π/Φ Pi in the Phi

Discussion in 'Physics & Math' started by sly1, Nov 1, 2011.

  1. James R Just this guy, you know? Staff Member

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    Yes. Do you agree that \(2\pi \times r = \pi \times 2r\)?
     
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  3. Motor Daddy ☼☼☼☼☼☼☼☼☼☼☼ Valued Senior Member

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    What is 2*pi?
     
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  5. Beer w/Straw Transcendental Ignorance! Valued Senior Member

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  7. theorist-constant12345 Banned Banned

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    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
     
  8. theorist-constant12345 Banned Banned

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    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.
     
    Last edited: Dec 10, 2014
  9. Motor Daddy ☼☼☼☼☼☼☼☼☼☼☼ Valued Senior Member

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    5,105
    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?
     
  10. rpenner Fully Wired Staff Member

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    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.
     
    Last edited: Dec 10, 2014
  11. Motor Daddy ☼☼☼☼☼☼☼☼☼☼☼ Valued Senior Member

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    5,105
    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?
     
    Last edited: Dec 10, 2014
  12. Beer w/Straw Transcendental Ignorance! Valued Senior Member

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    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.
     
  13. Motor Daddy ☼☼☼☼☼☼☼☼☼☼☼ Valued Senior Member

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    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?
     
    Last edited: Dec 10, 2014
  14. Beer w/Straw Transcendental Ignorance! Valued Senior Member

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

    Agreeing with or not would be irrelevant.
     
  15. Motor Daddy ☼☼☼☼☼☼☼☼☼☼☼ Valued Senior Member

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    So just clarify for me, then, what is 2pi?
     
  16. Beer w/Straw Transcendental Ignorance! Valued Senior Member

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    2 x a mathematical constant.
     
  17. Motor Daddy ☼☼☼☼☼☼☼☼☼☼☼ Valued Senior Member

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    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!
     
  18. Beer w/Straw Transcendental Ignorance! Valued Senior Member

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    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.
     
  19. Motor Daddy ☼☼☼☼☼☼☼☼☼☼☼ Valued Senior Member

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    5,105

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

    Please Register or Log in to view the hidden image!

     
  20. theorist-constant12345 Banned Banned

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    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.
     
  21. Beer w/Straw Transcendental Ignorance! Valued Senior Member

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

    Can you point out the variables in those equations?
     
  22. Motor Daddy ☼☼☼☼☼☼☼☼☼☼☼ Valued Senior Member

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    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?
     
  23. Beer w/Straw Transcendental Ignorance! Valued Senior Member

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

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