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January 29th, 2017, 11:03 PM   #1
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3y^4-32y-192=0

It has come to my notice that this equation 3y^4-32y-192=0 gives a value of (pi) a mathematical constant which is approximately to 3.1425.......can this equation be used to give a value of pi to any number of decimal places needed instead of known equation pi=circumference of a circle divide to its radius? kadomole

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January 30th, 2017, 02:11 AM   #2
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Whereas pi is 3.14159265358979..., your equation has solution 3.14248520690..., and so the two are rather different. To get closer to pi, your equation would need to be changed, and to get very close to pi would require very substantial changes.
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January 30th, 2017, 06:55 PM   #3
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Isn't pi transcendental?
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January 30th, 2017, 07:17 PM   #4
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As has been pointed out,

$y \approx 3.14248 = 3.14159 + 0.001 -0.00011 \implies y - \pi \approx 0.0089.$

In fact, y is an algebraic number, and $\pi$ is a transcendental number so the two are not even in the same subset of the real numbers.
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February 1st, 2017, 07:09 AM   #5
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pi is not an algebraic number, so pi cannot be a root of any polynomial with rational coefficients.
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February 11th, 2017, 06:15 AM   #6
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3y^4-32y-192=0

Quote:
Originally Posted by kadomole simon kadomole View Post
It has come to my notice that this equation 3y^4-32y-192=0 gives a value of (pi) a mathematical constant which is approximately to 3.1425.......can this equation be used to give a value of pi to any number of decimal places needed instead of known equation pi=circumference of a circle divide to its radius? kadomole
which method is used to measure radius and circumference of circle? hence "pi"?any error?it can be proved mathematically that y="pi" satisfies 3y^4-32y-192=0 ,what is your comment?kadomole
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February 11th, 2017, 06:33 AM   #7
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Quote:
Originally Posted by Monox D. I-Fly View Post
Isn't pi transcendental?
is y=3.14248520690....NOT a transcendental number?kadomole
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February 11th, 2017, 06:39 AM   #8
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Calculating pi is a bit like the guy who spent years sticking
together over a million matches to come up with a miniature
'London Bridge': got queer looks, some respect for his tenacity...but only 5 bucks at the corner pawnshop....

This stupidity seems to have started in England (where else!)
in the early 1900's. A British mathematician William Shanks
worked it out to 707 decimal places doing calculations by hand
for over 20 years. POOR BILL: an error in the 528th place was
discovered in 1945...wonder if they changed the inscription
on his tombstone
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February 11th, 2017, 07:52 AM   #9
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Quote:
Originally Posted by kadomole simon kadomole View Post
it can be proved mathematically that y="pi" satisfies 3y^4-32y-192=0
Ummm... no it can't. But please, show your proof that it is.

-Dan
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February 11th, 2017, 11:50 AM   #10
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Oh, for goodness' sakes.

$3y^4 - 32y - 192 = 0 \implies 3.1424 < y.$

$\pi < 3.1416 \implies -\ 3.1416 < -\ \pi.$

$\therefore (3.1424 - 3.1416) < (y - \pi) \implies 0.0008 < (y - \pi) \implies$

$\pi < y - 0.0008 < y \implies \pi < y.$

$\therefore \pi \ne y.$
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