Tag: pentagon

Pentagon

2015-01-02
Pentagon

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=\(\frac12\sqrt{5-2\sqrt5}\)  

Phi, the Golden Ratio

Phi \((\Phi, \phi)\) is a Greek letter that mathematicians have assigned to a specific ratio or proportion, called the golden ratio, that most people find to be attractive in art, architecture, and nature. The golden ratio is illustrated as \(\frac{A}{B}=\frac{A+B}{A}\equiv\phi\). The only positive solution is …Read the Rest