Skans » 05 Oct 2023, 11:51 am » wrote: ↑ I am certain that it is correct; i.e. that the infinite non-repeating decimal places of Pi is a function of a circle's roundness as it approaches perfect roundness. You just have to think of this from a different perspective. Stop thinking of Pi as a fixed number. Think of it as a dependent variable. Think of it in terms of a circle, or sphere perfecting its roundness, and then watch in your own mind what happens to the number Pi as the spherical or circular object approaches perfect roundness.
Fixed points and lines only create polygons, not perfect circles. The ratios between straight lines and circles, or even curved lines, are simply incompatible at their limits.Vegas » 05 Oct 2023, 11:58 am » wrote: ↑ But it isn't approaching a perfect roundness. It already is perfectly round. You are still taking the perspective of an infinite sided polygon merging into a circle. Ok, that is fine. However, that is not the only way to create a circle. It can be created by fixed points and lines.
Skans » 05 Oct 2023, 12:04 pm » wrote: ↑ Fixed points and lines only create polygons, not perfect circles. The ratios between straight lines and circles, or even curved lines, are simply incompatible at their limits.
It's a constant @Skans 3/1 equals 6/2 equals 1.5/0.5. The measure of the circumference increases and decreases incrementally and in perfect ratio with the length of a radius.Skans » 05 Oct 2023, 11:31 am » wrote: ↑ In your method, yes, the radius is a fixed, precise line. However, it's the circumference that is not precise. It only approaches perfect roundness. Nor can the radius ever perform a perfect "sweep" of the circumference. I believe this can be proved in the math discipline known as Contour Integration, but that is above my pay grade.
walkingstick » 04 Oct 2023, 1:33 pm » wrote: ↑ usa about to explode!!!! duck and cover. the atom bombs are on the way.

Dalai Lama created the three truth scenarios and I see you selected one of the three, literal translation of the word circle. That results in you only being 33 and a third percent accurate about the whole issue.Skans » 05 Oct 2023, 9:42 am » wrote: ↑ A circle doesn't exist. All "things" that resemble circles are polygons. There is no such thing as a perfectly round circle. Circles can only approach perfect roundness. This is why Pi is an irrational number.
All I'm doing is trying to get you to look at this another way. How would you define the "roundness" of natural circle? Does Pi have any relationship to this, or not?Vegas » 05 Oct 2023, 12:15 pm » wrote: ↑ I know, but if its fixed, then there is no longer any merging. The circle's lines, or sides of the polygon, will hit a finite limit since the radius is finite. The only way it can merge is if you start with a finite number of sides on a polygon and then increase the number of sides to infinity. However, if you begin with a finite line with an endpoint fixed, then the merging has reached a final finite destination.
You can read the answer I gave to Vegas. It addresses what you've said.Monderegal » 05 Oct 2023, 12:37 pm » wrote: ↑ It's a constant @Skans 3/1 equals 6/2 equals 1.5/0.5. The measure of the circumference increases and decreases incrementally and in perfect ratio with the length of a radius.
Skans » 06 Oct 2023, 7:41 am » wrote: ↑ All I'm doing is trying to get you to look at this another way. How would you define the "roundness" of natural circle? Does Pi have any relationship to this, or not?
You think of Pi as a fixed irrational number, just as you probably do with the speed of light (not an irrational number) - as a given, a constant. I think of Pi as a component of a circle in terms of a calculus limit approaching perfect roundness.
seems to me that set of figures just proves a measurement was off or you were just measuring the leg of a right angle to a hard sided object.Skans » 04 Oct 2023, 6:02 pm » wrote: ↑ Actually, Pi does change with the roundness of the circle. If you construct a near circle with a thousand tiny lines linked together around a centerpoint, Pi (not true Pi, because its not a true circle) will be a rational number. Lets take this to the extreme and perhaps you can follow me:
C = 2 π R
π = C/2R
Where the Circumference of the near-circle is actually 10 equal-length lines around a centerpoint, a Decagon, Pi will be a rational number:
Assume each line of the Decagon is exactly 10 centimeters long. The Circumference of this near-circle would be 100 centemeters. The radius is 16.18034. So, let's calculate π.
π = C/2R.
π = 100/2*16.18034
π = 100/32.36068
π (near pi) = 3.0901699222685 The digits to the right of the decimal will eventually repeat or stop.
As the circle approaches being perfectly round,π will approach the 3.1415....irrational number. With each iteration of smaller and smaller lines making up the near-circle, π needs to "shift" and morph to accommodate the new near-circle structure.
This should be able to be expressed as a calculus limit. But, its not that easy:
lim π→irrational number−C→more perfect roundness.
It's not easy because I don't know how to express something becoming "more round" to a point of perfect roundness. But, this guy, Yasuhiro Takashimizu, has some additional thoughts on this. https://progearthplanetsci.springeropen ... 015-0078-x
Pi is about measuring physical distance, not time an object occupying space. inside a circle the outside is same distances from the core at any angle going out or coming in on the linear plane.Skans » 06 Oct 2023, 7:41 am » wrote: ↑ All I'm doing is trying to get you to look at this another way. How would you define the "roundness" of natural circle? Does Pi have any relationship to this, or not?
You think of Pi as a fixed irrational number, just as you probably do with the speed of light (not an irrational number) - as a given, a constant. I think of Pi as a component of a circle in terms of a calculus limit approaching perfect roundness.