The dia and circum ARE finite - that isn’t the issue.
The issue is the effort to express those values with decimal digits - a value being finite and fixed does not mean that decimal digits can exactly represent it - pi is one of those values. The problem is how the value is being expressed.
And pi is NOT equal to an inaccurate measured circum divided by an inaccurately measured dia. If your measurements are not accurate - of course you are not going to get pi - that is one way to know that your measurements were inaccurate - and all measurements are always estimates - other than simple counting.
That is the whole point - there actually isn’t one - so we call it “pi”.
The problem is merely that some values cannot be exactly expressed by decimal numbers. They are called “irrational numbers” (should be called “irrational values”).
So I tell you that I have a circle with a diameter of 1.0 units, and ask you how many units the circumference is, and your answer is “there isn’t one.”
So what good is your Pi if you can’t use it to determine the number of units of a circumference, given a number of units for the diameter??
Pi x Diameter = Circumference
I know the diameter is 1.0 units. I am asking you how many units the circumference is. Are you saying you can’t do the math of Pi x Diameter and tell me how many units the circumference is?
All maths concepts are about perfect and ideal shapes and quantitative values to be used to gain more precise estimates of reality. That includes all shapes such as perfect squares, circles, spheres, as well as quantities such as 47.537, sqrt(2), and pi.
In reality - you don’t “need a number”. In real life all anyone ever really needs is a good enough estimate.
As everyone has told you - probably from your birth - that is a way of getting a close enough estimate because there is no perfectly accurate decimal number representation for pi (everyone seems to know that but you - wonder why).
But a circumference has an EXACT length. I can measure the circumference with a theoretical piece of string, and that string has an EXACT length. It is a FINITE NUMBER OF UNITS in length. It can even be EXACTLY 1.0 units!
A circumference of exactly 1.0 units divided by Pi means the diameter is what, an irrational number of infinite length???
How about if I have a theoretical piece of string the same length as the circumference, and a theoretical piece of string the same length of the diameter. They are both an exact finite length.
Now all I have to do is find out how many times longer the circumference string is than the diameter string.
You’re saying the circumference string is infinitely longer than the diameter string??? Isn’t the circumference string a finite number times longer than the diameter string?
We do not derive Pi by using strings to measure the diameter of a random circle someone drew on a piece of paper and then divide that by its circumference… measured by a string.
That too would be an approximation… but it would be a terrible inaccurate one compared to the method we’re utilizing currently.
We derive Pi by way of adding ever increasing number of polygons to approximate a circle and utilize basic geometry to derive Pi. Pointing out it’s an approximation isn’t news to anyone who knows how we got the number Pi in the first place
It will literally never end nor repeat in any pattern, because when you add another polygon to the growing approximation of a circle it changes the geometric formula… it’s not progressing in a rational way that would form repeating patterns. Likewise no matter how many polygons you add, you’re never done creating a circle… so repeat forever… but as you approach infinity Pi approaches the true number.
Math is just a more precise language we use to describe things… and as you’ve demonstrated very clearly… language can be misused. Like how I might say in english “the barking is dog, when park walked was in”
but my bungled speech does not render english useless… it just means I don’t know how to use the language properly.
I remember one poster on ILP a few years back thought she had broken math by stating 1+1=1… her proof?
1 pile of sand put onto another pile of sand… would result in one pile of sand. Which I suppose, if we’re being generous, is a category error. What she meant to say was 1a + 1b = 1c
A circumference is not some number of polygons, it is a “border” that has an exact radius from a point that is EXACTLY the same in every direction. It is a representation of a point with the same distance in every direction.
PI is a RATIO of the length of the circumference to the length of the diameter, which diameter is twice the radius, which is the distance from the point to the border.
…and oh, by the way, Circumference divided by diameter equals PI. It is the RATIO of the circumference to the diameter. It has nothing to do with “increasing number of polygons.” That is MORONIC!
A cylinder has an exact volume, and that volume is measured as Area x Length. Area is Pi(r^2).
If a circumference is 1.0 units, then the diameter is how many units, an infinite irrational number? Moronic!
Possibly… another possibility is that you’ve misunderstood or possible never been told why we do it that way… and absent that knowledge, you think it’s moronic.
You are absolutely correct, we can derive Pi by dividing the diameter of a perfect circle by its circumference…
Do you have a perfect circle for us to measure? and a means for us to measure it with perfect precision?
Can you conjure up a hypothetical perfect circle?
In this hypothetical how are you deciding what the diameter is relative to the circumference? are you just making up numbers for those two?
What’s your alternative… you know… that’s less moronic.
As for why polygons are useful for getting circumference and diameter, is because we can calculate the of hypotenuse of a triangle from the length of its legs or vice versa, so we can get both the diameter of the circle approximation and the circumference of the surface by adding the surface of the triangles together… add more triangles, it’s more like a circle… and the numbers become more accurate… approaching the real thing.
We can actually get a more accurate measurement than any circle could ever be measured in the real world, because the subatomic levels at which we’d have to measure it’s exact diameter or circumference would be too tumultuous and inconsistent compared to our current computer generated polygon circle… so… I’d love to hear your alternative.
All numbers and even language here are only approximations.
Now.
You can look at approximations and say referents don’t refer precisely, so they mean nothing.
There are axioms beyond the physical world though…
Ideal in fact.
Nobody wants their consent violated ever or forever.
Now. Let’s back up. The platonic forms are not about perfect shapes … they are about the abstraction of category.
Every tree I’m looking at is infinitely different from each other. If I used infinite precision, I wouldn’t have category to say… “hey look at these trees”
Categories are approximations.
If you have more questions, please ask. I try to keep my posts short.
No, I’m saying the measure of it is potentially infinite in precision…
Imagine a universe where atoms can be split into smaller subatomic particles and those particles can be split into yet more particles and so on forever… there is no “bedrock” of smallest thing.
Now imagine you asked me how tall are you? I could give you an infinitely long answer… depending on how precice you wanted me to be… are we counting to the atom? are we counting to electrons? are we counting to infinity?
it goes on infinitely… because it can calculate to infinite decimal places of accuracy… lucky for you and me, it doesn’t seem like we live in such a universe, so we’d probably stop at atomic length… or possible quarks… cuz it doesn’t get smaller than that.