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Circle Squared?


Robust

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Another set of formulae derived from the study and I think worthy of mention. It's calledthe Rule of 20.

 

1) Divide diameter of the circle by 180 degrees; thus giving the distance between each adjacent degree on the y axis

 

2) Multiply degree distance on the y axis by 20, giving the number of degrees on the circumference. Thus, given a diameter of 9: 9/180 = 0.05; 0.05 * 20 = 1 degree.

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4) D^2 (10) (DD) = area; where D is diameter; (10) is Base 10; DD the degree-distance between each adjacent angular degree on the circumference as given by the cardinal number 9; i.e., 0.0785....ad infinitum.

 

Example: 9^2 (10) (0.0785....) = 63.617....area;

8^2 (10) (0.0785....) = 50.265....area;

7^2 (10) (0.0785....) = 38.484....area;

 

ehm sorry, but i fail to understand this.....

- What do you mean by 'degree distence'? in particular: how did you calculate this particular number? it looks like pi/40, but why did you choose that? (in that case your formula just reads pi*r^2)

- What do you mean by 'base 10'? looking at your formulas, you basicly multiplied everything with 10.

 

 

I see it as no coincidence that the degree-distance given of a diameter of 9 is pi/40

well, your formula only works with this number, regardless of the diameter. Entering DD=pi/40 in your formula gives:

D^2*10*pi/40 = (2*r)^2*pi/4 = 4 r^2 pi/4 = pi*r^2 = area. any other value for (DD) won't give the correct answer.

 

1) Divide diameter of the circle by 180 degrees; thus giving the distance between each adjacent degree on the y axis

 

2) Multiply degree distance on the y axis by 20, giving the number of degrees on the circumference. Thus, given a diameter of 9: 9/180 = 0.05; 0.05 * 20 = 1 degree.

 

well what you say here is actually the following: D/(180 degrees)*20 = D/(9 Degrees). So if you put D=9 this becomes 1/Degree; but i dont think it has any more meaning than that (that 9/9=1 that is...)

 

what do you mean by the way with 'number of degrees on the circumference?' as far as i know the number of degrees of a circle is 360... (or 2pi radians)

 

Bo

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Bo, Hello!

 

The anomaly of the Base 10 formula is that the DD given for a diameter of 9 applies to giving the area to a circle of any diameter whatsoever. Look again at the examples given.

 

Have to be gone for a few days....will respond to the rest of your post on my return.

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  • 2 weeks later...

Bo, Hello....I'm back.

 

You ask what is meant by degree-distance and also what is meant by Base 10.

 

Degree-distance it seems is not a common maths term, yet used extensively in configuring navigational coordinates. It is simply circumference/360 degrees, giving the distance between each angular degree on the circumference. Base 10 is our common numbering system comprised of the cardinal numbers 0-9; where, according to Pythagoras and the ancients who gave us the system, the cipher is to be regarded as Base 10. Do you see the anomaly presented by the given Base 10 formula?

 

Your questions are important to me and most helpful, for as mentioned I'm not a maths person. I'm hoping by all this to be able to respond somewhat intelligently to the questions I know are forthcoming, for the paper has now been submitted. I trust y'all might find it interesting.

 

"All things number and harmony." - Pythagoras

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It appears that this topic has failed to find the interest hoped for...so no sense beating a dead horse...yet I will be happy to respond to any questions tha bmay arise. A paper has been submitted describing the anomaly of the Base 10 formula - will let you know the results.

 

In the meantime another paper is in preparation, ostensibly titled "Why 360 degrees?" The subject essentially deals with parameters of the imperfect circle - for except that the area of any given circle (or sphere) give a finite figure for its area it's not really a circle - is it? The answer (solution) to this question is to be found in the above given 12-tone scientific scale, which is copyrighted and resulting in the granting of 2 patents - one relating to quantum physics. Let's keep in touch!

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Robust, the lack of interest is probably because you are battling against a well-proven theory and fail to provide any understandable proof for you hypotheses. So there is not much for us to discuss. I would be very interested in hearing if your paper is accepted (and where).

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Thanks, Tormod, I'll certainly inform y'all as to outcome of the submission. In the meantime I'll try to come up with another topic of interest that correlates. Though I am curious as to why there is no interest in the given anomaly of the Base 10 formula.

 

 

"All things number and harmony." - Pythagoras

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Bo, hello again. I'm still curious as to the formula you used to give your drawing of the inscribed square with XY axes. I'm accustomed to thinking of the inscribed square as its corners touching the 4 cardinal points of the circle, thus giving chord length to the quadrant....so I find your square interesting. What for example is the ratio of the lines to the diameter?

 

Sorry, I see now it was Freethinker who gave the drawing....so if you will please, Freethinker.

 

 

"All things number and harmony." - Pythagoras

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It just makes common sense....whatever the oblateness of the circle, being a closed continuum it has to describe a finite area....right? How would one go about doing that except by the ability to relate line and arc by a finite ratio to one another?

 

I gather from the two topics I've put forward that y'all don't cotton much to controversy, yet I feel that these are questions that have to answered, so if you will, please.

 

 

"All things number and harmony." - Pythagoras

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Bo, I only now caught the significance of your earlier statement in which in which you say, "Your formula only works with this number - DD=pi/40 , where the diameter is 9."

 

That is preciseley the point, recognizing that the formula works for any and all circles regardless of diameter. That's the anomaly of it. Give me any arbitrary diameter and I'll show the working.

 

 

"All things number and harmony." - Pythagoras

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Originally posted by: Robust

I gather from the two topics I've put forward that y'all don't cotton much to controversy.

 

Hm...you obviously haven't taken part in the rest of our discussions. I say there is as much controversy here as anywhere...but not every topic catches on, like I explained above.

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Considering that the circle is but a continuum of the arc and the square ut a continuum of the line, plus our inability as yet to determine the exact length of either, all that we have than to relate the two is the ratio of one to the other by pi. Accordingly then, in consedering a squaring of the circle and knowing that the sqrt(pi)*r gives the area of a square with the same area as that of the given circle, it iseems only reasonable to assume that in graphing the two so as to show a true squaring of the circle, all lines interscting the arc and those extending beyond must conform exactingly to pi.

 

I don't have the computer expertise to present the drawing, yet having the formula one can easily grapf it. For the sake of conformity, we might consider the circle with a diameter of 9. In my own drawing, I find that the lines of the superinscribed square extending beyond the arc form a right angel to the arc in each quadrant, and by such facilitating a determining of the pi relationship.

 

Just setting these things down as they occur, so no big deal if found at fault.

 

 

"All things number and harmony." - Pythagoras

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Speaking of controversy, which frankly I do not try to avoid, here is a question that teems with it and possibly given answer by the Base 10 anomaly.

 

The square is a continuum of the line giving a finite area, The circle is a continuum of the arc also having a finite area; yet, at least by present standards, unable to be defined by a finite area. Why is that and how might it be resolved?

 

 

"All things number and harmony." - Pythagoras

 

 

 

 

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Yes, a lot of controversy over this question of squaring the circle. Here is something further to consider. In the Trianglature Formulae post the means is given for finding the circle's chord length and its distance on the arc. Applying this formulae to the circle's superinscribed square it is found that not only do the lines intersecting the arc give an exact pi value, but as well, and in direct ratio, those lines extending beyond the arc.

 

That being the case, I have to consider how squaring of the circle can be denied seeing as how all factors relate exactingly to pi?

 

 

"All things number and harmony." - Pythagoras

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  • 2 weeks later...

Being a new member, I've been somewhat in abeyance over the suggestion that the Base 10 anomaly is a controversial topic. I find that I can't rest easy with that - chiefly because I find it to be a highly important observation relevant to a number of geometric problems. Let me point out again that the anomaly lay in the fact that the degree-distance given for a closed continuum with a diameter of 9, i.e.,(pi/40) applies by the formula to give the area to any closed continuum whatsoever. I'm not the sharpest kid on the block and can at times get carried away, so would appreciate knowing if the finding is correct or not.before putting any more time into the thing.

 

There has been no response whatsoever to a submitted paper on the subject.

 

 

"All things number and harmony." - Pythagoras

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Being a new member, I've been somewhat in abeyance over the suggestion that the Base 10 anomaly is a controversial topic. I find that I can't rest easy with that - chiefly because I find it to be a highly important observation relevant to a number of geometric problems.

 

I understand your frustration. But Bo has already discussed some of your points, and I think we don't understand what the controversy is all about. And if there is no interest here, and no interest in your paper - then perhaps you have not managed to convey just why this controversy is so interesting.

 

I'm not trying to patronize you but not every new idea hits pay dirt the first time around.

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