11 Jul 06
Originally posted by GammastyleSPMars is right - calculation of pi is based on abstract understanding not concrete procedure on diagrams.
Being a non-math guy. How does one calculate pi. Is there a formula?. Do they measure a radius and diameter more and more exact? I don't understand how they keep getting more and more digits. Please explain.
Your post raises an interesting question, though. Is there such a thing as a circle? I mean in the real-world - is it possible to make a circle out of reality?
12 Jul 06
Originally posted by TommyCThe fact that they exist is easy enough for me to imagine but I cannot even begin to think about how to prove a number is indeed normal.
My undergraduate degree was in mathematics and frankly, I couldn't even understand what was meant to be proven or not most of the time, let alone anything more ambitious.
Btw, I was thinking about these 'normal numbers' (new to me as of this morning) - numbers whose decimal part contains all number sequences - just now on the tube. It's kind of anti-intuit ...[text shortened]... ess deliberately constructed as such from definition (ie unlike most important numbers)?
As to what a random decimal is I would view it as a number in which a decimal cannot be predicted in any way based on preceeding numbers. There is no pattern and every number is equally likely to occur.
A spigot algorithm (a way of generating the nth digit without knowing the preceeding digits) would seem like a good indicator of the first bit (no pattern) but it isn't a proof and even the second bit (all numbers being equally possible) isn't proven.
Apparently also Absolutely Normal numbers have been constructed. That is numbers that are normal in every base.
12 Jul 06
Originally posted by XanthosNZBut how tight is this. 0.123456789101112131415161718... is (trivially) normal, but how does it satisfy the definition of random as having 'no pattern'? The pattern is obvious to human eyes...
As to what a random decimal is I would view it as a number in which a decimal cannot be predicted in any way based on preceeding numbers. There is no pattern and every number is equally likely to occur.
17 Jul 06
Originally posted by uzlessNope, the answer is not a wife. Can we get of the subject of pi please? I only brought it up to show I had a brain, I actually used to know the first 140 #'s of pi, but as of right now I can only remember 18, it was 3 years ago on Mar 14 1:59, pi time. It was for a contest.
The answer is... a wife
17 Jul 06
Originally posted by LinkHyruleA computer can recite pi as far as you wish. It however doesn't have a brain.
Nope, the answer is not a wife. Can we get of the subject of pi please? I only brought it up to show I had a brain, I actually used to know the first 140 #'s of pi, but as of right now I can only remember 18, it was 3 years ago on Mar 14 1:59, pi time. It was for a contest.
Tommy, you have brought up and interesting problem, well at least in my mind. Are there indeed two catagories of normal numbers? Those that satisfy the definition of random and infinite and are therefore normal and those that have a pattern which will give all combinations.
17 Jul 06
1 edit
Originally posted by LinkHyruleI think that pi is much more interesting than your original puzzle!
Nope, the answer is not a wife. Can we get of the subject of pi please? I only brought it up to show I had a brain, I actually used to know the first 140 #'s of pi, but as of right now I can only remember 18, it was 3 years ago on Mar 14 1:59, pi time. It was for a contest.
To my mind there is only one definition of normal number:
Let x be a real number. Then x is normal if and only if for each k=0,1,2,....,9 the limit
lim_{n \to \infinity} ((number of k s in first n decimal places of x) / n )
exists and is equal to 1/10.
A number whose digits are drawn from a uniform distribution on {0,1,2,3,4,5,6,7,8,9} will of course be normal. The problem of course is to show this latter property is difficult!
17 Jul 06
Originally posted by LinkHyruleI say...hmm. I dunno. OHYEAH, my xbox 360.
I am your contant companion.
I am your greatest helper or heaviest burden.
I will push you onward or drag you down to failure.
I am completely at your command.
Half of the things you do you might just as well turn over to me and I will be able to do them quickly and correctly.
I am easily managed-you must merely be firm with me.
Show me exactly ho ...[text shortened]... , and I will place the world at your feet.
Be easy with me and I will destroy you.
Who am I?
