Pentagon

2015-01-02
Pentagon Dimensions

Pentagon Dimensions

A regular pentagon has the following dimensions:

AB=BC=CD=DE=AE=BG=EG=1 Height AH=EK=\(\frac12\cos 18 = \frac12\sqrt{5+2\sqrt5}\)
AC=AD=BD=BE=CE=Φ Circumcenter AJ=\(\frac{\sqrt{50+10\sqrt5}}{10}\)=BJ=CJ=DJ=EJ
BF=EF=Φ/2 Inradius JK=\(\frac{\sqrt{25+10\sqrt5}}{10}\)=HJ
CG=DG=Φ-1=1/Φ FH=\(\cos18 = \sqrt{\frac{5+\sqrt5}{8}}\)
AF=FG=cos 54= \(\sqrt{\frac{5-\sqrt5}{8}}\) FJ=JK/Φ
AG=\(2\cos 54 = \sqrt{\frac{5-\sqrt5}{2}}\) GJ=AJ/Φ
CH=DH=BK=CK=1/2 GH=AF/Φ=\(\frac12\sqrt{5-2\sqrt5}\)

 

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