My 'calculator Discovery' (And No One Believes Me).

I think I may have made a scientific discovery (on a calculator, if you can believe that). And no one believes me. One message board says it was a bug in the calculator (I cover that claim below, btw). And another more snooty message board hasn't even replied to me, after a whole week. You have to understand, my fellow brethren on the Hip Forums, you are my last hope.

But first some background.

Anyways, as I said, I play around a lot with calculators. And I'm not ashamed to admit it either. You know you can learn a lot that way, believe it or not. And I have even shared some of these things with others on the internet in the past (never here though, to my knowledge).

This next "discovery" is equally as bizarre as the rest. When you take the square root of .111111.... you get .3333333.... Naturally, since the square root of one-ninth is one-third. But one time, just as a lark, I thought I'd square root .11 alone. Then .111 (notice, only three digits), etc.. Long story short, you get the following pattern: 0.33333333331666666666624999999998. As you can see, the .33333... pattern is followed by an intrusive 1666666... pattern, and a 2499999... pattern (leading ultimately to 25, it would seem).

Yeah, it happens with other numbers too. Take .44444... The square root of this repeating decimal is .66666..., two-thirds, naturally. But when you do the same thing, you get 0.66666666663333333333249999999996. A "333..." pattern emerges, and then again that "25" pattern.

It doesn't just happen with these. Consider .9999... That equals one, of course. But when you do the same, you get 0.99999999994999999999874999999994. Now, you get "5" and "75" as your hidden pattern.

(Also odd, is that these patterns are "put off" until infinity. Which I guess is permissible, even if they are never part of the actual number.)

Now, my question. What is the explanation for these strange patterns? Because personally, I think I have hit upon something big and (possibly) undiscovered. I think I may have also hit upon a simpler way of finding irrational numbers. (That is, if they show unique patterns too--just think of how the slide rule uses simple addition and subtraction to find multiplication. Think about it.)

And now an important point. I don't think it is just something found in calculators alone. The square root of .1 is 0.3162277... (N.B. the "16" already there). In short, the pattern is already there, for all to see. It's clearly not a fluke.

So what do the rest of you think? And am I on to something with solving (other) irrational numbers?

 

Well, aren't you special? It's not as if a mathematician wouldn't have found something so simple by now, right?

...you DO realize that the root of .1 is a VERY different number from the root of .111111111...., right? Just the fact that you've found that does not certify the fact that it's not a fluke. I mean, it's hardly relevant.
Also, you do realize that irrational numbers have NO patterns, right? It's what defines them as irrational in the first place.
Sober up. Do it out by hand, don't rely on the calculator. Then we'll talk seriously.

 

OP, do you actually know how to find a square root mathematically? there are quite a few different algorithms and there will always be a a loss of precision on some numbers unless you compute the algorithm for an infinite number of iterations. also the chip in the calculator only has some limited precision (for various reasons such as register size and internal representation).

what exactly is it you think you have discovered? lots of intriguing patterns occur in mathematics.

 

There was "1" girl.
She was "16".
She had a "69" with "3" guys.
How'd she feel in the morning?

"11669x3"

Upside down "35007"

 

see what i said about precision loss .... also some numbers cannot be accurately represented in decimal notation if this is what you mean by the "actual number".

in the case of √2 the actual number is √2 .

 

58008

 

Very good Irminsul.

 

If 142 Israelis and 154 Arabs are fighting over 69 acres of land for 5 days, who won?" You "X" 14215469 by 5, turn upside down..

 

I just opened Calculator and tried .111111 (Square root) and got

0.333333166666624999979166653645824

Yes I do see a pattern within it......

I remember one time in the 80s I was using a calculator and I divided something by 0 and it said 0!! (All other calculators give you an error)

Why is this????? IF YOU DIVIDE SOMETHING BY ZERO,THE TECHNICAL ANSWER IS 0!!!!!!!!!!!

 

No it isn't. If you divide something by 0 you invalidate its existence

 

42

 

fractal geometry

 

As I said, I hope I found a new way to do irrational numbers. You are right though, there are a lot of intriguing patterns that occur in mathematics and on calculators. If anyone else "found" something unique (yes I know, there is probably nothing new in math), feel free to share it.

 

SHELL OIL! (See, I told you I play around too much with calculators .)

 

1134

 

55378008

 

Off hand, my fist thoughts would be that this is an anomaly due to the limitations of the calculator's logic and memory reserve. Probably 8 bit logic and the anomaly is found after 10 digits, The largest 8 digit hexadecimal character number converts into a 10 digit base 10 number. If I open my windows calculator with more digit memory and do the square of 0.111... to the 20th place, the return is 0.333... to the 20th place before the anomaly is seen.

 

this is the closest to describing the artifacts that are emerging. its actually an infinite recursive series embedded in the number. think about the difference between 111/1000 and 1/9 and the prime factors of the denominators.

get the difference and take the square root of that. also factor those numbers out and maybe some other stuff along those lines and see if you can get any closer to pinning it down.

1/4 ... 1/8 .. 1/16 .... well actually it's negative powers of ten for each of those but they are off a bit off course because your converging on one 1/9

I'm pretty sure 1/89 will be found as part of the patten (the error part or at least some fraction of 1/89 that is a common factor of 9, 10 and 89)and it would be interesting if this could be verified or disproved

 

so what does that all mean really?