Your article about the phi number in the da vinci code was awesome… I just want to tell you that when i tried it on various parts of my body, IT WORKED…it was amazing… :):):):)
THANK YOU
Welcome to the Straight Dope Message Boards, rf7627, we’re glad to have you with us.
For future ref, it’s helpful to other readers if you provide a link to the column when you start a thread. Saves search time and helps keep us all on the same page. In this case, I assume it’s: Is phi a mystical number as claimed in The Da Vinci Code? - The Straight Dope
No biggie, you’ll know for next time. And, as I say, welcome!
The exact value, by the way, is (1 + √5) / 2. (It only takes first-year algebra, but it’s too typographically messy to try to present it here.)
We have the definition ϕ[sup]2[/sup] = ϕ + 1, which is the same as saying (2ϕ - 1)[sup]2[/sup] = 5, as can be seen by distributing out (producing 4ϕ[sup]2[/sup] - 4ϕ + 1 = 5; i.e., 4ϕ[sup]2[/sup] = 4ϕ + 4; i.e., what we started with).
One special property of the Golden Ratio is that, informally, it is the “most irrational” number. (Its continued-fraction representation is the worst-case, [1,1,1,1,1,1,1,…], meaning it has only poor rational approximants.)
This property is useful in some heuristic scheduling algorithms.