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I'm making screens for my backyard and figured a pleasing shape would be the golden rectangle but I forgot the formula and my connection to the net via IE seems to be down at the moment.

The ratio of the sides is a little over 1.6

Steve

------------- the golden ratio = 1.61803399

Can't you just round it up to 2?

Regards, JT

i.e., (sqrt(5)+1)/2 But the estimates of 1.6, 1.62, or 1.618 are likely about as close as you want.

There is a whole (almost) cult that regards the Fibonacci series as holy. It turns out that the ratio of ~8:5 is very pleasing to the eye. That's all in a single sentence.

Look up Fibonacci, golden rule, golden ratio on you favorite search engine. Then go to Amazon and do the same. Finally go to your local library and read some <grin>.

Thanks Han, I understand clearly now!!

Oldun

My head is spinning! That strikes me as a very convoluted way of saying "take the rectangle and eliminate a square with side equal to the shorter side of the rectangle. What is left is another rectangle with the same proportion.

I have never heard of this definition of Golden Mean. Every place I have seen it, it is used as a synonym for golden ratio. The diagonal of a golden rectangle with sides 1 and 1.618 would be about 1.902. are you saying that this is the Golden mean, different from Phi or phi?

That's my understanding (although the trig representation seems superfluous--then again, trig was never my favorite math subject<g>) And of course, the interesting (and defining) relationship is that phi=1/Phi=Phi-1

BTDT<g>.

Well, you did say "and the diagonal (mean) of this rectangle is called the Golden Mean", after having already correctly defined the golden ratio. Since a diagonal is a line segment (which I have never heard referred to as a mean), I assumed (always dangerous<g>) that you meant the length of the diagonal. Especially since you were describing it as something distinct from the golden ratio.

(or diagonal). Yep

I agree, although I have never heard the length of a hypotenuse referred to as a mean either.

No, that was a separate post, which I have saved to try out and compare to another method that I posted in response to that post. I was talking about the description in this post, that appeared to be the feature of removing a square from a golden rectangle, leaving the same shape.

I have to concede that point--

From my dictionary, there are three derivatives of the American English word "mean" 1- common heritage with German word meinem, to have in mind 2- old English derived from /for common, common place 3- a derivative from Latin similar to median.

And from the 3ed dictionary entry, there is currently a seldom usage of the word "mean" or "median" to be a straight line with longest length that can be drawn inside any 2 dimensional geometric figure. The "mean" is the line, not its length dimension. Thus in a rectangle, the diagonal is the longest line, the diagonal is also the "mean" of the rectangle. And since I use the word interchangeably with diagonal, yes, I am showing my age. It seems to have more common usage as in Mean Distance in orbital mechanics of planets and satellites.

Phil

Well, I sure learned something! I guess my statistics background blinded me to other meanings (just as it raises my hackles to see it equated with "median"<g>)

Also (more commonly?) known as the geometric mean.

Interesting. I had to draw a picture, but then it is obvious, because of the similar triangles (is that the right term for identical angles, but not identical sides? 8th grade was a LONG time ago!<G>) created.

#### Site Timeline

- posted on April 21, 2005, 8:17 pm

I'm making screens for my backyard and figured a pleasing shape would be the golden rectangle but I forgot the formula and my connection to the net via IE seems to be down at the moment.

- posted on April 21, 2005, 8:25 pm

Steve

- posted on April 21, 2005, 9:02 pm

------------- the golden ratio = 1.61803399

- posted on April 21, 2005, 10:22 pm

Can't you just round it up to 2?

Regards, JT

- posted on April 21, 2005, 9:08 pm

There are many formulas but the simplest is
1/x = x-1
Which leads to the quadratic
x^2 -x -1 = 0
(ignore the negative root).

Art

I'm making screens for my backyard and figured a pleasing shape would be the golden rectangle but I forgot the formula and my connection to the net via IE seems to be down at the moment.

Art

I'm making screens for my backyard and figured a pleasing shape would be the golden rectangle but I forgot the formula and my connection to the net via IE seems to be down at the moment.

- posted on April 21, 2005, 9:25 pm

i.e., (sqrt(5)+1)/2 But the estimates of 1.6, 1.62, or 1.618 are likely about as close as you want.

--

Alex -- Replace "nospam" with "mail" to reply by email. Checked infrequently.

Alex -- Replace "nospam" with "mail" to reply by email. Checked infrequently.

- posted on April 22, 2005, 12:54 am

nick walsh wrote:

be the

net via IE

Quick and dirty:

8 to 5.

-Phil Crow

be the

net via IE

Quick and dirty:

8 to 5.

-Phil Crow

- posted on April 22, 2005, 7:31 am

snipped-for-privacy@yahoo.com wrote:

Or actually, the ratio of any two successive Fibonacci (sp?) numbers, depending on the accuracy you want. The F numbers is the sequence where each number is the sum of the previous two: 0,1,1,2,3,5,8,13,21,34,55,89,...

8:5 gives 1.6, probably good enough for any practical purpose in design, IMHO. Using it to proportion a door 78" tall gives a width of 48-3/4". Using 55 and 34 gives you a width of 48.218", which is within 1/64" of "true". 8:5 sounds like a darned good rule of thumb to me!

Or actually, the ratio of any two successive Fibonacci (sp?) numbers, depending on the accuracy you want. The F numbers is the sequence where each number is the sum of the previous two: 0,1,1,2,3,5,8,13,21,34,55,89,...

8:5 gives 1.6, probably good enough for any practical purpose in design, IMHO. Using it to proportion a door 78" tall gives a width of 48-3/4". Using 55 and 34 gives you a width of 48.218", which is within 1/64" of "true". 8:5 sounds like a darned good rule of thumb to me!

--

Alex -- Replace "nospam" with "mail" to reply by email. Checked infrequently.

Alex -- Replace "nospam" with "mail" to reply by email. Checked infrequently.

- posted on April 22, 2005, 10:22 am

Could someone please explain what on earth the "Golden Triangle" is, and how
is it used in designing a screen?

A clear explaination or simple sketch would help my ignorance.

Thanks.

Oldun

A clear explaination or simple sketch would help my ignorance.

Thanks.

Oldun

- posted on April 22, 2005, 10:50 am

There is a whole (almost) cult that regards the Fibonacci series as holy. It turns out that the ratio of ~8:5 is very pleasing to the eye. That's all in a single sentence.

Look up Fibonacci, golden rule, golden ratio on you favorite search engine. Then go to Amazon and do the same. Finally go to your local library and read some <grin>.

--

Best regards

Han

email address is invalid

Best regards

Han

email address is invalid

Click to see the full signature.

- posted on April 22, 2005, 11:27 am

Thanks Han, I understand clearly now!!

Oldun

- posted on April 22, 2005, 2:52 pm

Oldun:

Take any rectangle (which is not a square), there is one side longer than the other.

A very long time ago someone discovered that there is / was one, and only one, combination of dimensions of a rectangle that:

if you take the smaller side length and make that the long side of another rectangle and you take the difference in length of the smaller from the larger and use that difference as the smaller length in the new rectangle, you end up with the same ratio of sides as before. Thus the next smaller rectangle can be constructed. And repeat, and repeat,......

This very specific ratio of sides that have an infinite repeatable number of smaller rectangles of same ratio of sides is called the golden ratio and a rectangle of this golden ratio is called the golden rectangle, and the diagonal (mean) of this rectangle is called the Golden Mean.

A golden rectangle in and of itself is not that great. It is the rectangle within the rectangle within the rectangle that counts:

classic Greek statue: the whole statue can be boxed by golden rectangle the head can be boxed by golden rectangle the eyes also can be boxed by golden rectangle.

Engineers, and other calculator (slide rule) types are fascinated by Golden Rectangle, Golden Mean, and so forth. As in AH-HA, a math formula for creating ART!! (****** Art does not work well with Math formulas in real life,
trust me. ******)

Phil

Take any rectangle (which is not a square), there is one side longer than the other.

A very long time ago someone discovered that there is / was one, and only one, combination of dimensions of a rectangle that:

if you take the smaller side length and make that the long side of another rectangle and you take the difference in length of the smaller from the larger and use that difference as the smaller length in the new rectangle, you end up with the same ratio of sides as before. Thus the next smaller rectangle can be constructed. And repeat, and repeat,......

This very specific ratio of sides that have an infinite repeatable number of smaller rectangles of same ratio of sides is called the golden ratio and a rectangle of this golden ratio is called the golden rectangle, and the diagonal (mean) of this rectangle is called the Golden Mean.

A golden rectangle in and of itself is not that great. It is the rectangle within the rectangle within the rectangle that counts:

classic Greek statue: the whole statue can be boxed by golden rectangle the head can be boxed by golden rectangle the eyes also can be boxed by golden rectangle.

Engineers, and other calculator (slide rule) types are fascinated by Golden Rectangle, Golden Mean, and so forth. As in AH-HA, a math formula for creating ART!! (

Phil

- posted on April 22, 2005, 10:03 pm

Thanks everybody who replied to my question about these golden triangles. I
now know what you were talking about. A Google search was also a great help,
damn should have asked Google first instead of broadcasting my ignorance.

Cheers. Oldun

Cheers. Oldun

- posted on April 23, 2005, 12:17 am

My head is spinning! That strikes me as a very convoluted way of saying "take the rectangle and eliminate a square with side equal to the shorter side of the rectangle. What is left is another rectangle with the same proportion.

I have never heard of this definition of Golden Mean. Every place I have seen it, it is used as a synonym for golden ratio. The diagonal of a golden rectangle with sides 1 and 1.618 would be about 1.902. are you saying that this is the Golden mean, different from Phi or phi?

--

Alex -- Replace "nospam" with "mail" to reply by email. Checked infrequently.

Alex -- Replace "nospam" with "mail" to reply by email. Checked infrequently.

- posted on April 23, 2005, 2:05 am

Alexy:

AFAIK----

Phi (capital) is the ratio of large side to small side, or co-tangent of angle of large side to diagonal of the golden rectangle.

phi (lower case) is the ratio of small side to large side, or the tangent of the angle of the large side to the diagonal of the golden rectangle.

I saw one reference where this angel is called tau (lower case) and the complementary angle is Tau (capital)

I guess I was sloppy in my wording. I should have always stated golden mean ratio and not just golden mean, which could imply I was talking about the length of the diagonal of the golden rectangle. I am going to presume you got the 1.906 as a length of the hypotenuse (mean) which AFAIK, is not used or noted.

Do you have other information?

As far as being convoluted, using words to describe a very simple graphical technique, yes it does become convoluted because of the words. But you just may have to take my word that USING the graphical technique is fast and can be fairly accurate. The graphical technique is really simple to use in which to make marks on a story stick for all the dimensions needed for a series of golden rectangles. Which is how this thread got started; the need to make marks on wood which would, when cut and assembled, end up with a golden rectangle door.

BTW: source of some of my information: FWW September 1987 pages: 66:76-81 (sidebar to main article on Wall Paneling.) Article republished in Best of Fine Woodworking Traditional Woodworking Techniques by Tauton Press. Aside: there is a typo in the reprint sidebar. You will need to re-work the math for it to match the numbers found at web sites by google Golden Rectangle. step 3 should read: 0.61803.... not 0.01803...

In constructing the great churches and cathedrals in Europe, the carpenters, stone masons, and the like are not going to calculate no Fibonacci number or the like.

Phil

AFAIK----

Phi (capital) is the ratio of large side to small side, or co-tangent of angle of large side to diagonal of the golden rectangle.

phi (lower case) is the ratio of small side to large side, or the tangent of the angle of the large side to the diagonal of the golden rectangle.

I saw one reference where this angel is called tau (lower case) and the complementary angle is Tau (capital)

I guess I was sloppy in my wording. I should have always stated golden mean ratio and not just golden mean, which could imply I was talking about the length of the diagonal of the golden rectangle. I am going to presume you got the 1.906 as a length of the hypotenuse (mean) which AFAIK, is not used or noted.

Do you have other information?

As far as being convoluted, using words to describe a very simple graphical technique, yes it does become convoluted because of the words. But you just may have to take my word that USING the graphical technique is fast and can be fairly accurate. The graphical technique is really simple to use in which to make marks on a story stick for all the dimensions needed for a series of golden rectangles. Which is how this thread got started; the need to make marks on wood which would, when cut and assembled, end up with a golden rectangle door.

BTW: source of some of my information: FWW September 1987 pages: 66:76-81 (sidebar to main article on Wall Paneling.) Article republished in Best of Fine Woodworking Traditional Woodworking Techniques by Tauton Press. Aside: there is a typo in the reprint sidebar. You will need to re-work the math for it to match the numbers found at web sites by google Golden Rectangle. step 3 should read: 0.61803.... not 0.01803...

In constructing the great churches and cathedrals in Europe, the carpenters, stone masons, and the like are not going to calculate no Fibonacci number or the like.

Phil

- posted on April 23, 2005, 5:03 am

That's my understanding (although the trig representation seems superfluous--then again, trig was never my favorite math subject<g>) And of course, the interesting (and defining) relationship is that phi=1/Phi=Phi-1

BTDT<g>.

Well, you did say "and the diagonal (mean) of this rectangle is called the Golden Mean", after having already correctly defined the golden ratio. Since a diagonal is a line segment (which I have never heard referred to as a mean), I assumed (always dangerous<g>) that you meant the length of the diagonal. Especially since you were describing it as something distinct from the golden ratio.

(or diagonal). Yep

I agree, although I have never heard the length of a hypotenuse referred to as a mean either.

No, that was a separate post, which I have saved to try out and compare to another method that I posted in response to that post. I was talking about the description in this post, that appeared to be the feature of removing a square from a golden rectangle, leaving the same shape.

--

Alex -- Replace "nospam" with "mail" to reply by email. Checked infrequently.

Alex -- Replace "nospam" with "mail" to reply by email. Checked infrequently.

- posted on April 23, 2005, 1:45 pm

I have to concede that point--

From my dictionary, there are three derivatives of the American English word "mean" 1- common heritage with German word meinem, to have in mind 2- old English derived from /for common, common place 3- a derivative from Latin similar to median.

And from the 3ed dictionary entry, there is currently a seldom usage of the word "mean" or "median" to be a straight line with longest length that can be drawn inside any 2 dimensional geometric figure. The "mean" is the line, not its length dimension. Thus in a rectangle, the diagonal is the longest line, the diagonal is also the "mean" of the rectangle. And since I use the word interchangeably with diagonal, yes, I am showing my age. It seems to have more common usage as in Mean Distance in orbital mechanics of planets and satellites.

Phil

- posted on April 23, 2005, 2:36 pm

Well, I sure learned something! I guess my statistics background blinded me to other meanings (just as it raises my hackles to see it equated with "median"<g>)

--

Alex -- Replace "nospam" with "mail" to reply by email. Checked infrequently.

Alex -- Replace "nospam" with "mail" to reply by email. Checked infrequently.

- posted on April 23, 2005, 6:07 pm

On Sat, 23 Apr 2005 09:45:43 -0400, "Another Phil" <NoSpamming@one two
three four five.com> wrote:

Let's get it right:

The term "Mean" refers to the fact of it being a "Mean Proportional". The Mean proportional value, x, between two other values, a and b, is such that a/x = x/b.

Writing the proportion [equal ratios] 1/x = x/(x+1) defines "x" as the mean proprtional between 1 and x+1. There is no advantage except as consistent terminology, and this proportion gives the value needed for "x".

An "image" of a mean proplrtional is found by dawing a right triangle, then the distance from the right angle to the hypoteneuse is a mean proportional of the divisions it makes with the hypotenuse of that tgriangle.

The "median" of a triangle joins a vertex to the mid-point of the opposite side. It is easy to see that you can draw a line longer than that in general. The longest line in a polygon is a "diagonal".

Let's get it right:

The term "Mean" refers to the fact of it being a "Mean Proportional". The Mean proportional value, x, between two other values, a and b, is such that a/x = x/b.

Writing the proportion [equal ratios] 1/x = x/(x+1) defines "x" as the mean proprtional between 1 and x+1. There is no advantage except as consistent terminology, and this proportion gives the value needed for "x".

An "image" of a mean proplrtional is found by dawing a right triangle, then the distance from the right angle to the hypoteneuse is a mean proportional of the divisions it makes with the hypotenuse of that tgriangle.

The "median" of a triangle joins a vertex to the mid-point of the opposite side. It is easy to see that you can draw a line longer than that in general. The longest line in a polygon is a "diagonal".

- posted on April 23, 2005, 6:55 pm

Also (more commonly?) known as the geometric mean.

Interesting. I had to draw a picture, but then it is obvious, because of the similar triangles (is that the right term for identical angles, but not identical sides? 8th grade was a LONG time ago!<G>) created.

--

Alex -- Replace "nospam" with "mail" to reply by email. Checked infrequently.

Alex -- Replace "nospam" with "mail" to reply by email. Checked infrequently.

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