Loki Posted August 18, 2003 Posted August 18, 2003 :phi: = 1.618... uh... something like that, i don't remember So what do you guys think about this number? It appears mysteriously in nature in the most unexpected places. The leaves on plants base their "spiral" arrangement up the stem on this number. also, any number in the Fibonacci sequence divided by the preceding number in the sequence will approximately equal :phi: Fibonacci Sequence: 1,1,2,3,5,8,13,21,34,55,89... 1/1 = 1.000 2/1 = 2.000 3/2 = 1.500 5/3 = 1.667 8/5 = 1.600 13/8 = 1.625 21/13 = 1.615 . . . 89/55 = 1.618 This converges to :phi: There's some more crazy characteristics to this number... :phi:^2 = 2.618... 1/:phi: = 0.618... I could elaborate, but I'll open it to discussion first.
JaKiri Posted August 18, 2003 Posted August 18, 2003 Personally I think pi, the ratio between the diameter of a circle and its circumference, is much more amazing, and appears in a much wider variety of places, but we all recognise it as 'part of the woodwork', so it's invisible.
Loki Posted August 18, 2003 Author Posted August 18, 2003 but that doesn't mean that the underdog doesn't deserve any attention
Skye Posted August 18, 2003 Posted August 18, 2003 My last semester maths lecturer had a fetish for competitions and tried to get us to see who could memorise pi to a hundred places first. Didn't happen.
fafalone Posted August 18, 2003 Posted August 18, 2003 PI=3. 1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679 8214808651 3282306647 0938446095 5058223172 5359408128 4811174502 8410270193 8521105559 6446229489 5493038196 4428810975 6659334461 2847564823 3786783165 2712019091 4564856692 3460348610 4543266482 1339360726 0249141273 7245870066 0631558817 4881520920 9628292540 9171536436 7892590360 0113305305 4882046652 1384146951 9415116094 3305727036 5759591953 0921861173 8193261179 3105118548 0744623799 6274956735 1885752724 8912279381 8301194912 9833673362 4406566430 8602139494 6395224737 1907021798 6094370277 0539217176 2931767523 8467481846 7669405132 0005681271 4526356082 7785771342 7577896091 7363717872 1468440901 2249534301 4654958537 1050792279 6892589235 4201995611 2129021960 8640344181 5981362977 4771309960 5187072113 4999999837 2978049951 0597317328 1609631859 5024459455 3469083026 4252230825 3344685035 2619311881 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NSX Posted August 19, 2003 Posted August 19, 2003 Originally posted by fafalone PI=3.14....1032704178 my gosh..you didn't memorize all that, did you? We had a thread on pi somewhere, and a site that had alot of digits
fafalone Posted August 19, 2003 Posted August 19, 2003 I used to have an ftp with over a billion digits available for dl... it was in japan and the throughput was unbearable tho.
alt_f13 Posted August 19, 2003 Posted August 19, 2003 There is an ftp out there with the human genome on it. It takes a few gig of space I'm pretty sure.
Dave Posted August 19, 2003 Posted August 19, 2003 phi's pretty cool too, although I do have to agree that pi is (a) more important and (b) more interesting.
NSX Posted August 20, 2003 Posted August 20, 2003 How about Euler's Constant? I read that it's approx 0.5772.... and it's one of the most significant numbers trailing only :pi: (pi)and e (natural log).
Peter Dunn Posted August 20, 2003 Posted August 20, 2003 Hi Fafalone Did you actualy type all that stuff? Didn't your digits acquire a few blisters in the process? Your attention to detail and sustained manual dexterity is to be applauded. All the best Peter Dunn
Peter Dunn Posted August 20, 2003 Posted August 20, 2003 Hi Loki Surely plants do'nt 'base' their structure on anything; they are simply what they are - as nature intended (and hopefully edible). Whatever structure they do possess is probably more to do with structure at the molecular level which is reflected at higher levels (zooming out with your microscope) in fractal fashion. The recurrence of patterns and numbers in nature is a fascinating theme with, I think, the most amazing correlation being between early (neolithic) man's obsession with spiral patterns and the spiral patterns seen in particle accelerator detectors as 'bits' of particles spiral away to non existence (they disappear).
Loki Posted August 20, 2003 Author Posted August 20, 2003 Peter Dunn said in post #14 :Hi Loki Surely plants do'nt 'base' their structure on anything; they are simply what they are - as nature intended (and hopefully edible). they sure do! maybe my wording (the use of the word "base") didn't describe the phenomenon accurately, but nonetheless, certain plants have :phi: in their geometry. now whether you think that this occurance is a spectacular phenomenon or an easily-explainable happening makes no difference. I'm sure you think the latter, and you probably think that any attempt to show how :phi: exists in nature is just an attempt to romanticize the subject for the public. But the facts remain the same, and :phi: does in fact show up in the geometrical structure of plants.
Guest dux Posted September 17, 2003 Posted September 17, 2003 me lieks pie hmmm... you all should seriously consider reading Calvin C. Clawson's "Mathematical Mysteries", especially Chapter 6. It contains a huge number oc links between phi, prime numbers, the Fibonacci sequence, and even the Pascal triangle... great book, really. You don't even need to know about math to understand it: The book slowly explains all the terms in the first few chapters. Also read After Man: A Zoology of the Future, by Dougal Dixon
Qwik Posted January 17, 2004 Posted January 17, 2004 cool, I'll look into that book, it sounds interesting. I'm pretty good at math, but I think I could be a lot better if I'd be able to take the math classes that I want to. I'm currently in Algebra 2, which I should have taken last year... I should be taking Pre-Calculus this year
YT2095 Posted January 17, 2004 Posted January 17, 2004 Faf just copied that from the international telephone directory, it isn`t Pi at all really
Guest obecerra Posted April 21, 2004 Posted April 21, 2004 Those interested might want to read Alan Cromer's "Connected Knowledge" pp. 33-34 for a demithification of the golden ratio. I will try to do some measurements on my own after reading it
bloodhound Posted April 22, 2004 Posted April 22, 2004 How about Euler's Constant?I read that it's approx 0.5772.... and it's one of the most significant numbers trailing only :pi: (pi)and e (natural log). if u have a positive' date=' twice differentiable function f whose second derivative is positive on (0,inf) then the limit as n tends to infinity of SUM[f(k),k=1 to n'] - Integral[f(x)dx from 1 to n] exists if u put f((x)=1/x the limit above is the eulers constant i.e 1 + 1/2 + 1/ 3 + 1/4 + ... + 1/n - ln n converges. which is quite remarkable given that if u take about the (- ln n) bit , u get the harmonic series, which diverges.
AntiMagicMan Posted April 22, 2004 Posted April 22, 2004 Speaking of Euler, how about the greatest equation in the whole of mathematics, e i pi 0 and 1 all tied up in one nice little formula: [math]\[ e^{i\pi } + 1 = 0 \] [/math]
bloodhound Posted April 22, 2004 Posted April 22, 2004 yeah , u can do nifty things with that like finding i^i or -1^-i etc. etc
Dave Posted April 22, 2004 Posted April 22, 2004 It's useful because it crops up a lot in the solution of differential equations (i.e. when you try a solution y = e^(kx) and k turns out to be a complex number).
bloodhound Posted April 22, 2004 Posted April 22, 2004 yes y=e^(kx) is a nice trial solution but the one i like more is to try y= Sum [anxn] from 0 to inf but eventuall if y = e^kx is a solution , you would probably just end up with the series form of the exponential.
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