[FormerLurker]

Left out a square root sign, right at the beginning.

Funny, I don't notice any missing. Can you give me the equation that you're referring to?

[boris]

Right before "Things to Do":

Notice that earlier we defined Phi2 as Phi+1 and here we have g2 = 1–g or g2+g=1.

We can solve this in the same way as for Phi and we find that:

g =

and the math shows no square root symbol--at least on my browser.

[boris]

I viewed the source. The html is trying to show a square root but it is not being displayed. The problem is that the full reference to 'sqrt.gif' is not being used, only its short form, which is insufficient to tell the browser where to find it.

Euclid used this phrase to mean the ratio of the smaller part of this line, GB to the larger part AG (ie the ratio GB/AG) is the SAME as the ratio of the larger part, AG, to the whole line AB (ie is the same as the ratio AG/AB). If we let the line AB have unit length and AG have length g (so that GB is then just 1–g) then the definition means that

     GB = AG  or 1–g = g  so that 1–g=g2

     AG   AB      g    1

     

Notice that earlier we defined Phi² as Phi+1 and here we have g² = 1–g or g²+g=1.
We can solve this in the same way as for Phi and we find that

g =	–1 +5	or g =	–1 – 5