Ideal room dimensions for great system sound?

I know this is a reeeeeeally open-ended question, but what is in your opinion an ideal room size and dimensionn in which to put a great sounding system? For starters, let's say we are using a nice tube amp, a pair of legacy whispers, and a vpi super scoutmaster turntable? Let's not consider all the system tweeks, but maybe roon size, dimensions, and materials for and in the walls/ceilings. I have a large unfinished basement with 9 foot ceilings, and I am about start doing something with it.
Actually, the Fibonacci Series was named after an Italian mathematician named Leonardo of Pisa (c. 1170 - c. 1250) also known as "Fibonacci". He used it as an example in one of his writings.

Leonardo of Pisa

The earliest trace of this is not to the Greeks, but to the anciet writings of an Indian named "Pingala" in the 4th century BC.


The importance of this series on room design is, as Rodman points out, the avoidance of evenly divisible dimensions leading to overlapping room modes, as well as producing a pleasing room shape. I looked at a number of studies of room ratios, including one done by vast numbers of computer simulations of many potential combinations. The Fibonacci ratios fall nicely into the region of "best ratios". So while they are not the only ratios that can work, if you are starting out with the freedom to choose your ratios, I see no reason not to consider them.
Has anyone built a golden ratio room? And if so, where would the ideal speaker placement be?(according to the greeks!!!)
Golden ratio and Fibonacci series are mathmatically related.

The 'series' of Fibonacci is arrived at by starting with 0, 1 and adding them to produce the next number....0+1=1 .....Now, add the last 2 numbers AGAIN to produce the 4th number....1+1=2.
And so on.
By the time you get to 21 and 13, you can begin dividing them to get Phi, the right name for the Golden Ratio or Section.
Cool number. Phi squared = itself +1 and the SqRt is itself -1.

As for the origin? goes way back, but the Great Pyramid of about 4500BCE is made with that ratio. Pinga may have learned about it in Egypt as Pythagoras learned some 'sacred geometry' there, as well.
The ideal room dimensions would be none. But then, our home equipment isn't build for this and would sound quite small and lifeless.

Build yourself a nice comfortable room, not square, as large as you can and try to keep that height after adding a ceiling. Any money you were going to spend on the perfect room can be put to good room treatments. You will have a great room and you won't get all hung up on it.