Golden Rectangle

Golden Rectangle
In my searching and experimenting with geometric construction I’ve come back to an idea here that I previously overlooked. The diagonals that divide the Golden Rectangle, cross at the site that the spiral tends toward. The spiral, no matter how many iterations of division you make, creating squares and Golden Rectangles, and drawing 90 degree arcs within the squares you divide, the spiral never reaches the point where the lines cross, yet it forever tends toward this point.

The crossing lines are also perfectly perpendicular to each other. And they, like arcs or quadrants made with the compass, define the borders between the squares divided out of each nested golden rectangle. These coincidences are fascinating. And it is fascinating how convenient they are for determining how well you have constructed your rectangle, especially when working with the compass and pencil, since this is prone to many errors that construction in geometry programs is not. But I still reserve my judgment about any mystical, or law of nature type of significance to the Golden Ratio. It seems to me that many of the attempts to find the golden ratio, or any geometric correspondences to human beauty or beloved designs often seems extremely arbitrary in the choice of parts measured and ad-hoc, freely moving whichever parts to where they seem to fit, if you ask me. I’m prepared to believe, though, that this is a useful guide to composition, and reflects, imperfectly, some powerful underlying principle in nature, and sometimes any guide to composition or proportion are going to be better than none. But it seems clear to me that you can get away with very approximate correspondences to these geometric ideals and still project the spirit of beauty and the height of elegance.

This image was created with a piece of software I discovered and began using for these geometric doodles in the time since my last upload, called Geogebra. Which makes geometric construction with precision much easier than any vector-graphics or even many CAD programs I’ve worked with.

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Or QR code here: www.flickr.com/photos/sightrays/8672657341/
By Electric-Eye on 2012-01-08 05:05:11
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