User:Hopex/Vitruvian Woman

Some useful numbers.

$$\sqrt{2} \approx 1.414$$

$$\tfrac{1}{\sqrt{2}} \approx 0.707$$

$$\tfrac{24}{34} \approx 0.706$$

Showing the properties of a &radic;2 aspect ratio.

$$\tfrac{a}{b} = \tfrac{b/2}{a}$$

$$a^2 = \tfrac{b^2}{2}$$

$$a = \tfrac{b}{\sqrt{2}}$$

$$\tfrac{a}{b} = \tfrac{1}{\sqrt{2}}$$

$$a \cdot \sqrt{2} = b$$

Simple proof to show if circumferences are in &radic;2 ratio and approximated to circles, then diameters are in &radic;2 ratio also.

$$\tfrac{c^W}{c^H} = \tfrac{1}{\sqrt{2}}$$

$$c^W \cdot \sqrt{2} = c^H$$

$$d^W \cdot \pi = c^W$$

$$d^H \cdot \pi = c^H = c^W \cdot \sqrt{2}$$

$$d^W = \tfrac{c^W}{\pi}$$

$$\tfrac{d^H}{\sqrt{2}} = \tfrac{c^W}{\pi}$$

$$d^W = \tfrac{d^H}{\sqrt{2}}$$

$$d^H \cdot \sqrt{2} = d^H$$