The Pi sequency revealed ?, page 5
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reply posted on 31-7-2004 @ 11:00 AM by HeirToBokassa
Originally posted by Nans DESMICHELS
Nope, verify by yourself, the pattern end clearly with 14, and it has no correlation with the kind of calculator you use.

He is telling me that I should have better result with a double precision calculator than with a single precision one. He will never suppose think that I've tryied yet, with Simple, Double and infinite precisions.
[edit on 31-7-2004 by Nans DESMICHELS]


; epsilon(10^-1000)
; display(1010)
; acos(-1) 3.141592653589793238462643383279502884197169399375105820974944592*64062862089986280348253421170679821480865132823066470938446095505822317253594081 284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412 737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185 480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798609437027705392171762931767523846748184676694051 320005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235420199561121290219608640344181598136297747713099 605187072113499999983729780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083814206171776691473 035982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201989

Here I calculated Pi to 1000 decimal places. As you can see, I have no lack of precision

; Pi=acos(-1)
; Pi/2-atan(142857)
0.0000070000069998926663306693490823372643966250467550300016275153447109769632027978000917349908648380493515053459880724627083355712766058481055139495 833747343211781148401610841901839501513714938378133996906295954105516450689045096684454031155862459047721423013172684367039225914289317925365859961239 237790324573489579739239151894020082213338338238569482179083733657189354569494140342550630647305776649173488085440405889493795748406877339035320132220 323988096164879692234443058036418375577188270222971007253736644608395798636379354238346033523136019263191477583424644274233357011005516846749222806464 259116870007250706337280482940601277401176405057217297945365728449891369558132616479980922966916098671443983502690195731739659962883187320899978730473 756299151325754544153057922472973064644574305135670795216582080465069938020247163087523273707352578402359158249235842729724842656974893990886484775133 5894906048522122834484975798298278574237631181981813735909533636692023662371297299816079820211457962915

; Pi/2-atan(14285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714 2857142857142857142857142857142857142857142857142857142857142857142857142857142857)
0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000000000070000000000000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000069999 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 999999999999999999999999999999999999999999999999999999999999999998926666666666666666666666666666666666666666666666666666666666666666666666666666666666 666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666663306666666666 6666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666665


Clearly the pattern doesn't terminate regularly. Perhaps you can tell me what calculator or software you are using and I can solve your problem?

Also, I did the same experiment with 10,000 decimal places
here. You can verify that my calculator got Pi correct by searching "digits of Pi" on google and comparing.

Also, even without numerical computation, amantine's last post has the correct explanation, using atan's Taylor series, why the result will never be regular.


reply posted on 1-8-2004 @ 08:18 AM by Nans DESMICHELS
In other news, the speed of light is encoded in the Koran!


The speed of light can't be encoded in the Koran, because recents discoveries proven that speed of light is not a constant, but variable.

I've discovered 142857 when I was learning number-cryptography basics. This number unique properties are used in many crypto-algorithms, including RSA-public key. It's no the point, but I just let you a small article about that. When you know this number properties, you can't be surprised to see that 142857 have also weird properties with PI. I'm just a little bit deceipt by the attitude of some people here who pretend to have a scientific mood, but have a close mind and not a mind opened to world. And it's not a truth researcher attitude...



OP-ED: The queen of sciences


Daily Times
Munir Attaulla

Increasingly, beauty -- and delight -- is sought in the pure manipulation of the tools of the trade, be they colours, words, or the musical scale. Mathematicians have always known this form of intellectual pleasure.
Most people find mathematics a forbiddingly dry and boring subject. I suspect that that is because, to quote Russell’s famous epigram, "mathematics is a subject where we never know what we are talking about or, whether what we are talking about is true". That flippant remark, nevertheless, aptly sums up what a mathematician does.
Mathematics is the finest method we know for generalised and abstract thinking and is, without doubt, the supreme construct of the human mind. Without it, nothing of any significance would have been achievable in any of the sciences. Those school years spent in tedious struggle with decimal fractions, square roots, and learning mysterious formulae by rote, are necessary because nothing worthwhile is ever achieved by anyone without first painstakingly mastering the tools of his trade. For the mathematician, the tools are numbers and the great advance which made this possible was the decimal system of numbering and its modern Arabic notation.
‘Art for art’s sake’ is a relatively modern concept which inspires much of abstract art, free verse poetry, and even atonal music. The emphasis is on form rather than content. Increasingly, beauty - and delight - is sought in the pure manipulation of the tools of the trade, be they colours, words, or the musical scale. Mathematicians have always known this form of intellectual pleasure. Can you see anything beautiful about an apparently ordinary number such as 142857? No? Well, if you multiply it successively by 2,3,4,5,and 6 you get the following numbers: 285714, 428571, 571428, 714285, and 857142.
Notice anything odd about these numbers? Amazingly, they are all made up of the same digits as the original number. What is even more interesting, all the digits maintain their relative order vis-a vis the other digits. But what happens when you multiply the number by seven? Surprise! You get 999999! Intriguing? Certainly. Beautiful? I think so. It is as if Shane Warne, the magician, lulls you with five perfect leg-spinners before foxing you with a googly.
An endless source of delight is the mysterious and subtle ways the realities of Nature are mirrored in mathematics. We humans instinctively seem to find certain proportions pleasing to the eye. Coffee tables of roughly eight by five look good. The pyramids of Giza and the Parthenon exhibit a similar base to height ratio. The Greeks called this ‘the golden ratio’ (1.618 or 0.618 to be exact, depending on which dimension is being compared to which). Even artists pay homage to this mysterious number when they focus the attention of the eye not on the centre of the canvas but to one side. Your credit card and Mona Lisa’s face form a ‘golden rectangle’.
Consider next the series of numbers 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55... called the Fibonacci series, where each number is the sum of the previous two numbers. As uninteresting a set of numbers as you could ask for, till you notice that the further down the series you go, the closer two adjoining numbers approximate to the golden ratio. Curious. In the last hundred years Naturalists have unearthed the deep interconnections between cell growth, Fibonacci numbers and the golden ratio. The number of petals on most flowers are Fibonacci numbers (three on lilies, 34 on sunflowers, 13 on marigolds, 34, 55, or 89 on daisies etc.); If you count the clockwise and anti-clockwise spiral patterns on a pinecone or sunflower seed packing, you will find them to be two adjoining Fibonacci numbers; leaves around a stem and the spiral shell of a snail share a common growth pattern (a factor of 1.618 per whole turn) etc. etc.
From there it took some simple mathematics to show that cell growth based on the golden ratio was the optimal way of packing seeds on a flower bud, ensuring maximum sunlight for each leaf on a stem and collecting the most rainwater for the plant! If such deep interconnections fail to move you it is time for your siesta and time for me to say goodbye.



reply posted on 2-8-2004 @ 12:26 AM by HeirToBokassa
Well I just tried the same experiment on an UltraSparc 10 Elite, and same results:

; Pi=acos(-1)
; Pi
3.141592653589793238462643383279502884197169399375105820974944592*64062862089986280348253421170679821480865132823066470938446095505822317253594081 284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412 737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185 480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798609437027705392171762931767523846748184676694051 320005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235420199561121290219608640344181598136297747713099 605187072113499999983729780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083814206171776691473 035982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201989
;
; Pi/2-atan(142857)
0.0000070000069998926663306693490823372643966250467550300016275153447109769632027978000917349908648380493515053459880724627083355712766058481055139495 833747343211781148401610841901839501513714938378133996906295954105516450689045096684454031155862459047721423013172684367039225914289317925365859961239 237790324573489579739239151894020082213338338238569482179083733657189354569494140342550630647305776649173488085440405889493795748406877339035320132220 323988096164879692234443058036418375577188270222971007253736644608395798636379354238346033523136019263191477583424644274233357011005516846749222806464 259116870007250706337280482940601277401176405057217297945365728449891369558132616479980922966916098671443983502690195731739659962883187320899978730473 756299151325754544153057922472973064644574305135670795216582080465069938020247163087523273707352578402359158249235842729724842656974893990886484775133 5894906048522122834484975798298278574237631181981813735909533636692023662371297299816079820211457962915
;
; Pi/2-atan(14285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714 2857142857142857142857142857142857142857142857142857142857142857142857142857142857)
0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000000000070000000000000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000069999 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 999999999999999999999999999999999999999999999999999999999999999998926666666666666666666666666666666666666666666666666666666666666666666666666666666666 666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666663306666666666 6666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666665
;

I hope you now agree with me that the results are not due to x86 architecture.


reply posted on 2-8-2004 @ 05:11 AM by Nans DESMICHELS
Originally posted by TACHYONHow do you insult such a learned individual who is correct. The poofs he presented were mathematically correct. Mathematical proofs are undeniable. I for one agree with Amantine. I wish I was as smart as Amantine. Maybe if you stop insulting people who are more intelligent than you and listen to what they say maybe you will understand what they have to say."You know nothing" What a joke.


You're intervention is unwelcomed

Kss, Kss, Kss

Keep your bad spirit away


[edit on 2-8-2004 by Nans DESMICHELS]

Err... Amantine is not a girl ? I tought Amantine was a french female surname ?

[edit on 2-8-2004 by Nans DESMICHELS]

[edit on 2-8-2004 by Nans DESMICHELS]


And think that Mr TACHYON :

"The knowledge of man is as the waters, some descending from above, and some springing from beneath; the one informed by the light of nature... the other inspired by divine revelation." - Francis Bacon, 1605


Where are you coming from ?

[edit on 2-8-2004 by Nans DESMICHELS]
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