If the lengths of sides of a rectangle are in the golden ratio, then the rectangle is a golden rectangle. It is possible to divide a golden rectangle into a square and a golden rectangle. We could continue this process indefinitely, producing smaller and smaller golden rectangles. The point at which all the golden rectangles converge is referred to as the "Eye of God". We can magnify the figure but can never get to the 'Eye' using finite magnifications. If we connect all the vertices's, we form a logarithmic spiral that envelops the "Eye of God".
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3 comments:
Nice to know.
It doesn't have to be this intersecting point - No intersecting point, for that matter just any point at all, cannot be seen no matter how much we magnify! If you think a little deeper into this uncertainty thingy, it is same as saying we can never get the area of a circle right. Yes it is Pi*R^2, but we are never 100% sure what Pi is...We can keep 'magnifying' it - to 10 decimal points, 100, 3 million..-but we will never 'see' it.
Some thoughts here on the naming (I know you didn't christen it..:))- Generally 'God' is the area that lies outside the current circle of knowledge, like the area that lies beyond what our car headlights show - There will always be such an area even if the headlights keep revealing the previously dark area as the car moves forward. This area filled with speculation is where generally 'God'ists take refuge in when they can't explain it away. But this is one of the instances when even a perfectly explainable mathematical concept is dubbed 'God' something. If this is God's eye then every irrational number, including Pi, is God's number!
Dinesh, I knew mention of the word God will set you off. :-) May be we should start calling it "The Golden Eye"? - 007 point!
Kidding aside; All sort of divine properties were attributed to the golden ratio over centuries and used in various fields of study. It is a simple explanation for "infinity", I think. The golden ratio, pi and many other natural constants turn out to be infinite series. However a geometric point is by definition a single dimension. So magnifying a point don't make sense.
Ironically, your head light example seems to explain the concept well, weather you call it God or infinity or something else.
Hahaha, Golden eye is better. You are exactly right about magnifying a single dimensional object. Like you said there is no rationality in trying to magnify the figure in an attempt to see a single dimensional object!
Another funny thought - Last winter on a snowy day I was driving to my brother's place through back country roads (because I am stupid). There was an obstacle on the road in that dark area beyond my headlights, so when my headlights actually revealed it it was too late to apply breaks on snow - But I did and the car started skidding - when it was over, I stepped out to see if there was any damage on my car. I noticed the skid mark on the snow and it looked exactly like that logarithmic spiral. Thank 'God' I thought!. Car headlights, Logarithmic spiral, God,.. everything perfectly makes sense now!
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