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(71 votes) Published: Jan 03, 2009 8:50 a.m. In 1 Favorites Lists Viewed 880 times
How to make a Golden Rectangle.
For those of you who are not so savy in math, the a rectangle is golden (sometimes called perfect) if the ratio of one side to it’s perpendicular side is one to phi. This is one of the finest examples of the Fibonacci conspiracy. A golden rectangle is said to be the most astheticaly pleasing that a quadralateral can be. It occurs everywhere. The Greek Parthenon? A golden rectangle. In lay terms: It’s a shape that nature seems to like.
Here’s how to construct one. First, you’ll need the following items:
1. Pencil (multiple colors optional)
2. A compass (Or a pin and some string)
3. A ruled strait edge (I’m using a drafting square)
4. Some paper
(The pictures will help greatly, I’m sure)
*NB: I drew everything by hand first, but couldn’t get the lighting I needed with a crappy cell phone, so I traced the pictures in paint for clarity.
Step 1.
Draw a square.
Step 2.
Draw a bisecting line at the midpoint of one edge. You should have 2 equal rectangles.
Step 3.
Draw a line from the midpoint to the opposite corner.
Step 4.
This is where you will need a compass. If you don’t have one, simply tie a piece of string (or in this case, necklace cord) around a pin, and hold the pin in one hand on your point. Hold the pencil in the other hand at the other point (making a radius line with the sting) and use your thumb to keep the string taught against the pencil.
Step 5.
Make an arc by placing the pin of the compass on the midpoint and the pencil on the opposing corner (Step 3 but with the compass) and make an arc that runs from the corner to a point past the outside perimeter of your square.
Step 6.
Extend the lower side to intersect with the arc.
Jan 03, 2009 10:31 am - Thats the thing. It’s not just any rectangle. It’s a rectangle who’s sides form the ration phi. Phi is a number that occurs in nature with freakish consistancy. It’s the golden number, and it’s irrational (1.61803399).
The natalus shell? the ration is phi. Parthenon? Phi. The proportions on the human face? Phi. get it now?
Jan 03, 2009 11:31 am - I was looking at your last image, and thought to my self: "Self, that looks like the same ratio as your (25.6cm x 40.9cm) monitor". So I measured with your method, and I think it is! (Did I do it right?)
Jan 03, 2009 12:12 pm - Actually, yes. 25.6*1.6=40.9, so 25.6:40.9 = 1:1.6 (The golden ratio is 1:1.618...)
Crazy, I hadn’t even thought to check that.
Jan 03, 2009 6:56 pm - While the ‘golden rectangle’, ‘golden spiral’ and other ‘golden’ ratios do exist, most are man made. True, rectangles with this ratio are very pleasing to the eye, which is why designers of consumer products employed the dimensions. Monitors, matchboxes, and any number of other rectangular object. Some buildings come close by chance more than design, such as the Parthenon. However, nature is relatively oblivious to this ratio.
Author of the Da Vinci Code, Dan Brown (and many others such as George Cardas) claims these mathematical curiosities can be found in the nautilus shell. (I have only seen reference to this fact and can only recall the use of the Golden Ratio as a password.) The golden ration is found in a nautilus shell by measuring from the centre to the outer radius and dividing that by the distance from the centre to the inner radius. Most often the ratio of these shells is 3.104.
Please stand in a mirror and measure your face for the golden ratio. I really wonder if you do have a rectangular face. While is has been mentioned that the most beautiful women in the world do have faced proportioned close to the golden ratio, that is a matter of taste.
Postcards, credit card, photos and paintings, to name a few, all conform to the golden ratio but, obviously they are man made.
Quote:
This is one of the finest examples of the Fibonacci conspiracy.
Please make sure your facts are not related to the x-files, not part of folklore, taken seriously by real mathematicians and, above all else, tested to be valid by yourself.
Jan 03, 2009 7:12 pm - 1. I called it Fibonacci conspiracy as a joke. If you didn’t realize this, realize that you made an error and just want to move on, don’t continue reading this comment. If you still want to argue, continue.
2. The golden number is represented everywhere. Jackson Pollock paintings, for instance. Are you going to tell me he did that on purpose?
And I’m not saying to read anything into it. This is merely a guide to make a golden rectangle. Use it to build a fucking miniature Parthenon. I don’t care. I like Math. I decided to teach something pertaining to math that is Interesting.
I know the DaVinci Code is mostly bullshit. It was still an entertaining book.
The nautilus shell represents Phi in the way that one segment corresponds to the next. Its nearly a fractial pattern. i.e. segment 1: segment 2= 1:1.618...
The Face represents Phi in quite a few ways when taken in a broader sense. The head forms a golden rectangle with the eyes at its midpoint. The mouth and nose are each placed at golden sections of the distance between the eyes and the bottom of the chin. For fucks sake a persons ear often represents the same spiral as the stupid sea shell.
Before you tell me to quit making shit up, DO SOME RESEARCH YOURSELF. Geeze man, don’t hide behind superfluous writing and think you can knock everyone’s stuff.
-The great lord Kapraxis, ruler of all things and savior of worlds.
Jan 03, 2009 7:29 pm - I’ll be moving along, in a minute…
I voted your egg a 5*.
If you were semi-serious about your apparent appreciation of the math and application of it to nature, perhaps a little indication somewhere may be beneficial.
I tried very hard to be inoffensive and as factual as possible, with references where applicable.
While some of my post is personal opinion and parts are inaccurately reworded from other people’s web pages, I’ve always anagrammatically indicated when I may have created or incorporated fictional content in all of my posts by way of a footnote.
I made no intentional attack on you personally.
Lastly, I always write in this manner, with superfluous words or not.
J n 04, 2009 6:46 am - HOLY SHIT. This intrigued me so i went to research it on google and i typed in GOLDEN TRIANGLE. This is what popped up:
Quote:
The Golden Triangle is a region of Saint Charles County, Missouri, with Route 94 forming the east side; Interstate 70 the north; and U.S. Route 40 and U.S. Route 61 the south. The region has been the site of rapid growth since the 1980s. Cities found within the Golden Triangle include St. Charles, St. Peters, O’Fallon, Lake St. Louis, Dardenne Prairie, Cottleville, and Weldon Spring.
I live in St.Peters! Does this mean that im like the second coming of christ?
Jan 04, 2009 11:02 am - I remember watching a video about this in like 6th grade. You know...the one with Donald Duck and Goofy and Micky Mouse? Oookay well yeah, don’t really understand it but I’ll look into it later. 5* because my mommy said I could.
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