Are you sure you have written it correctly? As I read it now it would vary with different scales: One side is twice as long as the other plus one unit of measurement. For example: if n equals one meter, the other side equals three meters - one side is therefore one third of the other. But if n equals half a meter, the other side equals two meters - one side is then half of the other? Or is it a series of numbers approaching a proportion of 0,5? 0,1,3,7,15,31,63 etc.

thank you for your comments. As I understand, the proportion does indeed change. When n=1, it is as you say 1:3. but as n grows larger and larger, the ratio more approaches 1:2 (plus an increment). I was put on this formula by Janosh in his comments in the thread
http://www.archinect.com/forum/threads.php?id=18751_0_42_0_C
I hope Janosh has got it right. It would help if we had an expert out there to comment.

again with this ratio thing? what's the deal?

Maybe Alberto Perez-Gomez has written something on the subject. Check "Architecture and the crisis of modern science", specifically the section about Francois Blondel and Claude Perrault. If I remember it correctly, historically there have been numerous different proposals for the proportions of columns, of which some authors have attributed the deviations to "perspective correction".

Sorry, the aforementioned book doesn't have anything on the specific formula, but is good reading anyway.... just flipped it through it at home.

thanks anyway, it was considerate of you to suggest it

sorry to revisit this formula: it comes back like an unwanted ghost to haunt me. One possible reason for the enduring appeal of the Parthenon (there are many other theories, I imagine). Perhaps I am lost in some sort of hell here. If I were a PhD I could explore with intellectual rigour. But, alas, I am an amateur. Hence condemned to wander from theory to theory and never find rest. They say the truth will out. Music has its intervals: time architecture settled on ITS intervals. Tell me at once if I'm spouting garbage.

If you do some research on the meaning of the proportions of the Parthenon you'll find that many feel that the Parthenon does NOT follow this ratio. A 2n +1 ratio would mean that the Parthenon is based on a 4:9 system, which is something that is often stated. But there is a lot of evidence for a 4:6, 6:9 system - in other words a geometry that builds on a simple "two thirds" system.

I was referring only to the columns of the Parthenon, and there are indeed 8 columns across the front and 17 down the side which is n:2n+1
or 8:2x8 + 1 = 8:17


I was not referring to the proportions of the Parthenon, but the arrangement of columns down the long and across the short sides.

are we talking about phi, here?
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if by phi you mean the Golden Section: no this is not it.

pi = 3.14
golden section ratio= 1:1.618
another interesting bit of numerology is the fibonaci sequence...
0, 1, 1, 2, 3, 5, 8, 13...etc

steve holl often uses these kinds of proportions, especially when he gets all decorative. i believe there was an explanation of the use of number and proportion in "questions of perception" with m. Alberto Perez-Gomez contributing a cent or two as well.

these numbers are fun to play with but are of the same sort of tool as eisenmann's formulaed adventures with form-z. the formula helped to generate form but he was pretty specific about which bits he used and that all comes down to intuition again...so if you don got the eye to begin with, the numbers don' help nun really.

I suppose these are all just abstract methodologies for the generation of form, but the proof of the pudding is in the eating. If they generate ugly designs they are useless methodologies. Curious, yes, but still useless.

Amen devlin, I used to be all keen on this type of proporationalism but after a while I was getting away from the "architecture." But still I do like to read about it. rather fascinating that folks like Eisenman can give a "spin" to clients about some farse he's whipped up on FormZ