The further in the sequence of Fibonacci, the closer the quotient of two succesive numbers approches the number [math]\Phi=1.618...[/math].[br]The applet below shows the result for rectangles.[list][*]A thin black line shows a rectangle in whitch the quotient [math]\frac{lenght}{width}[/math] equals the quotiënt of two successive numbers in the sequence of Fibonacci. By dragging the slider you always take the next quotient.[/*][*]A thicker blue line shows a golden rectangle with ratio [math]\frac{lenght}{width}=\Phi=\frac{\sqrt{5}+1}{2}=1.618...[/math][br][/*][/list]

The further in the sequence of Fibonacci the closer the quotient of two succesive numbers approaches the number [math]\Phi=1.618...[/math].[br]Already at the ratio [math]\frac{5}{3}[/math] the difference between both rectangles is fairly little and at [math]\frac{8}{5}[/math] the black rectangle disappears behind the thicker blue line.[br]So, why would you, when measuring dimensions on a picture say that the ratio is 'approximately' equal to [math]\Phi=1.618...[/math] instead of [math]\frac{3}{2}[/math], [math]\frac{5}{3}[/math] or [math]\frac{8}{5}[/math]?