courier New" color="#7f0000"><span style="font-size:10pt">t1,</span></font></div>
<div align="left"><font face="Courier New" color="#7f0000"><span style="font-size:10pt">pu home pd repeat 8 [fd :x rt 45]</span></font></div>
<div align="left"><font face="Courier New" color="#7f0000"><span style="font-size:10pt">t2,</span></font></div>
<div align="left"><font face="Courier New" color="#7f0000"><span style="font-size:10pt">pu home pd repeat </span></font><font face="Courier New" color="#ff0000" size="5"><span
style="font-size:18pt"><b>2</b></span></font><font face="Courier New" color="#7f0000"><span style="font-size:10pt"> [fd :x rt 45]</span></font></div>
<div align="left"><font face="Courier New" color="#7f0000"><span style="font-size:10pt">op distance "t1</span></font></div>
<div align="left"><font face="Courier New" color="#7f0000"><span style="font-size:10pt">end</span></font></div>
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<div align="left"><font face="Courier New"><span style="font-size:10pt">------------------</span></font></div>
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<div align="left"><font face="Courier New"><span style="font-size:10pt">to octagon :x</span></font></div>
<div align="left"><font face="Courier New"><span style="font-size:10pt">cg</span></font></div>
<div align="left"><font face="Courier New"><span style="font-size:10pt">t1,</span></font></div>
<div align="left"><font face="Courier New"><span style="font-size:10pt">pu home pd repeat 8 [fd :x rt 45]</span></font></div>
<div align="left"><font face="Courier New"><span style="font-size:10pt">t2,</span></font></div>
<div align="left"><font face="Courier New"><span style="font-size:10pt">pu home pd repeat </span></font><font face="Courier New" color="#0000ff" size="5"><span style="font-size:18pt"><b>3</b></span></font><font
face="Courier New"><span style="font-size:10pt"> [fd :x rt 45]</span></font></div>
<div align="left"><font face="Courier New"><span style="font-size:10pt">op distance "t1</span></font></div>
<div align="left"><font face="Courier New"><span style="font-size:10pt">end</span></font></div>
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<div align="left"><font face="Courier New"><span style="font-size:10pt">------------------</span></font></div>
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<div align="left"><font face="Courier New"><span style="font-size:10pt">to octagon :x</span></font></div>
<div align="left"><font face="Courier New"><span style="font-size:10pt">cg</span></font></div>
<div align="left"><font face="Courier New"><span style="font-size:10pt">t1,</span></font></div>
<div align="left"><font face="Courier New"><span style="font-size:10pt">pu home pd repeat 8 [fd :x rt 45]</span></font></div>
<div align="left"><font face="Courier New"><span style="font-size:10pt">t2,</span></font></div>
<div align="left"><font face="Courier New"><span style="font-size:10pt">pu home pd repeat </span></font><font face="Courier New" color="#ff00ff" size="5"><span style="font-size:18pt"><b>4</b></span></font><font
face="Courier New"><span style="font-size:10pt"> [fd :x rt 45]</span></font></div>
<div align="left"><font face="Courier New"><span style="font-size:10pt">op distance "t1</span></font></div>
<div align="left"><font face="Courier New"><span style="font-size:10pt">end</span></font></div>
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<div align="left"><font face="Courier New"><span style="font-size:10pt">------------------</span></font></div>
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<div align="left"><font face="Courier New"><span style="font-size:10pt">Since we want the distance that is the output of octagon</span></font></div>
<div align="left"><font face="Courier New"><span style="font-size:10pt">to be 139.25 in each case we could use trial and error</span></font></div>
<div align="left"><font face="Courier New"><span style="font-size:10pt">for each of the three possible lengths. But we can also use</span></font></div>
<div align="left"><font face="Courier New"><span style="font-size:10pt">this "find" procedure. It is fun to see it working.</span></font></div>
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<div align="left"><font face="Courier New"><span style="font-size:10pt">to find :func :ini :fin</span></font></div>
<div align="left"><font face="Courier New"><span style="font-size:10pt">if 0.001 > abs :ini - :fin [op :ini]</span></font></div>
<div align="left"><font face="Courier New"><span style="font-size:10pt">let [mid (:ini + :fin) / 2]</span></font></div>
<div align="left"><font face="Courier New"><span style="font-size:10pt">let [fini run se :func :ini]</span></font></div>
<div align="left"><font face="Courier New"><span style="font-size:10pt">let [ffin run se :func :fin]</span></font></div>
<div align="left"><font face="Courier New"><span style="font-size:10pt">let [fmid run se :func :mid]</span></font></div>
<div align="left"><font face="Courier New"><span style="font-size:10pt">if :fini * :fmid < 0 [op find :func :ini :mid]</span></font></div>
<div align="left"><font face="Courier New"><span style="font-size:10pt">if :fmid * :ffin < 0 [op find :func :mid :fin]</span></font></div>
<div align="left"><font face="Courier New"><span style="font-size:10pt">end</span></font></div>
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<div align="left"><font face="Courier New"><span style="font-size:10pt">; with repeat 2</span></font></div>
<div align="left"><font face="Courier New"><span style="font-size:10pt">show find [139.25 - octagon] 50 100</span></font></div>
<div align="left"><font face="Courier New"><span style="font-size:10pt">75.3608703613</span></font></div>
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<div align="left"><font face="Courier New"><span style="font-size:10pt">; with repeat 3</span></font></div>
<div align="left"><font face="Courier New"><span style="font-size:10pt">show find [139.25 - octagon] 50 100</span></font></div>
<div align="left"><font face="Courier New"><span style="font-size:10pt">57.6789855957</span></font></div>
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<div align="left"><font face="Courier New"><span style="font-size:10pt">; with repeat 4</span></font></div>
<div align="left"><font face="Courier New"><span style="font-size:10pt">show find [139.25 - octagon] 50 100</span></font></div>
<div align="left"><font face="Courier New"><span style="font-size:10pt">53.288269043</span></font></div>
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<div align="left"><font face="Courier New"><span style="font-size:10pt">Project attached.</span></font></div>
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<div align="left"><font face="Courier New"><span style="font-size:10pt">Daniel</span></font></div>
<div align="left"><font face="Courier New"><span style="font-size:10pt">OpenWorld Learning</span></font></div>
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