Publishing equations without images

Fibonacci number is the sum of the two previous ones, yielding the sequence.

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ... .

Fibonacci numbers are related to the golden ratio ? and to its conjugate , which are given by the following

phi = [1 + sqrt{5}]/2 = 1.61803

 

bar{phi} = [1 + sqrt{5}]/2 = -0.61803

F_{i} = (phi -bar{phi}) / sqrt{5}

Note the above formulae are neither  image files on server  nor the special characters in HTML.

They are just images  which are dynamically generated by Google charts upon request with desired formula as parameter.

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