π/Φ Pi in the Phi

[James R]

Yes. Do you agree that $$2\pi \times r = \pi \times 2r$$?

 

[Motor Daddy]

Yes. Do you agree that $$2\pi \times r = \pi \times 2r$$?

What is 2*pi?

 

[Beer w/Straw]

You just don't like $$\pi$$ for being an irrational real number?


"The constant pi, denoted

, is a real number defined as the ratio of a circle's circumference

to its diameter

"

http://mathworld.wolfram.com/Pi.html

 

[theorist-constant12345]

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.

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

 

[theorist-constant12345]

You just don't like $$\pi$$ for being an irrational real number?


"The constant pi, denoted

, is a real number defined as the ratio of a circle's circumference

to its diameter

"

http://mathworld.wolfram.com/Pi.html

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.

 

[Motor Daddy]

You just don't like $$\pi$$ for being an irrational real number?

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?

 

[rpenner]

We could say Pi = 0.00872664625*360=Pi

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 $$ 278567576 \, \sin ( \pi ) = 0$$

69.0975850864/0.00872664625=7918.00000904

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.

 

[Motor Daddy]

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?

 

[Beer w/Straw]

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.

 

[Motor Daddy]

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?

 

[Beer w/Straw]

Mathematics uses abstraction and you want to use physical things that are not.

Agreeing with or not would be irrelevant.

 

[Motor Daddy]

Mathematics uses abstraction and you want to use physical things that are not.

Agreeing with or not would be irrelevant.

So just clarify for me, then, what is 2pi?

 

[Beer w/Straw]

2 x a mathematical constant.

 

[Motor Daddy]

2 x a mathematical constant.

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!

 

[Beer w/Straw]

I did post this earlier:

Radius, circumference and diameter are not defined numbers like $$\pi$$ Otherwise, all circles would be the same size.

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.

 

[Motor Daddy]

I did post this earlier:



Spheres and cylinders are not constant. So how can I be wrong?

So you measure variable spheres and cylinders? Do they change colors too?

 

[theorist-constant12345]

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.

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.

 

[Beer w/Straw]

So you measure variable spheres and cylinders? Do they change colors too?

$$V=\frac{4 \text{$\pi $r}^3}{3},A=4 \text{$\pi $r}^2,\text{and } V=h \text{$\pi $r}^2$$

Can you point out the variables in those equations?

 

[Motor Daddy]

$$V=\frac{4 \text{$\pi $r}^3}{3},A=4 \text{$\pi $r}^2,\text{and } V=h \text{$\pi $r}^2$$

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?

 

[Beer w/Straw]

Why don't you just be quiet and think for once.