Eratosthenes calculated the circumference of the Earth without leaving Egypt. Maybe history used Pyramids bases and shadows to make the measurements of time and distance. Indeed, wrap a piece of string, around a circle and the distance is always the value of 2Pi*2r, and this is why the values work. They are not numeric values just pulled from fresh air, they are measurable values that always ''predict'' the correct results. I never personally use to see the true value of maths, but I am starting to see why the importance of the values match Physical process.

A string the length of the circumference is always 3.1416 (rounded off) times as much string length as the length of sting that is the diameter. It is not 4.3 times longer than the diameter length of string. It is not 2.13 times longer, or 3.07 times longer, or even 8.32 times longer, it is 3.1416 times longer! So diameter*3.1416=circumference. If you want to use radius then r=d/2 so (d/2)2*3.1416=circumference.

It is not 2*pi, where do you get that from? You measure the diameter with a length of string. You measure the circumference with a length of string. The circumference string is 3.1416 times longer than the diameter string, so circumference/diameter=3.1416 (which we refer to as pi) If you measure the radius with a length of string, the circumference is 6.2832 times the length of the radius string. If the radius is .5 units then the circumference is 3.1416 units. See? If the diameter is .5 units then the circumference is 1.5708 units.

"2pi" is a math thing you do, which has nothing to do with reality. As I explained, pi is a ratio, so multiplying pi by 2 is saying what in reality?

It is not saying anything, it is just another way of calculating the same numerical value of what the circumference is equal to. pi*2r 2pi*r pi*diameter All give the same results but are just written differently.

Did you understand the words, ""2pi" is a math thing you do, which has nothing to do with reality."?? Again, since you missed it: 2 strings, one the length of the diameter and one the length of the circumference. The circumference string is 3.1416 times longer than the diameter string. There is no 2*pi about it!

pi*dia is the way it is used and written. This does not mean that written differently does not give the exact same result in a numberang sense. di7918/2=r3959 pi*di=24875.1306311 pi*2*r=24875.1306311

I suppose it is to do with how many times you wrap the string around. Halving the di , meaning twice has many times around but still being equal to the length etc. I am pretty sure from of recent events and learning, Pi, is pretty irrefutable.

What? There is no "wrapping how many times." Where do you get that from? A string is the length of the circumference. A different string is the length of the diameter. circumference/diameter=pi. There is no "2pi" about it!

There is in numberang. You are saying if we had 2 pieces of string, one being 10m in length, and the other being pi times longer than the 10m string. The longer string is 31.4159265359m The 31.4159265359m string, will fold around the 10m string and make a perfect 360 degrees, one end of the string touching exactly the other end of the string at 0 degrees. And the shorter string being exactly at 90 degrees a horizontal linearity to 270 degrees to give exactly 360/2=180 of the original 31.4159265359 cir. 31.4159265359/2=15.7079632679 So now we have 3 pieces of string. pi/2=1.57079632679 15.7079632679 /1.57079632679=10

We'll call them, diameter (10 meters), .5 circumference (15.7079632679 meters), and a full 1.0 circumference (31.4159265359 meters). What is pi/2? A half of a full ratio of a circumference to a diameter?

Yes, pi/2 gives half of the full ratio to a circumference. 1 degree equals the 69.xxx miles I mentioned, 24875.1306311/360=69.0975850864 Pi/360=0.00872664625 69.0975850864 /0.00872664625=7917.99966879 di

So you're trying to figure out what the length of half of the circumference of a 10 meter diameter circle is? Well a 10 meter diameter circle has a circumference of 10*3.1416=31.416 meters. If you divide that by two, well there's your answer! You can find 1/360th of that circumference by dividing by 360, so 31.416/360=0.0872666666666667 meters. So each degree has a length of 0.0872666666666667 meters along the circumference of a 10 meter diameter circle. 29.385 degrees is a length of 29.385*0.0872666666666667=2.564331 meters along the circumference of a 10 meter diameter circle.

I think he's trying to tell you that for a circle \(c = 2\pi r = \pi d\), where \(c\) is the circumference, \(r\) is the radius and \(d\) is the diameter. The reality is that \(d=2r\). Due to the wonders of mathematics, it turns out that for "ordinary" kinds of numbers (the kind you're familiar with) \((2a)\times b = a\times (2b)\) for any \(a\) and \(b\). Put, for example, \(a=\pi, b=r\) and we miraculously find that \((2\pi)r = \pi(2r)\).