Guest guest Posted November 2, 2006 Report Share Posted November 2, 2006 Sent to me by my sister-in-law (who got it from someone else). Subject: FW: The Beauty of Mathmagic Date: Thu, 02 Nov 2006 15:32:04 +0100 Very pretty numbers!!! The Beauty of Mathemagic 1 x 8 + 1 = 9 12 x 8 + 2 = 98 123 x 8 + 3 = 987 1234 x 8 + 4 = 9876 12345 x 8 + 5 = 98765 123456 x 8 + 6 = 987654 1234567 x 8 + 7 = 9876543 12345678 x 8 + 8 = 98765432 123456789 x 8 + 9 = 987654321 1 x 9 + 2 = 11 12 x 9 + 3 = 111 123 x 9 + 4 = 1111 1234 x 9 + 5 = 11111 12345 x 9 + 6 = 111111 123456 x 9 + 7 = 1111111 1234567 x 9 + 8 = 11111111 12345678 x 9 + 9 = 111111111 123456789 x 9 +10= 1111111111 9 x 9 + 7 = 88 98 x 9 + 6 = 888 987 x 9 + 5 = 8888 9876 x 9 + 4 = 88888 98765 x 9 + 3 = 888888 987654 x 9 + 2 = 8888888 9876543 x 9 + 1 = 88888888 98765432 x 9 + 0 = 888888888 Brilliant, isn't it? And finally, take a look at this symmetry: 1 x 1 = 1 11 x 11 = 121 111 x 111 = 12321 1111 x 1111 = 1234321 11111 x 11111 = 123454321 111111 x 111111 = 12345654321 1111111 x 1111111 = 1234567654321 11111111 x 11111111 = 123456787654321 111111111 x 111111111=123456789 87654321 awesome Quote Link to comment Share on other sites More sharing options...
Guest guest Posted November 2, 2006 Report Share Posted November 2, 2006 142857 x 7 = 999999 142857 / 7 = 020406.142857142857142857...(etc.) Kate Gladstone Quote Link to comment Share on other sites More sharing options...
Guest guest Posted November 3, 2006 Report Share Posted November 3, 2006 Need a scientific hand calculator to experience this: the simplest true Chaotic Number generator ! Pick any non-0 number, then press repeatedly x^2, then ln... The number series has all the requisite properties: - Infinite sensitivity to initial conditions - Positive Lyapunov exponent - Ergodicity (after a time numbers will come in various intervals with given frequencies, regardless of the starting number !) - Fills all the number space (after enough tries, it will come as close as wanted to any given number) Makes a very interesting " numeric stim " ! Discovered by me at 6 years of age, when first exposed to a calculator... Also soothing and utterly useless: Enter " Radian " mode, pick a positive number (say 0,1) then: sin, sin, sin... a slowly ever-decreasing sequence OR tan, tan, tan... a slowly ever-increasing sequence OR sin, sin, tan... a much subtler decreasing sequence. All have very interesting " moire " effects in counting how many pushes of the button are needed to move from one number to another (say from 0,06 to below 0,05)... Also: 1/100th of a stopwatch give a physical d10 random generator statistically proved better than any dice I could find. Thank you for thinking about this, Mircea Pauca, Bucuresti, Romania Re: beautiful numbers > > > > > 142857 x 7 = 999999 > > > > 142857 / 7 = 020406.142857142857142857...(etc.) > > > > > > Kate Gladstone > > > > 2^64 - 1 = 3 X 5 X 17 X 257 X 65537 X 641 X 6700417 > > Jerry Newport > > That is how many grains of rice you get if you put one grain on a > square of chessboard, two on the next and keep doubling until alo > squares are covered Quote Link to comment Share on other sites More sharing options...
Guest guest Posted November 3, 2006 Report Share Posted November 3, 2006 Mircea notes ... > the simplest true Chaotic Number generator ! > > Pick any non-0 number, then press repeatedly > x^2, then ln... > > The number series has all the requisite properties: > - Infinite sensitivity to initial conditions What does this mean, please? > - Positive Lyapunov exponent Also — please, what does this mean? Kate Gladstone Quote Link to comment Share on other sites More sharing options...
Guest guest Posted November 3, 2006 Report Share Posted November 3, 2006 > The number series has all the requisite properties: > - Infinite sensitivity to initial conditions [Kate Gladstone] > What does this mean, please? If you start with two very close initial numbers (say 2 and 2,0000001), the series started from them will continue to be close only a short, predictable time then will get completely different and unpredictable from one another. This is Chaos ! > > - Positive Lyapunov exponent [Kate] > Also — please, what does this mean? A measure of how different two close 'histories' grow. A compound interest rate is a good example of an artificially-made Lyapunov exponent, intended to mirror the one implied in the growth of real things in an economy. (Another thing to think on: can/should an interest rate exist in a stagnant economy ?) Mircea Quote Link to comment Share on other sites More sharing options...
Guest guest Posted November 3, 2006 Report Share Posted November 3, 2006 [Kate] > Mircea — does " 0,1 " in your statement mean what > " 0.1 " means in the USA (namely, 1/10)? Yes. That's the European standard. I'll be glad if some of you tested my number stims ;-) Mircea Quote Link to comment Share on other sites More sharing options...
Guest guest Posted November 3, 2006 Report Share Posted November 3, 2006 I am so into sightings of the number 1. Like when my car mileage has a lot of ones in it, or the time is 1:11 or 11:11. I always seem to look at the clock just then. Also 4. So if I see 111444 or something like that during the day I always have a special feeling. It was cool when my mileage was 141111. I always reset the mileage counter so i can maybe see 111 and 444... but then I sometimes reset it so that I will NOT look at it when I am supposed to be driving. I didn't know about the symmetry. It makes me want to memorize them... those are very very beautiful. Rhonda > > Sent to me by my sister-in-law (who got it from someone else). > > Subject: FW: The Beauty of Mathmagic > Date: Thu, 02 Nov 2006 15:32:04 +0100 > > Very pretty numbers!!! > > The Beauty of Mathemagic > > 1 x 8 + 1 = 9 > 12 x 8 + 2 = 98 > 123 x 8 + 3 = 987 > 1234 x 8 + 4 = 9876 > 12345 x 8 + 5 = 98765 > 123456 x 8 + 6 = 987654 > 1234567 x 8 + 7 = 9876543 > 12345678 x 8 + 8 = 98765432 > 123456789 x 8 + 9 = 987654321 > > 1 x 9 + 2 = 11 > 12 x 9 + 3 = 111 > 123 x 9 + 4 = 1111 > 1234 x 9 + 5 = 11111 > 12345 x 9 + 6 = 111111 > 123456 x 9 + 7 = 1111111 > 1234567 x 9 + 8 = 11111111 > 12345678 x 9 + 9 = 111111111 > 123456789 x 9 +10= 1111111111 > > 9 x 9 + 7 = 88 > 98 x 9 + 6 = 888 > 987 x 9 + 5 = 8888 > 9876 x 9 + 4 = 88888 > 98765 x 9 + 3 = 888888 > 987654 x 9 + 2 = 8888888 > 9876543 x 9 + 1 = 88888888 > 98765432 x 9 + 0 = 888888888 > > Brilliant, isn't it? > And finally, take a look at this symmetry: > > 1 x 1 = 1 > 11 x 11 = 121 > 111 x 111 = 12321 > 1111 x 1111 = 1234321 > 11111 x 11111 = 123454321 > 111111 x 111111 = 12345654321 > 1111111 x 1111111 = 1234567654321 > 11111111 x 11111111 = 123456787654321 > 111111111 x 111111111=123456789 87654321 > > awesome > Quote Link to comment Share on other sites More sharing options...
Guest guest Posted November 5, 2006 Report Share Posted November 5, 2006 That´s fun. After 11, every finite group of ones in base ten <i have tried hasn´t been prime so far. 111 = 3 X 37 1111 = 11 X 101 The strings with an even number of ones are easy to prove. It´s the odd prime ones that challenge.. 11111 = 41 X 271 1111111 = 239 X 4649 etc.... Jerry Newport aka The Whale Quote Link to comment Share on other sites More sharing options...
Guest guest Posted November 5, 2006 Report Share Posted November 5, 2006 Hey, Jerry, in the Star Trek episode " The Trouble with Tribbles " , Spock said that if you started with one tribble, and a tribble had a litter of ten more tribbles every twelve hours over a period of three days, you'd end up with 1,771,561 tribbles. Is that figure correct? (Knowing the author as I do, I'd suspect the answer is " yes " , since he's a stickler for details.) Quote Link to comment Share on other sites More sharing options...
Guest guest Posted November 6, 2006 Report Share Posted November 6, 2006 > > Hey, Jerry, in the Star Trek episode " The Trouble with Tribbles " , > Spock said that if you started with one tribble, and a tribble had a > litter of ten more tribbles every twelve hours over a period of three > days, you'd end up with 1,771,561 tribbles. Is that figure correct? > (Knowing the author as I do, I'd suspect the answer is " yes " , since > he's a stickler for details.) > Well, 11 ^ 6 is that number so it looks good to me. Jerry Quote Link to comment Share on other sites More sharing options...
Guest guest Posted November 6, 2006 Report Share Posted November 6, 2006 Yes, but only if the mortality of Tribbles is exactly 0 over 6 generations. No living thing I know can be so... Mircea > > > > > Hey, Jerry, in the Star Trek episode " The Trouble with Tribbles " , > > Spock said that if you started with one tribble, and a tribble had a > > litter of ten more tribbles every twelve hours over a period of > three > > days, you'd end up with 1,771,561 tribbles. Is that figure > correct? > > (Knowing the author as I do, I'd suspect the answer is " yes " , since > > he's a stickler for details.) > > > > Well, 11 ^ 6 is that number so it looks good to me. > > Jerry Quote Link to comment Share on other sites More sharing options...
Guest guest Posted November 6, 2006 Report Share Posted November 6, 2006 > Yes, but only if the mortality of Tribbles is exactly 0 over 6 > generations. No living thing I know can be so... Tribbles are unusual creatures in more ways than one, so I wouldn't be surprised. (Although lifespan was never discussed in any of the canon that I'm aware of, either.) Quote Link to comment Share on other sites More sharing options...
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