Binet's formula | Lecture 5 | Fibonacci Numbers and the Golden Ratio

แชร์
ฝัง
  • เผยแพร่เมื่อ 23 ม.ค. 2025

ความคิดเห็น • 21

  • @ProfJeffreyChasnov
    @ProfJeffreyChasnov  5 ปีที่แล้ว +2

    Find other Fibonacci and the Golden Ratio videos in my playlist th-cam.com/play/PLkZjai-2JcxleC9l3RjEG9yyV3XU9WLOc.html

  • @dayday_13
    @dayday_13 8 ปีที่แล้ว +30

    good explanation, but you look like the villain in a james bond movie

    • @reyou7
      @reyou7 5 ปีที่แล้ว

      Here we go craigfay.com/wp-content/uploads/2018/08/Blofeld-1-e1534175757812.jpg

  • @omparikh4426
    @omparikh4426 4 ปีที่แล้ว

    at 5:20, how did you combine two solutions to create a general solution? can you please explain that or point to some resources which explain that?

    • @ProfJeffreyChasnov
      @ProfJeffreyChasnov  4 ปีที่แล้ว +1

      It is called the Principle of Superposition. You can prove that the sum of two solutions is also a solution.

    • @derda3209
      @derda3209 4 ปีที่แล้ว +1

      @@ProfJeffreyChasnov careful! this only works with linear functions

    • @ProfJeffreyChasnov
      @ProfJeffreyChasnov  4 ปีที่แล้ว

      @@derda3209 That is correct!

  • @DistantLights
    @DistantLights 8 ปีที่แล้ว +4

    Is little phi (phi) being equal to the negative reciprocal of big phi (PHI) the reason that you put c1(PHI + phi) instead of c1(PHI - phi)? When you expand the former, you get c1PHI + c1phi, which is a different equation.

    • @ProfJeffreyChasnov
      @ProfJeffreyChasnov  7 ปีที่แล้ว +2

      phi=1/Phi = Phi-1. Both numbers are defined to be positive, with Phi = (sqrt(5)+1)/2 and phi=(sqrt(5)-1)/2.

  • @chungli7424
    @chungli7424 7 ปีที่แล้ว +1

    teach so well that easy to understand. thx.

  • @sainadh7
    @sainadh7 4 ปีที่แล้ว +1

    how do you know that it is the appropriate guess even before solving it !!

    • @ProfJeffreyChasnov
      @ProfJeffreyChasnov  4 ปีที่แล้ว +2

      It is a well-known guess for linear difference equations. There is something similar for linear differential equations.

  • @emilmller4316
    @emilmller4316 4 ปีที่แล้ว

    How du you get C2=-C1

  • @samirelzein1978
    @samirelzein1978 3 ปีที่แล้ว

    no wonders teaching is free, cause it has no price!

  • @mathsmontage1070
    @mathsmontage1070 7 ปีที่แล้ว

    Interesting, and there is a whole more . . . Maths Montage, Fibonacci.

  • @berhanumoges9696
    @berhanumoges9696 4 ปีที่แล้ว

    Wonderful , Sir

  • @Fas2Fun
    @Fas2Fun 4 ปีที่แล้ว +2

    😩 you lost me at Try Xn = ƛ^n
    I thought I could handle this. I'm so illiterate in Math

  • @SHUBHAMGI
    @SHUBHAMGI 7 ปีที่แล้ว

    appreciable & thanks..

  • @tv..6531
    @tv..6531 6 ปีที่แล้ว

    피보나치 수열(Fibonacci Sequence)의 일반항을 초간단 쉽고 빠르게 구하며
    f(m+n-1) = f(m-1)f(n-1) + f(m)f(n).
    그 외 피보나치 수열의 관련 공식들도 유도합니다.
    th-cam.com/video/656P79nawsA/w-d-xo.html

  • @fluffiddy6515
    @fluffiddy6515 11 หลายเดือนก่อน

    Lesson 5

  • @nur-ansappayani6524
    @nur-ansappayani6524 2 ปีที่แล้ว

    Ok