Oh, Dearest Mother, Sweetest Virgin of Altagracia, our Patroness. You are our Advocate and to you we recommend our needs. You are our Teacher and like disciples we come to learn from the example of your holy life. You are our Mother, and like children, we come to offer you all of the love of our hearts. Receive, dearest Mother, our offerings and listen attentively to our supplications. Amen.



Active Topics || Favorites || Member List || Search || About Us || Help || Register || Login
Living and Loving Numbers
 4Real Forums : Living and Loving Numbers
Subject Topic: Golden Mean -- Rectangle Post ReplyPost New Topic
Author
Message << Prev Topic | Next Topic >>
JennGM
Forum Moderator
Forum Moderator
Avatar

Joined: Feb 07 2005
Location: Virginia
Online Status: Offline
Posts: 17702
Posted: June 13 2012 at 4:22pm | IP Logged Quote JennGM
I'm trying to figure out how to apply the Golden Mean to some booklets I am creating.

Problem is, I don't remember learning anything about the Golden Ratio or Golden Rectangle or Golden Mean or Golden Section. NOTHING.

We watched Donald Duck in Mathmagic Land which gave me a better idea of what it is and a bit how to figure it out, but I'm still confused.

I'm trying to figure out proportions for a booklet and can't seem to APPLY this knowledge very well.

The booklet needs to be about 7 inches tall (about, give or take an inch). So how do I figure out the width so that it is proportional as in nature? This is the cover.

And then the inside needs to be just smaller, but proportional, also.

I'm totally feeling inadequate here... HELP????

__________________
Jennifer G. Miller
Wife to & ds1 '03 & ds2 '07
Family in Feast and Feria
Back to Top View JennGM's Profile Search for other posts by JennGM Visit JennGM's Homepage
 
JodieLyn
Forum Moderator
Forum Moderator
Avatar

Joined: Sept 06 2006
Location: Oregon
Online Status: Offline
Posts: 12234
Posted: June 13 2012 at 4:37pm | IP Logged Quote JodieLyn
ummm steal from pictures? since a picture with a long side of 7 inches would have a width of 5 inches.. then just put a half inch margin around the text for 6x4.

__________________
Jodie, wife to Dave
G-18, B-17, G-15, G-14, B-13, B-11, G-9, B-7, B-5, B-4

All men who have turned out worth anything have had the chief hand in their own education.
-Sir Walter Scott
Back to Top View JodieLyn's Profile Search for other posts by JodieLyn
 
JennGM
Forum Moderator
Forum Moderator
Avatar

Joined: Feb 07 2005
Location: Virginia
Online Status: Offline
Posts: 17702
Posted: June 13 2012 at 5:13pm | IP Logged Quote JennGM
JodieLyn wrote:
ummm steal from pictures? since a picture with a long side of 7 inches would have a width of 5 inches.. then just put a half inch margin around the text for 6x4.


I know I could steal from pictures, but I kind of wanted to be able to figure it out a bit...understand what I'm doing.

__________________
Jennifer G. Miller
Wife to & ds1 '03 & ds2 '07
Family in Feast and Feria
Back to Top View JennGM's Profile Search for other posts by JennGM Visit JennGM's Homepage
 
Maryan
Forum All-Star
Forum All-Star
Avatar

Joined: Jan 02 2007
Online Status: Offline
Posts: 3145
Posted: June 13 2012 at 6:35pm | IP Logged Quote Maryan
Woodworking explanation of golden section

"The long dimension of a golden rectangle is 1.618 times greater than the shorter dimension."

So... I *think* if you wanted your longer side to be 7 inches than you would divide 7 by 1.618 which is about 4.3 inches.

But I would ask our friend Pete S.

__________________
Maryan
Mom to 6 boys & 1 girl: JP('01), B ('03), M('05), L('06), Ph ('08), M ('10), James born 5/1/12
A Lee in the Woudes
Back to Top View Maryan's Profile Search for other posts by Maryan
 
Maryan
Forum All-Star
Forum All-Star
Avatar

Joined: Jan 02 2007
Online Status: Offline
Posts: 3145
Posted: June 13 2012 at 6:42pm | IP Logged Quote Maryan
Hmm... I just cut that out and it doesn't seem right. Another option using the golden section ration (if I'm doing it correctly) is if your long side is 8", then the width would be 4.94... which is close to 8" x 5" and that seems to look better to me.

It could also be as Jodie pointed out that my eye is accustomed to paper (or photos) to be certain sizes?

__________________
Maryan
Mom to 6 boys & 1 girl: JP('01), B ('03), M('05), L('06), Ph ('08), M ('10), James born 5/1/12
A Lee in the Woudes
Back to Top View Maryan's Profile Search for other posts by Maryan
 
CrunchyMom
Forum Moderator
Forum Moderator
Avatar

Joined: Sept 03 2007
Online Status: Offline
Posts: 6385
Posted: June 13 2012 at 7:32pm | IP Logged Quote CrunchyMom
Well, a rule of thumb is that the golden mean is roughly 2/3s, so if you have a height in mind, the width would be roughly 2/3s of it.

If you want to better understand just what it is you are doing, you can think about the golden mean in relation to the Fibonacci sequence: 1, 1, 2, 3, 5, 8, 13, and so on. The mean is the ratio between the two, so you can find the golden mean by dividing a lower number in the sequence by the following number. This is more accurate the higher you go in the sequence.

For instance, 8/13 is .61538..., leaving .38 as the approximate ratio. .38x7 is 2.66, and 2.66/.61532 will leave you with 4.3225

So, I would probably go with 4.3 inches if I wanted to be "fussy" about making a golden rectangle from a height of 7.

So, Maryan's original answer is correct.

There might be a reason that doesn't look "right" to her.

In terms of making a booklet, you might visually see the spine or side margin as "extra" depending on how you bind it. So, perhaps your eye wants to make the golden mean happen spacially to the side. Does that make sense?

Hope that helps. I'm sure the article from Fine Woodworking is excellent as well and probably much better than my convoluted methods. It was the way it was first explained to me (in my music history class, oddly), and I've thought of it that way since. My husband has different way of processing it when he's assessing his carpentry designs, so it is probably just a matter of preference how you choose to do the math and evaluate.

__________________
Lindsay
Five Boys(6/04) (6/06) (9/08)(3/11),(7/13), and 1 girl (5/16)
My Symphony

[URL=http://mysymphonygarden.blogspot.com/]Lost in the Cosmos[/UR
Back to Top View CrunchyMom's Profile Search for other posts by CrunchyMom
 
AtHomeScience
Forum Pro
Forum Pro
Avatar

Joined: Oct 29 2009
Location: Massachusetts
Online Status: Offline
Posts: 154
Posted: June 13 2012 at 9:31pm | IP Logged Quote AtHomeScience
If you do have some play in the size then you could use the Fibonacci sequence like Lindsay said to get the golden ratio, ie. make it 8 x 5 and you know it must be the right proportion.

__________________
Kris, Mom to 3 rambunctious boys
At Home Science
A Private Eye Nature
Science Of Relations
Back to Top View AtHomeScience's Profile Search for other posts by AtHomeScience Visit AtHomeScience's Homepage
 
CrunchyMom
Forum Moderator
Forum Moderator
Avatar

Joined: Sept 03 2007
Online Status: Offline
Posts: 6385
Posted: June 14 2012 at 6:15am | IP Logged Quote CrunchyMom
AtHomeScience wrote:
If you do have some play in the size then you could use the Fibonacci sequence like Lindsay said to get the golden ratio, ie. make it 8 x 5 and you know it must be the right proportion.


Yes, or find a unit of measurement to fit the Fibonacci numbers that will get you closer to your desired size but easier to measure accurately than weird decimals.

You could use centimeters instead of inches.

Or, you could use half inches or even quarter inches with the bigger numbers.

For instance, 8x13 half inches would end up as 4x6.5 inches, a bit easier to measure than 4.3x7 but closer to your desired size and more "perfect" than the standard 4x6 .

__________________
Lindsay
Five Boys(6/04) (6/06) (9/08)(3/11),(7/13), and 1 girl (5/16)
My Symphony

[URL=http://mysymphonygarden.blogspot.com/]Lost in the Cosmos[/UR
Back to Top View CrunchyMom's Profile Search for other posts by CrunchyMom
 
MaryM
Board Moderator
Board Moderator
Avatar

Joined: Feb 11 2005
Location: Colorado
Online Status: Offline
Posts: 13104
Posted: June 18 2012 at 2:48am | IP Logged Quote MaryM
CrunchyMom wrote:
I'm sure the article from Fine Woodworking is excellent as well


That article does have a great method that could be used with paper. Any golden rectangle can be made proportionally smaller or larger very easily with that bisect method illustrated.

Scale a golden rectangle
Using a golden rectangle of any size, you can create another golden rectangle with different dimensions. Simply draw a golden rectangle and bisect it with a diagonal line that stretches from one corner to another. Then extend the diagonal line. Any rectangle that shares this diagonal, whether it is smaller or larger, will be golden.


CrunchyMom wrote:
Yes, or find a unit of measurement to fit the Fibonacci numbers that will get you closer to your desired size but easier to measure accurately than weird decimals.

You could use centimeters instead of inches.


...or even going with millimeters. I found chart on this website which give the relation of the golden ratio to the Fibonacci sequence. The higher you go in the sequence the closer it comes to estimating the ratio, hence the use of millimeters would allow you to fit a sample golden rectangle on paper to manipulate in size with that bisect method.



__________________
Mary M. in Denver

Our Domestic Church
Back to Top View MaryM's Profile Search for other posts by MaryM Visit MaryM's Homepage
 

If you wish to post a reply to this topic you must first login
If you are not already registered you must first register

  [Add this topic to My Favorites] Post ReplyPost New Topic
Printable version Printable version

Forum Jump
You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot delete your posts in this forum
You cannot edit your posts in this forum
You cannot create polls in this forum
You cannot vote in polls in this forum

Hosting and Support provided by theNetSmith.com