Hello everyone, I have been pondering a problem that I hope someone here can help with. I am trying to figure out how to construct a golden rectangle by starting with just one line and using only a compass or straight edge. In other words, if I have a line of any given length, how does one go about constructing a golden rectangle from it? I haven't studied geometry in a long while and the method for producing a true right angle using only these two tools evades me. Don't have any real purpose for this, it was just a thought I had the other day and I can't give up on it. Thanks!
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Austin
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Unsu...
Re: Golden Rectangle from a line?
Tue, November 22, 2005 - 7:14 AMI'm assuming that this question arrose from something you read about
the golden ratio being the division of a line so the smaller to the larger equals the larger to the whole. a/b=b/(a+b)
What does this mean? What is a golden rectangle?
Why is it so interesting?
What is the golden ratio? What species of number is it?
Is there anything else you need to know in order to construct it?
Have you constructed any other idea/forms with compass and ruler that you can build on?
A few years ago I would probably just have told you how to do it all.
But what learning will come out of that?
Tell me what you know and perhaps I can help guide you toward the discovery.
Dan
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Re: Golden Rectangle from a line?
Tue, November 22, 2005 - 3:18 PMHi Gary,
I did this to explain how I would do it, knowing that there are many creative ways to use the geometric construction sequences...
orbitalmonkeys.com/phiseg.jpg
I have not created a PHI rectangle, but I am showing how to find PHI on any arbitrary segment.
You will probably be able to expand on it.
Dan, I think it is great that you are very interested in this stuff, the language of abstraction, as the Greeks call it. I read in some other comments that you caution calling the number 1.618 a golden ratio because it is imperfect and only 'refers' to it.
I would like to point out that PHI, much like PI, is an imperfect ratio precisely because it deals with the non-absolute nature of nature and that it is by methodical approximation that we approach and close-in on the mystery of endlessness.
It is only in our human mind that the imperfection of perfection is projected on everything we see and seek.
That said, a precise geometric construction is as good as I have known to sense truth. Such sequence is far more enhanced by modern tools like CAD than it was by using the hand instruments of the past and backing them up by calculations.
Peace
Aris -
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Re: Golden Rectangle from a line?
Mon, March 27, 2006 - 5:15 PMGreat discussion and contrast of philisophical bent in each of you...If you struggle with the solution of this problem(the making of a golden rectangle from a line with just the two simple instruments), AS THE ANCIENTS DID AND TAUGHT,there is a visceral learning that takes place. You'll never have to ponder this same problem again because you'll KNOW in the deepest part of your memory and being how it's done.If the solution can be teased out of the initiate and he surmounts the task by his own diligence and efforts ,the sustantive aspect of learning is crystalized within him.Building upon these self discoveries through struggle and intellectual conceptual tenacity excercises a muscle of will and leads to greater and greater geometric discoveries.This is some of what the Ancients knew and why they offered this learning with the simplist of tools and instruments.This is why Dan didn't just give over the answer...Yes the CAD thing is easy ,but insubstantial at fixing the solution and the process for getting there in memory.
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