If there are more than one straight lines, and if none of them, if combined, all or some, create any angle or angles, what would they become. After some engrossing effort, I concluded that they would describe only a straight line of a length given the sum total of the lines thus joined.
And I wondered again: Is that the only possibility? It dawned on me then, that if Lines join with the primary condition that they do not create an angle, then the only other possibility would be formation of a Circle.
This was amusing, because any other form of combination of lines would become, at least as I inferred, an Angle, Triangle, Parallelogram, Quadrangle and so on; but given the condition that they should not remain only straight, and at the same time, should not form an angle, the only possibility left would be the Lines forming a Circle.
If some of you chance upon this musing and would like to comment, and demonstrate other possibilities, I would look forward to hearing your argument, and getting a kindred feeling that many minds today have so much in common, as much as so much in opposition, as did the minds that founded what we call our civilisation, whatever that means.
3 comments:
Thank you for the post.
Read again, no argument.
One observation:
A circle in effect becomes a never ending (NE) straight line.
:)
I did not see this before, since your blog was dormant for a long time.
By mathematical definition a line can be straight or curved. In your hypothesis, you have defined a curved line being straight. Also a curved line always has an angle called radian, albeit to a center or a focus (if it is not a circle), but then we have normal or tangential angle. The circle you have shown has 360 degrees or 2x (pai)x radians.
By the way, this reminds me of the e-mail I sent you about Arabic numerals. That was a clever way of defining each number by how many anglles each line made. Each increasing number made additional angle out of a line.
Bhupen
I am glad to receive your aminadversions, if indeed they are so. With my acutely limited formal education, my write-up on theorem called Hypotenuse and Other News was purely in the area of inquiry and speculation, devoid of assertion (As I said, "If some of you ... would like to comment, and demonstrate other possibilities, I would look forward to hearing your argument.").
From your learned and really impressive argument, I have failed to figure out whether you are correcting me in part or in full, or augmenting my proposition by providing more extensive information on the subject, which doubtless is part of your qualified education.
In either case, it is a matter of delight to me that you have participated. Continue to do so, even as you clarify to me in simpler language what you have stated so well in your response.
Best,
Bhai
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