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Golden section
(kultainen leikkaus)

Picture:

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

Mathematics:

Pentagon:

Single line:	a = side of the pentagon (lenght)
Area:	A_{_a} = (a²)/4 * Ö(25+10*Ö5)
Circumference:	p = 5a
Angle:	a = 180° * (5-2) / 5

Pentagram:

Longest line:
(golden section)

b = 1/2 * (Ö5 -1)	\| 1/(...)
b = 2 / (Ö5 -1)	\| *2a + a
b = a + 4a / (Ö5 -1)

Angle:

ß = 180° -a -a/2

Area:

A_{_p} = A_{_a} + 5 * A_{_s} | A_{_s}= (a²)/4 * tan(-a)
A_{_p} = (a²)/4 * Ö(25+10*Ö5) + 5 * (a²)/4 * tan(-a)
A_{_p} = (a²)/4 * ( Ö(25+10*Ö5) + 5*tan(-a) )

Circle:

Radius:	r_{_c} = a/10 * Ö(50+10*Ö5)
Circumference (circle):	p_{_c} = p * a/5 * Ö(50+10*Ö5)
Area (circle):	A_{_c} = p * (a/10)² * (50+10*Ö5)