Referring to the cosmos as a whole is it a linear progression or is it cyclic or is it both linear and cyclic at one and the same time because it appears to grow and develop and yet the basic patterns seem to repeat themselves. Therefore I am stepping aside what I believe are restrictive parameters to explore an alternative way of looking at this phenomenon because I believe there is in fact no magic in space it is just another dimension of reality subject to laws no different to here on earth, I hope it raises a spark somewhere to achieve an answer to it all.
3.1415926535897932 is a typical example of long division however in terms of the relationship between a circle and its diameter this long division goes on for ever in an attempt to show that when a diameter is 1 the circulation is (Pi), the make up of this relationship appears to favor a cyclic universe. However there is another imperfect constant for this relationship which appears to favor a linear progression that is the ratio 22/7 which appears to be totally ignored.
This ratio has a denominator made up of a linear straight line 0 to 7 split up into 7 stride lengths of 1 leaving 8 footprints that define where 4 magnifications of circulation crosses its path, the centre circle formed through these footsteps having a diameter = to 1 However this circle has the room to expand around the clock. This clock is the numerator 22 that defines a time constant in circulation by using the smallest possible straight line that is 21 segmentation's in circulation giving segmentation of distance and time for all circle sizes so giving the velocity constant for the circle and the straight line.
The arithmetic for constant 22/7
A circle of maximum velocity = 186032- through natural constant acceleration
Its diameter = 59192 divided by 7 = 8456 steps of 7
186032 divided by 8456 = 22/1 exact
A circle to a straight line through constant acceleration over 4 magnifications
21x21x21x21= 194481- circle to straight line adds 1 footprint and a stride 7
which in circulation overlap in equal and opposite reaction = 194488
194488 divided by 23 footprints = 8456 exact
This is basically what I see in picture form and not being a mathematician I have stepped aside from its personal restrictive parameters to present this for your perusal.
For an overview see my recent topic The Cosmos and the Greek Constant (Pi) also
http://www.cosmosview.com/images/ThisNaturalCosmos.pdf
God no, not another one ...
So, D V (if I may be so familiar), what is so exact about 22/7? Can you respecify that number in an exact number of decimal digits for me? It's just "long division" ...
So, D V (if I may be so familiar), what is so exact about 22/7? Can you respecify that number in an exact number of decimal digits for me? It's just "long division" ...
it appears that 22/7 doesnt need decimal points
Nor does "pi"; what's your point?
I have learned that what I call 'spirograph thingies', are not unlike what often have been referred to as Lissajous Curves.
http://en.wikipedia.org/wiki/Lissajous_curve
It is interesting that 1 / (22/7 - 3) = 7.
It also might be interesting to compare the continued fractions of 22/7, (22/7 - 3), and Pi and the Golden Ratio.
http://en.wikipedia.org/wiki/Continued_fraction
In your calculations, it appears you use 22/7 instead of a more precise representation for Pi like 3.1415926535897932384626433832795. Using 22/7 would for sure lead one to see patterns that are not so common. Another thing is the language and terms you use, which also are not so common, make it very difficult for me to understand.
http://en.wikipedia.org/wiki/Lissajous_curve
It is interesting that 1 / (22/7 - 3) = 7.
It also might be interesting to compare the continued fractions of 22/7, (22/7 - 3), and Pi and the Golden Ratio.
http://en.wikipedia.org/wiki/Continued_fraction
In your calculations, it appears you use 22/7 instead of a more precise representation for Pi like 3.1415926535897932384626433832795. Using 22/7 would for sure lead one to see patterns that are not so common. Another thing is the language and terms you use, which also are not so common, make it very difficult for me to understand.
does (Pi) take into consideration any equal and opposite reaction in circulation perhaps this is the reason for its imperfection
QUOTE (different view+Nov 30 2007, 02:55 PM)
does (Pi) take into consideration any equal and opposite reaction in circulation perhaps this is the reason for its imperfection
Of course; go "pi" around a circle from opposite directions and you meet exactly opposite your starting point. pi is the queen of cycles. What's more, it doesn't need representation as lowly digits to reign supreme. The fact that mere digits can't contain it only demonstrates how it evades our human control.
"pi" is far more perfect than most numbers. Consider its relationship with "e", "i", "1", and "0" all in the same equation. What other number can make that boast? By contrast, the singularly uninteresting "22/7" is woefully inadequete. Witness the pathetic formula mentioned in the post above.
You really ought to ask pi's forgiveness for straying from it.
Of course; go "pi" around a circle from opposite directions and you meet exactly opposite your starting point. pi is the queen of cycles. What's more, it doesn't need representation as lowly digits to reign supreme. The fact that mere digits can't contain it only demonstrates how it evades our human control.
"pi" is far more perfect than most numbers. Consider its relationship with "e", "i", "1", and "0" all in the same equation. What other number can make that boast? By contrast, the singularly uninteresting "22/7" is woefully inadequete. Witness the pathetic formula mentioned in the post above.
You really ought to ask pi's forgiveness for straying from it.
QUOTE (different view+Nov 30 2007, 07:55 AM)
does (Pi) take into consideration any equal and opposite reaction in circulation perhaps this is the reason for its imperfection
Pi does not change.
When we calculate Pi = circumference / diameter, we get a funny stream of numbers that never ends. This is a phenomenon that occurs as a result of using the base 10 number system. It looks funny, different, strange. This does not mean it is not perfect.
Pi is Pi and does not change and since it never changes, it does not need to be calculated.
http://en.wikipedia.org/wiki/Circle
http://en.wikipedia.org/wiki/Pi
Pi does not change.
When we calculate Pi = circumference / diameter, we get a funny stream of numbers that never ends. This is a phenomenon that occurs as a result of using the base 10 number system. It looks funny, different, strange. This does not mean it is not perfect.
Pi is Pi and does not change and since it never changes, it does not need to be calculated.
http://en.wikipedia.org/wiki/Circle
http://en.wikipedia.org/wiki/Pi
but surly using decimals in (Pi) takes away the straight line circle relationship
I would like to add the point that where space is concerned it apparently comes down to the view point of what is the relationship between the circle and the straight line is it a diameter or is it a segment, in the view of the latter what is (Pi) measuring.
QUOTE (different view+Nov 30 2007, 05:00 PM)
but surly using decimals in (Pi) takes away the straight line circle relationship
Yes, but that is always true of decimals, or for that matter any "positional notation system".
And it's not just an irrational like "pi" that is susceptible to "loss of precision", but most of the rationals (like 22/7) as well. In fact, every rational number must be a non-terminating, repeating decimal. (Now, in many cases this decimal value is "all zeros", but that's the rare exception)
In general, the properties of a number are independent of representation. "7" is a prime number in base-10, base-2, or Roman numerals. Some representations of a number are more "compact" than others: while in base-10 "1/3" is an endless repetition of "3"s, it is merely "0.3" in base-9. On the other hand, 1/2 in base-10 is "0.5" but in base-9 I think it's something like "0.454545...".
For the most part, relationships between numbers have their roots in pure geometry. In some ways, what we call numbers are just a way of solving geometric problems without having to draw figures in the sand. So, you are not to be faulted in your geometric interpretation. In fact, you are coming up against the same philosphical problem that confronted the Greeks when they discovered to their horror that simple rational numbers could not describe the hypotenuse of a 1x1 right triangle.
Yes, but that is always true of decimals, or for that matter any "positional notation system".
And it's not just an irrational like "pi" that is susceptible to "loss of precision", but most of the rationals (like 22/7) as well. In fact, every rational number must be a non-terminating, repeating decimal. (Now, in many cases this decimal value is "all zeros", but that's the rare exception)
In general, the properties of a number are independent of representation. "7" is a prime number in base-10, base-2, or Roman numerals. Some representations of a number are more "compact" than others: while in base-10 "1/3" is an endless repetition of "3"s, it is merely "0.3" in base-9. On the other hand, 1/2 in base-10 is "0.5" but in base-9 I think it's something like "0.454545...".
For the most part, relationships between numbers have their roots in pure geometry. In some ways, what we call numbers are just a way of solving geometric problems without having to draw figures in the sand. So, you are not to be faulted in your geometric interpretation. In fact, you are coming up against the same philosphical problem that confronted the Greeks when they discovered to their horror that simple rational numbers could not describe the hypotenuse of a 1x1 right triangle.
i would like to point out that i haven't the problem it appears(Pi) has because in decimal form it cannot define a segment because it gets lost in the long division of ten
If you draw a very very very very very large circle, say a 10^15 light years in diameter, you will find the curve to appear really rather straight like. An ant walking along that line would think it looks straighter. However, it has been some time since some claimed the world to be flat.
lookup 'great circle'
lookup 'great circle'
Actually, D V, I have no idea what you're asking about as your first post was all metaphysical babble and the only thing I could glean from it was the old hand-calculating dodge of using 22/7 instead of pi. Fine for carpenters, but I wouldn't build a suspension bridge with it. 
You have something against the modern number system? By modern, I mean the one we've been using for the last 2,500 years or so.
You have something against the modern number system? By modern, I mean the one we've been using for the last 2,500 years or so.
QUOTE (different view+Nov 30 2007, 11:11 AM)
I would like to add the point that where space is concerned it apparently comes down to the view point of what is the relationship between the circle and the straight line is it a diameter or is it a segment, in the view of the latter what is (Pi) measuring.
From a point on a piece of paper, we draw a circle using a compass. We can use various methods to communicate the properties of that circle. Flat. Round. Small. White. If we need to be more precise, we usually draw a diameter and measure it with a ruler.
If the diameter is exactly 1.0, we know the circumference is exactly 1Pi.
If the diameter is exactly 2.0, we know the circumference is exactly 2Pi.
If the diameter is exactly 3.0, we know the circumference is exactly 3Pi.
If the diameter is exactly 4.0, we know the circumference is exactly 4Pi.
If the diameter is exactly 5.0, we know the circumference is exactly 5Pi.
And so on.
We quickly see that:
When the diameter increases, the circumference increases.
IN PROPORTION.
Pi is a number.
It does not measure.
People measure.
In conclusion,
the diameter is a line which passes through the center of the circle.
The diameter is a straight line.
A line is sometimes called a segment.
Pi does not measure.
The circumference is a curved line and is not straight.
The diameter is a straight line and is not curved.
So we end up with a circle drawn on a piece of paper.
Please, do not try this at home without parental supervision.
From a point on a piece of paper, we draw a circle using a compass. We can use various methods to communicate the properties of that circle. Flat. Round. Small. White. If we need to be more precise, we usually draw a diameter and measure it with a ruler.
If the diameter is exactly 1.0, we know the circumference is exactly 1Pi.
If the diameter is exactly 2.0, we know the circumference is exactly 2Pi.
If the diameter is exactly 3.0, we know the circumference is exactly 3Pi.
If the diameter is exactly 4.0, we know the circumference is exactly 4Pi.
If the diameter is exactly 5.0, we know the circumference is exactly 5Pi.
And so on.
We quickly see that:
When the diameter increases, the circumference increases.
IN PROPORTION.
Pi is a number.
It does not measure.
People measure.
In conclusion,
the diameter is a line which passes through the center of the circle.
The diameter is a straight line.
A line is sometimes called a segment.
Pi does not measure.
The circumference is a curved line and is not straight.
The diameter is a straight line and is not curved.
So we end up with a circle drawn on a piece of paper.
Please, do not try this at home without parental supervision.
QUOTE (different view+Nov 30 2007, 10:00 AM)
but surly using decimals in (Pi) takes away the straight line circle relationship
A circle does not change.
Pi does not change.
A circle does not change.
Pi does not change.
QUOTE (different view+Nov 30 2007, 12:14 PM)
i would like to point out that i haven't the problem it appears(Pi) has because in decimal form it cannot define a segment because it gets lost in the long division of ten
Yes. Once we have calculated enough digits, we round it up. So 3.1415926535897932384626433832795... becomes 3.141593
That tells us that 3.141593 is approximately equal to Pi.
It is so because 3141593/1000000 is approximately equal to Pi.
3141593/1000000 is closer to Pi than 6/2 = 3.0
3141593/1000000 is closer to Pi than 22/7 = 3.142857142857142857142857...
Do you not think it is interesting that 1 / (22/7 - 3) = 7
Yes. Once we have calculated enough digits, we round it up. So 3.1415926535897932384626433832795... becomes 3.141593
That tells us that 3.141593 is approximately equal to Pi.
It is so because 3141593/1000000 is approximately equal to Pi.
3141593/1000000 is closer to Pi than 6/2 = 3.0
3141593/1000000 is closer to Pi than 22/7 = 3.142857142857142857142857...
Do you not think it is interesting that 1 / (22/7 - 3) = 7
all this doesn't explain why pi cannot define a segment
For all who are reading these replies i quote Nobel Laureate David Gross
That is he thought something fundamental was missing and a leap of understanding was necessary
That is he thought something fundamental was missing and a leap of understanding was necessary
QUOTE (different view+Nov 30 2007, 10:15 PM)
For all who are reading these replies i quote Nobel Laureate David Gross
That is he thought something fundamental was missing and a leap of understanding was necessary
Yes, that pretty much sums up your situation as far as I can see. I have no idea whatsoever where you are trying to go, or why I should care to help you get there.
That is he thought something fundamental was missing and a leap of understanding was necessary
Yes, that pretty much sums up your situation as far as I can see. I have no idea whatsoever where you are trying to go, or why I should care to help you get there.
these comments only strengthens my belief that there is something fundamentally wrong with pi for there doesn't seem to be an explanation why it cant deal with segmentation there surly must be an explanation. or is it considered as sacrosanct and beyond question
QUOTE (different view+Nov 30 2007, 10:00 AM)
but surly using decimals in (Pi) takes away the straight line circle relationship
Mmm... it's taken some time, but I actually think I'm starting to understand what you mean by that. I find if I don't think ''too'' much, I can begin to understand what you are trying to say.
I think what you might be saying is, using decimal approximations for Pi is not as precise as simply using Pi.
Could you please explain what you mean by, pi can't deal with segmentation?
To me, it seems you have discovered a novel way of diagramming the to and fro motions of the pendulum. Each to & fro represents one revolution around the circle. Due to dissipating energy, the circle gets smaller and smaller. Eventually over time, the pendulum stops swinging as it tends towards equilibrium.
I think pendulums, pulleys, and scales, could be used to explain the same thing.
Best of luck.
PJ Parent
P.S. So it leaves me wondering what sort of pendulum might produce the prime numbers in its wake. A pendulum that creates the multiplication table for all n, positive/negative? Now is it any wonder I can hear the theme song for Dr. Who in my brain?
Mmm... it's taken some time, but I actually think I'm starting to understand what you mean by that. I find if I don't think ''too'' much, I can begin to understand what you are trying to say.
I think what you might be saying is, using decimal approximations for Pi is not as precise as simply using Pi.
Could you please explain what you mean by, pi can't deal with segmentation?
To me, it seems you have discovered a novel way of diagramming the to and fro motions of the pendulum. Each to & fro represents one revolution around the circle. Due to dissipating energy, the circle gets smaller and smaller. Eventually over time, the pendulum stops swinging as it tends towards equilibrium.
I think pendulums, pulleys, and scales, could be used to explain the same thing.
Best of luck.
PJ Parent
P.S. So it leaves me wondering what sort of pendulum might produce the prime numbers in its wake. A pendulum that creates the multiplication table for all n, positive/negative? Now is it any wonder I can hear the theme song for Dr. Who in my brain?
QUOTE (different view+Nov 30 2007, 02:01 PM)
all this doesn't explain why pi cannot define a segment
um...
Pi/n
um...
Pi/n
QUOTE (different view+Nov 30 2007, 04:01 PM)
all this doesn't explain why pi cannot define a segment
pi is a value that cannot be accurately represented in any base numerical system. It is what is known as an irrational number. Take a rational number and use it as the angle at which a single line turns. Eventually, that line will meet up with itself, forming a geometrical shape. However, if you count, you will see that there is a finite number of turns before the line meets itself, again. (Depending on whether the number you chose is a factor of 360, the final turn may or may not be at the same angle as the rest. This is valid for any system of degrees other than the 360 base system that we currently use, as well; Simply divide a circle up into a number of slices equal to the base system that you wish to use, then substitute the base you chose for the number 360 in the previous sentence. )
The moral of this story is: Pi MUST be an irrational number in order to create an infinite number of turns, or more succinctly, a smoothly curving shape.
Pi is valid in calculating curved line segments. Anything which is smoothly curving can be calculated with the use of pi. Pi is not valid for calculating anything involving sharp angles or straight lines, however, and there is no reason for us to expect it to be.
I hope this was helpful.
pi is a value that cannot be accurately represented in any base numerical system. It is what is known as an irrational number. Take a rational number and use it as the angle at which a single line turns. Eventually, that line will meet up with itself, forming a geometrical shape. However, if you count, you will see that there is a finite number of turns before the line meets itself, again. (Depending on whether the number you chose is a factor of 360, the final turn may or may not be at the same angle as the rest. This is valid for any system of degrees other than the 360 base system that we currently use, as well; Simply divide a circle up into a number of slices equal to the base system that you wish to use, then substitute the base you chose for the number 360 in the previous sentence. )
The moral of this story is: Pi MUST be an irrational number in order to create an infinite number of turns, or more succinctly, a smoothly curving shape.
Pi is valid in calculating curved line segments. Anything which is smoothly curving can be calculated with the use of pi. Pi is not valid for calculating anything involving sharp angles or straight lines, however, and there is no reason for us to expect it to be.
I hope this was helpful.
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