## Geometry

2015-01-02

A regular pentagon has the following dimensions: AB=BC=CD=DE=AE=BG=EG=1 AC=AD=BD=BE=CE=Φ BF=EF=Φ/2 = cos 36 = sin 54 = $\frac{1+\sqrt{5}}{4}$ CG=DG= Φ-1 = 1/Φ = $\frac{\sqrt5-1}{2}$ AF=FG= cos 54 = sin 36 = $\sqrt{\frac{5-\sqrt5}{8}}$ AG= 2cos 54 = 2sin 36= $\sqrt{\frac{5-\sqrt5}{2}}$ CH=DH=BK=CK=1/2 Height AH=EK=$\frac12\cos 18 = \frac12\sin …Read the Rest ### Phi, the Golden Ratio 2011-10-23 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

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