Looks like nonsense to me. A circle inscribed in a shape in a circle is not a theorem, it's just a very simple geometric design, and easy to construct with rope (knotted at a few intervals) and two guys. The ratios arise naturally, and there's no measurement needed. There have been vastly more complex designs done since then.
No. They are not new theorems. They are just simple geometric relationships. If you take a circle, and inscribe a regular polygon inside of it, and then inscribe a circle inside of that, all you have done is precisely that. It's not a theorem and more than a square inclined and inscribed inside another square is Pythagoras' theorem, or a circle bisected by a line represents pi.
The people who made the circles just started with simple shapes because they looked nice and were easy to do.
This is a high-school geometry exercise. It's not a new euclidean theorem.
It's not a new euclidean theorem.
What is the fifth theorem?
So does this fifth theory actually exist? Because I could just say:
V: The ratio of the area of a circumscribed and inscribe circle of a regular N-gon is proportional the ratio of the squares of the cosecant and cosine of half the Nth segment of a circle.
and that would fit.
They are neither historic nor epistemic. They are trivial geometry exercises.
I'm sorry, but I don't follow what the questions actually are. You claim that he came up with five new theorems. I showed that three of them were just a trivial geometric relationship, and the fifth does not seem to exist. So what is the question?
Question: When hawkin's can describe in which section of Euclid's works are missing from ("They should be in Book 13, after proposition 12") what is he saying, then?
I'm sure they did. He's a little vague on what actually transpired. He claims:Question: Why didnt one of these 250K+ "math-fans" just call him up on it as you have done just now?
New Question: Are you saying Hawkins is a Liar or mistaken?
No, I'm saying he seems to be ascribing meaning where there is none. Cherry picking ratios that appear on the diatonic scale : 9/8, 5/4, 4/3, 3/2, 5/3, 15/8 - ratios which are bound to appear in many geometric patterns.
I dont understand? Are you saying that you can find other examples comparable with his? That seems to be what you are saying? Can you show me one other example of this? if you cannot you simply are not entitled to make that claim as if that closes the case.
Where is your evidence, Mick?
Cheers
Mat
And I'm a little unsure why you are banging on this, when two years ago you said:
http://www.skepticforum.com/viewtopic.php?p=211274#p211274
So how exactly is this "the most astounding mystery that I am aware of"?
Amazing the trails people leave - talk about coming back to "bite yer bum"
And I'm a little unsure why you are banging on this, when two years ago you said:
http://www.skepticforum.com/viewtopic.php?p=211274#p211274
So how exactly is this "the most astounding mystery that I am aware of"?
Encoded information that a school child could figure out?
Diagrams of a really really simple form, of a circle inside and outside a regular polygon?
You are asking me where the encoded information comes from, when that information is the stuff of high school geometry lessons?
I'm afraid I'm going to have to assume at this point that you are trolling. Unless you can demonstrate some statistical significance in the amount of diatonic ratios in the crop circles, then it's just cherry picking.
I am saying it is special you are saying it is mundane. Kindly show me why you are right and I am wrong
Three of the theorems are just plugging in a number to "ratio = (secant(pi/N))^2", hence it is mundane.
If this is true then why did Hawkin's not know how mundane it was. Or the editors of these magazines? Or his academic colleagues?
How come you know, and they don't?
They probably did.
And yet it seems to me this is exactly what you have done in this thread?
Don’t be an expert
It does not matter what your credentials are. Don’t assume that makes you right. Being an expert gives you easier access to information, and it provides mental tools to help process that information. But you can’t just then say “because I say so”. You still have to explain, to demonstrate, and to provide the means of verifying your point of view.
Look, why don't you find the fifth theorem, and then we can go from there? If it does not exist then maybe the whole thing was a joke? Or he was mistaken?
Let me ask you a direct question. Do you think theorems 2-3 are significant in any way? If so, why?
Clearly they are very very euclidean, so I'm not sure what you mean.
I said "Three of the theorems are just plugging in a number to "ratio = (secant(pi/N))^2", hence it is mundane." so why don't you address that.
I mean, do you think that the theorems could have been in Euclid's body of work even though they are absent from that body of work?
Don't believe me. Go ask some math professors. Report back.
I am sure If I reported back in years to come, "Mick, look I have spoken with 50 Professors of mathematics and they concurred with Professor Hawkin's claims," you would still not be persuaded to proceed on with the debate about the possible meanings of the information. Maybe you would even call me a troll again
First you must ignore all his misdirection about circles or their areas - his "theorems" are stolen from ancient theorems about regular polygons (equilateral triangles, squares and hexagons).
"Theorem" #1
Hawkins' first theorem was suggested by a triplet of crop circles discovered on June 4, 1988, at Cheesefoot Head. Hawkins noticed that he could draw three straight lines, or tangents, that each touched all three circles. By drawing in the equilateral triangle formed by the circles' centers and adding a large circle centered on this triangle, he found and proved Theorem I: The ratio of the diameter of the triangle's circumscribed circle to the diameter of the circles at each corner is 4:3.
Forget the circles and think about what this really is: the incenter to vertex distance of an equilateral triangle and the same distance less the incenter to side distance of an equilateral triangle inscribed in the first equilateral triangle. There's the 4:3 ratio. The circles are misdirection.
"Theorem" #2
The areas of an equilateral triangle's circumscribed and inscribed circles have a 4:1 ratio.
That's all it really says, and it's ancient (at least since the Pythagoreans) knowledge stemming from the fact that the distance from an equilateral triangle's incenter to one of its vertices is twice the distance from the incenter to one of its sides. These distances are also the radii of the triangle's circumscribed and inscribed circles, so the radii have a 2:1 ratio and the circles' areas will obviously have a 4:1 ratio.
"Theorem" #3
The areas of a square's circumscribed and inscribed circles have a 2:1 ratio
Also ancient knowledge. A square's diagonal and side have a sqrt(2):1 ratio as do the circumscribed and inscribed circles' radii, so their areas have a 2:1 ratio.
"Theorem" #4
The areas of a regular hexagon's circumscribed and inscribed circles have a 4:3 ratio.
More ancient knowledge. The maximal and minimal diameters (which are the diameters of the circumscribed and inscribed circles) of a regular hexagon have a 2:sqrt(3) ratio, so the circles' areas have a 4:3 ratio.
I don't know whether Hawkins was a nutter or purposefully perpetuating a hoax but those geometric ratios are trivial and well known.
Clearly not to the readers of those magazines, the math-fans.
Why did the people in this video not call him out, do you think?
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