Differences

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--- math:geometry [2025/12/01 22:00] – ron
+++ math:geometry [2025/12/01 22:05] (current) – ron
@@ Line 13: / Line 13: @@
 ### Pentagon
   * Θ = 360/5 = 72 degrees (2π/5 radians)
-  * s = R * √(2 - 2 * cos(72-deg))
+  * s = R * √(2 - 2 * cos(72-deg)); cos(72) = (-1 + √(5)) / 4 (see [this](https://www.quora.com/How-can-I-get-the-fraction-value-of-cos-72))
-      * cos(72) = (-1 + √(5)) / 4
+    * = R * √(2 - 2 * (-1 + √(5)) / 4) = R * √(2 - (-1 + √(5)) / 2) = R * √( (4 + 1 - √5)/2)
-      * see [this](https://www.quora.com/How-can-I-get-the-fraction-value-of-cos-72)
+    * = R * √( (5 - √5)/2)
-    * = R * √(2 - 2 * (-1 + √(5)) / 4) = R * √(2 - (-1 + √(5)) / 2) = R * √((4 + 1 - √5)/2)
-    * = R * √((5 - √5)/2)
     * ≅ R * 1.17557
 ### Hexagon
   * Θ = 360/6 = 60 degrees
-  * s = R * √(2 - 2 * cos(60-deg)) = R * √(2 - 2 * 0.5) = R * √(1)= R
+  * s = R * √(2 - 2 * cos(60-deg)) = R * √(2 - 2 * 0.5) = R * √(1)
+    * = R