3.141592653589 blah blah blah.

Let's just work base 3 say, to make an example fit on the screen.

Champernowne for this base is .(1)(2)(10)(11)(12)(20)(21)(22)(100)...

Brackets around each number for clarity.

I'll put inserted digits in bold and remove the brackets. Do you mean:


.121102111102202111221012...

where you are considering the two digit numbers as shifts, that is you will eventually be shifting by very large amounts, or maybe

.12110211011112120220221201...

where you're just viewing the Champernowne constant as a string of digits, here you will never shift by more than 2. Or maybe something in between?

Actually, I don't really know what the answer would be for either one. Both seem like they might still be normal (base 3), but that's nothing more than a hunch.

ps. you might like http://www.armory.com/tests/math.html
 
shmoe said:
...where you're just viewing the Champernowne constant as a string of digits, here you will never shift by more than 2. ...
Click to expand...
Basically Yes. I knew or at least thought initially that the "Normal Property" must prevent any correlation between adjacent single characters of the base.
For example, in your base three, decimal 0,1,2,3,4,5... is 0,1,2,10,11,12...(6 elements shown)
but I was naively considering it to be the string: 012101112.....(9 characters shown)
This does not make a lot of math sense to me now, but guess it could be considered also.
I think the more reasonable thing mathematically to be asking about is the insertion of the next element, which will have eventually a very big value, (lots of characters) and thus this very big value will have a lot of "female characters"* between two pieces of the male string. (The males, pieces / elements, of coures, get bigger and bigger as more females come between them.

I am trying to repress my DOM tendencies, but lacking proper math terminaology, this is the clearest way to try to communicate my ideas.

Consequently this "more reasonable" insert the whole male value / element, not just a character, will leave the female relatively "contaminated" by the male. As a result of this, I think surely the combined string is still "normal"
-------------------------------------
*If it were lot of 'female elements" eventually for each male element then we get back to low contamination of the females again.

Alternatively, to give it more of a chance to remain "normal" perhaps my original naieve idea (characters inserted between skipped characters) is also interesting. For example, in your base three, 1/3 of the inserts result in zero female characters between two male characters, 1/3 will have one female character between two males characters and 1/3 will have two females characters between two male characters, but none of the original elements of either string survive, except a few at the start of the resultant "combined string." Also as the average number of females characters skipped is one per male character inserted, the combined string is 50% of each. An offspring favoring neither mother nor father, (but only in the base three case? or only in odd base cases? - it is late for me, so will not think this question out clearly, now).

There is good chance I will be away for two days, so may not get back to you for a while. This is becoming mainly an exercise to stimultate your more serious thoughts and amuse me with the terminology I seem to need, purely for mathematical reasons, nothing to do with my DOM nature. :D
 
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Hapsburg said:
Heh. Wuss. :p
Click to expand...

pi is sqrt[2-sqrt[2+sqrt[2+sqrt[2+sqrt[2]...]]]] times 2^no. of square root signs. ie one can find pi on a calculator by entering only 2's & the no. or radical signs
 
the_almighty said:
pi is sqrt[2-sqrt[2+sqrt[2+sqrt[2+sqrt[2]...]]]] times 2^no. of square root signs. ie one can find pi on a calculator by entering only 2's & the no. or radical signs
Click to expand...

That doesn't yield pi.

sqrt[2-sqrt[2+sqrt[2+sqrt[2+sqrt[2+...

is zero (although the convergence is very slow).
 
There's a "times 2^no. of square root signs" term, the sequence is:

sqrt(2)*2, sqrt(2-sqrt(2))*2^2, sqrt(2-sqrt(2+sqrt(2)))*2^3,...

the nth term is sin(Pi/2^(n+1))*2^(n+1), (use half angle formulas). This is approximating pi by calculating the perimiter of a circle with the perimiter of an inscribed regular polygon with 2^(n+1) sides.
 
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