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where pi is a whole number square root and cube root and a proof
Chapt13.40085 Maxwell Equations placing demands on mathematics #634 New
Physics #754 ATOM TOTALITY 5th ed
Posted:
Jun 16, 2012 2:21 AM
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On Jun 15, 5:39 pm, Archimedes Plutonium
<plutonium.archime...@gmail.com> wrote:
> On Jun 15, 5:23 pm, Archimedes Plutonium
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> <plutonium.archime...@gmail.com> wrote:
> > On Jun 15, 1:18 pm, Archimedes Plutonium
> (snipped in parts)
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> > If you look at the number "e" it is a constant of 2.71828.. and I
> > could have written
> > it out to 603 digits and removed the decimal point and asked if it is
> > cube-root whole number anywhere along its string of digits? 271828..
> > and the answer is yes because the
> > first two digits 27 is 3^3.
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> > The same sort of question I am asking about pi, if perchance the first
> > time that pi is
> > evenly cube rooted is this number of pi:
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> > 31415926535 8979323846 2643383279 5028841971 6939937510 5820974944
> > 5923078164 0628620899 8628034825 3421170679 8214808651 3282306647
> > 0938446095 5058223172 5359408128 4811174502 8410270193 8521105559
> > 6446229489 5493038196 4428810975 6659334461 2847564823 3786783165
> > 2712019091 4564856692 3460348610 4543266482 1339360726 0249141273
> > 7245870066 0631558817 4881520920 9628292540 9171536436 7892590360
> > 0113305305 4882046652 1384146951 9415116094 3305727036 5759591953
> > 0921861173 8193261179 3105118548 0744623799 6274956735 1885752724
> > 8912279381 8301194912 9833673362 4406566430 8602139494 6395224737
> > 1907021798 6094370277 0539217176
> > 293176752384674818467669405132000
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> Now the cube root of that number would be 146459189..
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> So the question is, at digit 10^201 for 10^603, does that cube root
> have a 0 ending digit?
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> I found plenty of specialness about pi at 10^603 for geometry, but if
> pi is evenly cube root
> at 10^603 would be a beautiful algebra specialness for pi.
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Now I did promise to immediately turn back again and focus on physics,
but let me
just do a little more while on this island of mathematics. As the
example above shows
that "e" is a whole number cube root at 27. So we ask whether e and pi
have more such
whole number square roots or cube roots. Now some may think that only
"27" is a whole
number square or cube root of both "e and pi". But I think we can
immediately draw up
a pattern that both pi and e have a lot more of square root and cube
roots.
This reminds me of the proof that pseudosphere area catches up with
attendant sphere area,
due to the three zeroes in a row in pi allow incremental add ons to
the pseudosphere but no
new add ons to the sphere area and so the pseudosphere catches up,
perhaps even surpasses the associated sphere when pi has those three
zeroes in a row.
So the same pattern applies to square root and cube root in that pi
and e will at some moment have
4 zeroes in a row and at some point have 6 zeroes in a row. And the
message here is that when pi has
those many zeroes in a row, that the associated square root or cube
root number will need to be able to
multiply two or three digits (square or cube root) in order to muster
a "0" And the only two way to muster that
zero or string of zeroes is by carryover, or by the digit being "0".
Now that does not constitute a proof but only
a strong indication that 27 = 3^3 is not the only whole cube root
number in both pi and e, and that there are
far more such roots.
What I really want to know is whether that number above of pi at
3x10^603 has a whole number cube root
due to those three zero digits in a row. Now in 2011, the Computer
said no, it is not a even whole number
cube root there. But perhaps the computer made a mistake or was
insufficiently programmed for the task?
Archimedes Plutonium
http://www.iw.net/~a_plutonium
whole entire Universe is just one big atom
where dots of the electron-dot-cloud are galaxies
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