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AsAsAsBsAsAsAt.html
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AsAsAsBsAsAsAt.html
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<!DOCTYPE html>
<html>
<head>
<meta charset="UTF-8">
<style>
* { font-family: sans-serif; }
.A { color:#0d0; }
.B { color:#08f; }
.s { color:#f00; }
.t { color:#f80; }
img.right {
width: 300px;
float:right;
margin:0 5px 0 0;
}
dd { padding: 2px 0 10px; }
pre { font-family: monospace; }
</style>
</head>
<body>
<h1>Heptagons families</h1>
<h2>AsAsAsBsAsAsAt</h2>
<h3>Formulas</h3>
<p>
<img src="AsAsAsBsAsAsAt_draft.svg" class="right">
The heptagon at the right has six equal angles <b class="A">A</b> and a single angle <b class="B">B</b>. Also has six equal sides <b class="s">s</b> and a single side
<b class="t">t</b>.
<dl>
<dt>At vertex P1 there are two angles</dt>
<dd>
<b>A</b></li> and <b>C = π - A</b>
</dd>
<dt>At vertex P2 there are two angles</dt>
<dd>
<b>C</b></li> and <b>D = A - C</b>
</dd>
<dt>At vertex P3 there are three angles</dt>
<dd>
<b>D</b>, <b>E = π - D</b> and <b>F = A - E</b></li>
</dd>
<dt>Simplifying, we get</dt>
<dd>
<pre>
D = 2A - π
F = 3A - 2π
</pre>
</dd>
<dt>So, the value of seventh side <b class="t">t</b> can be found</dt>
<dd>
<pre>
t = 2s[ cos(A) + cos(D) + cos(F) ]
= 2s[ cos(A) + cos(2A - π) + cos(3A - 2π) ]
</pre>
</dd>
<dt>For any heptagon with six angles <b class="A">A</b> and one angle <b class="B">B</b> we have</dt>
<dd>
<b> B = 4π - 6A</b>
</dd>
</dl>
</p>
<h3>Iterator</h3>
<p>
Define the iterator <b>i</b> = <b class="B">B</b> / <b class="A">A</b> as a real number
ranging from zero to infinity.
</p>
<dl>
<dt>Then, angle <b class="A">A</b> can be described as factor of the iterator:</dt>
<dd>
<pre>
A = 4π / (i + 6)
</pre>
</dd>
</dl>
</p>
</body>
</html>