Re: Polaris proves the earth is round.
« Reply #20 on: February 12, 2016, 03:54:16 PM »
you're not wrong that the c/d ratio of real, physical circles is not pi.  pi isn't a real constant.

you're very wrong that this means that pi is a constant and that that constant is 4.  you're wronger to imply that 4 is a better approximation of c/d for real circles than pi.  your 'proof' is even more wronger.  the 'crinkled up' perimeter of the square is never going to actually 'straighten' up in a way that gets closer and closer to the perimeter of the circle.  no matter how much you zoom in, it will never appear to approximate the perimeter of a circle.  if you were to keep zooming in on the circle's perimeter, you'll only ever see this, no matter how much you zoom in:


except it wouldn't look so shitty since i presume nature to be way better at ms paint than i am.




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Offline Tom Bishop

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Re: Polaris proves the earth is round.
« Reply #21 on: February 12, 2016, 06:13:58 PM »
Exactly Tom! That's why I choose an orange - because it's not perfectly round. I'll have water to fill up all of it's 'imperfections' so I can measure it's 'real' volume, and thereby estimate pi (which will be larger than 3,1415xx because of the orange's imperfections).

What's wrong with the experiment?

Well, it's really the same experiment Daguerrohype is proposing. He seems to think that two shapes with the same perimeter should have the same total area within those shapes. He is wrong. I brought up the example of a triangle and a square with the same perimeters having different total areas within those shapes.
« Last Edit: February 12, 2016, 06:38:11 PM by Tom Bishop »
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Offline Panzerfaust

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Re: Polaris proves the earth is round.
« Reply #22 on: February 12, 2016, 06:30:41 PM »
Exactly Tom! That's why I choose an orange - because it's not perfectly round. I'll have water to fill up all of it's 'imperfections' so I can measure it's 'real' volume, and thereby estimate pi (which will be larger than 3,1415xx because of the orange's imperfections).

What's wrong with the experiment?

Well, it's really the same experiment Daguerrohype is proposing. He seems to think that two shapes with the same parameter should have the same total area within those shapes. He is wrong. I brought up the example of a triangle and a square with the same parameter having different total areas within those shapes.

How would YOU best estimate the volume of e.g. an orange?

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Offline Tom Bishop

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Re: Polaris proves the earth is round.
« Reply #23 on: February 12, 2016, 06:42:18 PM »
Exactly Tom! That's why I choose an orange - because it's not perfectly round. I'll have water to fill up all of it's 'imperfections' so I can measure it's 'real' volume, and thereby estimate pi (which will be larger than 3,1415xx because of the orange's imperfections).

What's wrong with the experiment?

Well, it's really the same experiment Daguerrohype is proposing. He seems to think that two shapes with the same parameter should have the same total area within those shapes. He is wrong. I brought up the example of a triangle and a square with the same parameter having different total areas within those shapes.

How would YOU best estimate the volume of e.g. an orange?

Your experiment is irrelevant. Surface area is not related to interior area in any meaningful with polygons. See the square vs triangle with identical perimeter example above.
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Offline Panzerfaust

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Re: Polaris proves the earth is round.
« Reply #24 on: February 12, 2016, 06:46:35 PM »
Exactly Tom! That's why I choose an orange - because it's not perfectly round. I'll have water to fill up all of it's 'imperfections' so I can measure it's 'real' volume, and thereby estimate pi (which will be larger than 3,1415xx because of the orange's imperfections).

What's wrong with the experiment?

Well, it's really the same experiment Daguerrohype is proposing. He seems to think that two shapes with the same parameter should have the same total area within those shapes. He is wrong. I brought up the example of a triangle and a square with the same parameter having different total areas within those shapes.

How would YOU best estimate the volume of e.g. an orange?

Your experiment is irrelevant. Surface area is not related to interior area in any meaningful with polygons. See the square vs triangle with identical perimeter example above.

I'm just asking you a very simple question. How would you estimate the volume of an orange?

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Re: Polaris proves the earth is round.
« Reply #25 on: February 12, 2016, 11:29:14 PM »
And what does all this rubbish on π = 4 have to do with the topic?
or with the OP:
The flat earth and heliocentric models are opposites in almost every way. Is it really that hard to tell which is correct?
The answer is NO. The earth is a sphere. It's obvious by the apparent positions of the celestial objects in the sky as observed from earth. By simple observation you can determine conclusively that the earth is round and that a flat earth is impossible.
One of the simplest examples illustrating this is Polaris. See why here:
http://debunkingflatearth.blogspot.com/2016/02/debunking-flat-earth-how-polaris-proves.html

Re: Polaris proves the earth is round.
« Reply #26 on: February 12, 2016, 11:43:54 PM »
here's an easy way to demonstrate why this proof is unsound.  let's try see if we can approximate the length of a line segment with sine waves of increasingly smaller amplitudes.

consider the following sine function, y=4sinx, and let's restrict the domain from x=0 to x=6.28. 

it's obvious just from looking at the graph that the length of the sine wave is greater than the length of the domain (6.28 units).  and, math-doing-robots confirm that the length of that line is ~17.628.  it's also obvious that if we want to approximate the length of the domain, then we must decrease the amplitude.

next we're going to add more sine functions to the graph.  the pi=4 proof demands that the perimeter of the square remain constant by changing its shape in a specific way.  likewise, we're going to keep the length of the sine wave constant while we decrease its amplitude.  the only way to do that is to increase its period proportionally.  in other words, if we decrease the amplitude by half, then we must increase the period by half.  if i'm not making sense, just check out the following graph.  this is y=4sinx, y=2sin(2x), y=sin(4x), y=.5sin(8x), all from x=0 to x=6.28

if you plug all those formulae into the math-wizard-robot, it will confirm that they all have the same length, ~17.628.  but now we have a problem.  as you can see, we can keep iterating and the sine wave will get smaller and smaller and smaller and smaller until it appears to be approximating the length the line, but since ~17.628 != 6.28, we know that it never does.

in fact, this notion of keeping the length of the sine wave constant by only letting amplitude vary inversely proportional to period is exactly what your proof does.  just look at the corners.  each time they "fold" the perimeter in the corners, they're doing it in a specific way that keeps the length the same, halves the amplitude, and doubles the period.  graphing the absolute values of the same sine functions from before illustrates this.  each iteration, starting with purple, has half the amplitude and double the period of the previous iteration, but their lengths are all the same.  it might appear that they would approximate the length of a line as the amplitude approaches zero, but it never does, and they never do.


/total thread derailment
« Last Edit: February 13, 2016, 12:39:13 AM by garygreen »
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Offline rabinoz

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Re: Polaris proves the earth is round.
« Reply #27 on: February 13, 2016, 03:22:05 AM »
Exactly Tom! That's why I choose an orange - because it's not perfectly round. I'll have water to fill up all of it's 'imperfections' so I can measure it's 'real' volume, and thereby estimate pi (which will be larger than 3,1415xx because of the orange's imperfections).
What's wrong with the experiment?
Well, it's really the same experiment Daguerrohype is proposing. He seems to think that two shapes with the same perimeter should have the same total area within those shapes. He is wrong. I brought up the example of a triangle and a square with the same perimeters having different total areas within those shapes.
Referring to Daguerrohype, you say "He seems to think that two shapes with the same perimeter should have the same total area within those shapes." His actual statement was:
Quote from: Daguerrohype
If we compare the area of a circle of radius 10 cm using both pi = 3.142 (to three decimal places) and pi = 4.000
10 x 10 x 3.142 = 314.2 cm^2
10 x 10 x 4.000 = 400.0 cm^2
The difference is an area of 85.8 cm^2.
I cannot visualise a circle with radius 10 cm and area 400 cm^2. If anyone can draw one, then please do. It might be useful to compare it (to scale) with a square of side length 20cm, as they have the same area.
Where he said that if we use the correct (to 3 places) value of π=3.142, we get the area of 314.2 cm2 but if we take π=4.000, we get of 400.0 cm2.

From what I can see what Daguerrohype actually says is quite correct. The circle and square only have the same perimeter and area if YOU insist on using YOUR stupid value of π=4. The sooner you can forget this "matter of definition" the better for everybody!
As I have tried to point out your so called proof is completely fallacious.
It's not a matter of definitions or maths it is simply wrong!

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Offline Tom Bishop

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Re: Polaris proves the earth is round.
« Reply #28 on: February 13, 2016, 05:58:13 AM »
you're not wrong that the c/d ratio of real, physical circles is not pi.  pi isn't a real constant.

you're very wrong that this means that pi is a constant and that that constant is 4.  you're wronger to imply that 4 is a better approximation of c/d for real circles than pi.  your 'proof' is even more wronger. the 'crinkled up' perimeter of the square is never going to actually 'straighten' up in a way that gets closer and closer to the perimeter of the circle.  no matter how much you zoom in, it will never appear to approximate the perimeter of a circle.  if you were to keep zooming in on the circle's perimeter, you'll only ever see this, no matter how much you zoom in:


except it wouldn't look so shitty since i presume nature to be way better at ms paint than i am.

That's not really my point. My point is that there is no such thing as a circle in the universe. So therefore pi != 3.14159...

How would YOU best estimate the volume of e.g. an orange?

We could do the water experiment to get the volume. But the way you used it as a proof is irrelevant. Different shapes with the same perimeter don't all have the same interior area.
« Last Edit: February 13, 2016, 06:01:06 AM by Tom Bishop »
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Offline Tom Bishop

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Re: Polaris proves the earth is round.
« Reply #29 on: February 13, 2016, 06:29:27 AM »
Exactly Tom! That's why I choose an orange - because it's not perfectly round. I'll have water to fill up all of it's 'imperfections' so I can measure it's 'real' volume, and thereby estimate pi (which will be larger than 3,1415xx because of the orange's imperfections).
What's wrong with the experiment?
Well, it's really the same experiment Daguerrohype is proposing. He seems to think that two shapes with the same perimeter should have the same total area within those shapes. He is wrong. I brought up the example of a triangle and a square with the same perimeters having different total areas within those shapes.
Referring to Daguerrohype, you say "He seems to think that two shapes with the same perimeter should have the same total area within those shapes." His actual statement was:
Quote from: Daguerrohype
If we compare the area of a circle of radius 10 cm using both pi = 3.142 (to three decimal places) and pi = 4.000
10 x 10 x 3.142 = 314.2 cm^2
10 x 10 x 4.000 = 400.0 cm^2
The difference is an area of 85.8 cm^2.
I cannot visualise a circle with radius 10 cm and area 400 cm^2. If anyone can draw one, then please do. It might be useful to compare it (to scale) with a square of side length 20cm, as they have the same area.
Where he said that if we use the correct (to 3 places) value of π=3.142, we get the area of 314.2 cm2 but if we take π=4.000, we get of 400.0 cm2.

From what I can see what Daguerrohype actually says is quite correct. The circle and square only have the same perimeter and area if YOU insist on using YOUR stupid value of π=4. The sooner you can forget this "matter of definition" the better for everybody!
As I have tried to point out your so called proof is completely fallacious.
It's not a matter of definitions or maths it is simply wrong!

I was referring to this statement:

Quote from: Daguerrohype
Thanks Tom, now if you can show the most refined "circle" next to a square with side length 2 x radius [edited], we can see whether they have the same area.

In fact if you can (apologies, I cannot), overlay the two figures to show the difference in area. I wager the "circle" will fit inside the square with room to spare.

If that is the case, then where is the missing area from the "circle"? Very well hidden indeed!

This doesn't really make sense, since the interior area within different shapes of the same perimeter are not related.

As far as the statement you quoted, an attempt to calculate the area of a circle using A = pi*r^2 with 4 in the place of pi, the error in the logic is that circles do not exist. You can't use traditional circle math to calculate that. The shape is not a circle, and the correct way to calculate the area is to use a method of calculating the area within a polygon.
« Last Edit: February 13, 2016, 06:35:14 AM by Tom Bishop »
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Offline rabinoz

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Re: Polaris proves the earth is round.
« Reply #30 on: February 13, 2016, 09:42:37 AM »
And how many angels can dance on the head of a pin?
Makes as much sense to me! But maybe I'm just too practical!

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Re: Polaris proves the earth is round.
« Reply #31 on: February 13, 2016, 10:18:04 AM »
And how many angels can dance on the head of a pin?
Makes as much sense to me! But maybe I'm just too practical!
that depends
on how you define
an angel
since no such thing exists in the real world
(so you can make up your own terms :D)
Read the FAQ before asking your question - chances are we've already addressed it.
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Offline rabinoz

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Re: Polaris proves the earth is round.
« Reply #32 on: February 13, 2016, 08:54:31 PM »
And how many angels can dance on the head of a pin?
Makes as much sense to me! But maybe I'm just too practical!
that depends
on how you define
an angel
since no such thing exists in the real world
(so you can make up your own terms :D)
Yes,
since as far as we know no such thing exists in the "physical" world.
But, the expression has long been used as a description of the ultimate pointless discauusion.

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Offline Rounder

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Re: Polaris proves the earth is round.
« Reply #33 on: February 14, 2016, 07:17:11 PM »
A lot of the assumptions turned out to be mistakes. For one, circles do not actually exist, since the universe is quantized, and any such related math is inaccurate. If one were to trace a line along all of the little pixilated plancks which make up the circumference of the most perfect "circle" in the universe one would find that pi is actually equal to 4, rather than the theoretical value of 3.14159...

Wow.  So you think the whole world has been underestimating the circumference and area of every circle ever, by about 25 percent?  That the dimensions of a 55 gallon drum, calculated based on 3.14159, are wrong?  It actually contains closer to 70 gallons, but nobody in a very money-driven industry has noticed they are shipping more oil than they thought?  That every round tower ever built has required more bricks than it should have, because the circumference was about 25% bigger than the math said, but not one single mason or architect in history ever noticed they consistently needed 25% more bricks?  That the commonly available measuring tool known as a Pi Tape http://www.amazon.com/Lufkin-W606PD-Executive-Diameter-Engineers/dp/B0002JT2AI/ref=sr_1_1?ie=UTF8&qid=1455477163&sr=8-1&keywords=pi+tape+measure, which gives you the diameter of a round object you wrap it around, is off by 25%?  I have used a Pi Tape, me, myself, personally, and guess what: it wasn't 25% off, not ever, not even close!
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Re: Polaris proves the earth is round.
« Reply #34 on: February 14, 2016, 11:05:17 PM »
That's not really my point. My point is that there is no such thing as a circle in the universe. So therefore pi != 3.14159...
... the error in the logic is that circles do not exist.

I would contend that you are wrong on this. While perfect circles may not actually exist in the physical world, as abstract mathematical concepts they absolutely do exist. What's more, these abstract conceptual circles have useful real world applications, albeit implicitly as approximations.

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Offline Tom Bishop

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Re: Polaris proves the earth is round.
« Reply #35 on: February 15, 2016, 12:15:17 AM »
Wow.  So you think the whole world has been underestimating the circumference and area of every circle ever, by about 25 percent?  That the dimensions of a 55 gallon drum, calculated based on 3.14159, are wrong?  It actually contains closer to 70 gallons, but nobody in a very money-driven industry has noticed they are shipping more oil than they thought?

Using pi to calculate area does not make any sense if the shape is a polygon, since unlike a circle, the perimeter of a polygon is not related to its area.

Please refer to my example above of a triangle and a square with identical perimeters having different interior areas.
« Last Edit: February 15, 2016, 12:31:10 AM by Tom Bishop »
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Offline rabinoz

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Re: Polaris proves the earth is round.
« Reply #36 on: February 15, 2016, 06:49:21 AM »
Wow.  So you think the whole world has been underestimating the circumference and area of every circle ever, by about 25 percent?  That the dimensions of a 55 gallon drum, calculated based on 3.14159, are wrong?  It actually contains closer to 70 gallons, but nobody in a very money-driven industry has noticed they are shipping more oil than they thought?
Using pi to calculate area does not make any sense if the shape is a polygon, since unlike a circle, the perimeter of a polygon is not related to its area.
Please refer to my example above of a triangle and a square with identical perimeters having different interior areas.
I fail to see any polygon mentioned in the post you were answering!
In Australia these drums are 44 (imperial) gallons and are cylindrical, so π would be very relevant.

So I can't make sense of your statement "Using pi to calculate area does not make any sense if the shape is a polygon"!

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Re: Polaris proves the earth is round.
« Reply #37 on: February 15, 2016, 08:07:19 AM »
Using pi to calculate area does not make any sense if the shape is a polygon, since unlike a circle, the perimeter of a polygon is not related to its area.
As rabinoz points out, I'm not talking about a polygon.  I'm talking about a circle.  If you're talking about polygons in reference to your own earlier statement that
Quote
circles do not actually exist, since the universe is quantized, and any such related math is inaccurate
well, even a jagged not-perfect circle does in fact follow the calculations of Pi to enough decimal places to be accurate enough to satisfy the needs of engineering, science, and math.

Please refer to my example above of a triangle and a square with identical perimeters having different interior areas.
I don't think anybody is disputing the difference between triangles and squares.  Just don't see how it relates to circles, or Pi.  But, since you've brought them up: why did you choose a square to use as your perimeter shape, why not a triangle?  Same principle, right?  Only....collapsing corners forever on a triangle gives you an answer of about 5.19.  Why not some other regular polygon?  Maybe a hexagon?  That would give about 3.46 instead of 4 for Pi.  In fact, the CORRECT way to approach an accurate value for the perimeter of a circle is to take polygons of ever more and more sides, no collapsing corners.  For each polygon, calculate their perimeter, and do this over and over.  If you do, you will find the value approaching the true circumference of the circle.  I did this once as a student, in high school, when it became time to move from rote memorization of Pi and Pi R Squared into understanding of those concepts.
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Re: Polaris proves the earth is round.
« Reply #38 on: February 15, 2016, 05:37:54 PM »
Ok Tom, here's a question.  How would you go about finding the area of a circle?  What formula do you prefer?

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Re: Polaris proves the earth is round.
« Reply #39 on: February 15, 2016, 06:45:11 PM »
Ok Tom, here's a question.  How would you go about finding the area of a circle?  What formula do you prefer?

Or, as a good Zetetic SHOULD do, just go find a round thing in your house and measure it for yourself!  For example, I happen to have a bunch of gallon paint cans handy.  Diameter: 6 and 9/16 inches, circumference 20 and 3/4 inches.  Ratio of those two numbers: 3.16    Slightly bigger than Pi due to imprecise measurement no doubt, but had Pi actually been 4 and the diameter accurate, the circumference would be 26 and 1/4 inches.  I promise you I did not make a 5 and 1/2 inch measurement error in the circumference.   Or maybe I got the circumference right, but botched the diameter measurement.  With a 20 and 3/4 inch circumference and a Pi of 4, the diameter 'should' have been 5 and 3/16 inches.  Again, I know I didn't make an error of 1 and 3/8 inches.
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