Consider a line segment of length AB, point X divides AB into extreme and mean ratio if and only if AX or XB is the mean proportional of AB and the other length.
If X divides AB into extreme and mean ratio, then AB/AX = AX/XB or AB/XB = XB/AX. If length AB =1, then length AX =0.618, with the equivalent proportionality for
Then point X divides segment AB into the golden number (phi or golden section, mean, ratio, or divine proportion, division in extreme and mean ratio, etc.).

2. Read Clement Falbo's article on the Golden Ratio

Dr. Simon Singh hosts a discussion of the golden ratio on a BBC Radio 4 show about numbers. The program is about 14 minutes long. Click here then under Listen Again, click on radio show 3. Golden Ratio.