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Topic: would the formulas for area, volume of pseudosphere be affected by
much if infinity were defined as 10^500 #837 Correcting Math

Replies: 254   Last Post: Dec 9, 2017 7:56 PM

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 plutonium.archimedes@gmail.com Posts: 18,225 Registered: 3/31/08
would the formulas for area, volume of pseudosphere be affected by
much if infinity were defined as 10^500 #837 Correcting Math

Posted: Aug 24, 2010 4:06 AM

Let me for a moment change my tactic; instead of trying to get 10^500
as a special number, let me assume it is infinity from the start.

Now the formulas for area and volume of the pseudosphere are :
surface area is
4*pi*R*R while its volume is
(2/3)*pi*R*R*R

So now we define pseudosphere cutaway as a euclidean planar cut.

And we define the boundary of finite versus infinite at
10^500 where that number is infinity itself and all numbers higher.

Now we ask the question of the pseudosphere of radius 1 where it ends
at 10^500 of its poles as a Euclidean
planar cut.

And now we ask, how much of a tiny piece of area do we have missing
from the formula 4*pi*R*R and again ask how much volume is missing
from (2/3)*pi*R*R*R

So when we do the integral, the infinity is replaced by the number
10^500.

So the formulas would no longer be equal to the above but have a tiny
subtraction of missing area and missing volume.

Now maybe that is the specialness of the number 10^500 in that the
missing portions of area and volume, by the selection of infinity as
10^500 is a portion that is
special elsewhere.

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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