You just don't like \(\pi\) for being an irrational real number? "The constant pi, denoted Please Register or Log in to view the hidden image!, is a real number defined as the ratio of a circle's circumferencePlease Register or Log in to view the hidden image! to its diameterPlease Register or Log in to view the hidden image!" http://mathworld.wolfram.com/Pi.html
Yes, you got it, I think, You can divide any circumference by 360 You can then divide Pi by 360 A division of the two gives the diameter. 1 degree =cir/360 1 degree=Pi/360 cir/Pi =2r or 1 di t.s per rotation/360 = 1 degree
We could say Pi = 0.00872664625*360=Pi 69.0975850864/0.00872664625=7918.00000904 edit-sorry had to change value copied and pasted wrong one from my notes.
If 2*pi*r=pi*2*r, if you divide the left hand side and the right hand side by 2, they cancel and what you're left with is pi*r on both sides. pi*r=pi*r is what you're trying to prove?
But then we would be mathless slaves of a calculator and wrong. \(0.00872664625 = \frac{872664625}{10^{11}} = \frac{6981317}{8 \times 10^8}\) so \(0.00872664625 \times 360 = \frac{62831853}{2 \times 10^7} = 3.14159265\) which is a ratio of integers or a "rational number", and not equal to pi. Two demonstrations with precision math that \(\pi \neq 3.14159265\): \( \frac{62831853}{2 \times 10^7} + \frac{1}{ 278567576} \lt \pi \lt \frac{62831853}{2 \times 10^7} + \frac{1}{ 278567575} \) \( 278567576 \, \sin \left( \frac{62831853}{2 \times 10^7} \right) > 1\) but \( 278567576 \, \sin ( \pi ) = 0\) By 69.0975850864 did you mean \(\frac{6909758508635}{10^{11}}\), \(\frac{21179239}{306512}\), \(\frac{690975850864}{10^{10}}\), \(\frac{6909758508645}{10^{11}}\), \( \frac{3959 \pi}{180}\), or \(\frac{24604199}{356079}\) (which I have listed in ascending order)? How do you know? Does your source have that many digits of precision? Is this a physically measured quantity? What is the source? Conventionally, a decimal quantity on a display with a fixed amount of display digits can stand for the whole range of numbers that round to that displayed number, so 69.0975850864 stands for all numbers, x, in the range \(\frac{6909758508635}{10^{11}} \leq x \lt \frac{6909758508645}{10^{11}}\). But if you don't know which one, multiplication (on a calculator with only finite precision in operations) doesn't guarantee all the digits of your answer are exact. But, garbage in leads to garbage out, so if you don't have a reason to know how accurate your source is, you can't know how accurate your answer is even if you do use arithmetic with absolute precision.
circumference = diameter*pi (ratio of circumference to diameter (~3.1416:1)) = radius (1/2 of the diameter)*ri (ratio of circumference to radius (~6.2832:1)) How ya say...how do ya like them apples?
1+1 = 2 and 2+2=4 and dividing both sides of that equation by 2 we get 1+1=2! Radius, circumference and diameter are not defined numbers like \(\pi\) Otherwise, all circles would be the same size.
There is a unit of measure of distance called the meter. It is defined as the length of the path that light travels in 1/299,792,458 of a second in a vacuum. If a light sphere is emitted at t=0 it has a radius of 1 meter and a diameter of 2 meters at t=1/299,792,458 of a second. Agreed?
Mathematics uses abstraction and you want to use physical things that are not. Agreeing with or not would be irrelevant.
That constant is a constant RATIO, like the gear ratio in the rear end of your car. If a gear ratio is 3.1416:1, that means that 3.1416 turns of the input shaft is equal to 1 turn of the output shaft. If the tire has a diameter of... and the rpm is... oh you do the math! The point is, you're wrong!
I did post this earlier: Spheres and cylinders are not constant. So how can I be wrong? They all use the same mathematical constant as \(\pi\), but not the others.
So you measure variable spheres and cylinders? Do they change colors too? Please Register or Log in to view the hidden image!
Pffff, I got the 69 number from a circumference divided by 360. Your maths is far to advanced for me, I do not have a clue what all your numbers mean.
\(V=\frac{4 \text{$\pi $r}^3}{3},A=4 \text{$\pi $r}^2,\text{and } V=h \text{$\pi $r}^2\) Can you point out the variables in those equations?
Trying to avoid how you explain how you measure a changing cylinder's diameter and circumference?? You said, "Spheres and cylinders are not constant." So you're trying to say the cylinder is changing?
