Golden section
(kultainen leikkaus)

 

Picture:

Golden section as pentagram and pentagon. Picture is selfdrawn line by line.

Golden section as pentagram and pentagon. Picture is selfdrawn line by line.

 

Mathematics:

Pentagon:

Single line: a = side of the pentagon (lenght)
Area: Aa = (a2)/4 * (25+10*5)
Circumference: p = 5a
Angle: a = 180 * (5-2) / 5


Pentagram:

Longest line:
(golden section)

 

b = 1/2 * (5 -1) | 1/(...)
b = 2 / (5 -1) | *2a + a
b = a + 4a / (5 -1)
Angle: = 180 -a -a/2
Area:

 

 

Ap = Aa + 5 * As                | As= (a2)/4 * tan(-a)
Ap = (a2)/4 * (25+10*5) + 5 * (a2)/4 * tan(-a)
Ap = (a2)/4 * ( (25+10*5) + 5*tan(-a) )


Circle:

Radius: rc = a/10 * (50+10*5)
Circumference (circle): pc = p * a/5 * (50+10*5)
Area (circle): Ac = p * (a/10)2 * (50+10*5)

 

 

Copyright 2003 Kim Ervasti
http://doom.servehttp.com/penta/