Polynomials | Fibonacci numbers
In mathematics, the Fibonacci polynomials are a polynomial sequence which can be considered as a generalization of the Fibonacci numbers. The polynomials generated in a similar way from the Lucas numbers are called Lucas polynomials. (Wikipedia).
What do Fibonacci numbers have to do with combinatorics?
Part II: https://youtu.be/_RHXmGWXUvw Note: You ABSOLUTELY DON'T NEED TO HAVE KNOWN ANY COMBINATORICS because the combinatorics required in this video would be explained thoroughly. Source of the beautiful thumbnail: https://www.videoblocks.com/video/winter-stargate-deep-space-fibonacci-
From playlist Fibonacci
Exercise - Write a Fibonacci Function
Introduction to the Fibonacci Sequence and a programming challenge
From playlist Computer Science
Greatest Common Divisor of Fibonacci Numbers
We prove a result regarding the greatest common divisor of Fibonacci numbers. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Identities involving Fibonacci numbers
This video introduces the Fibonacci sequence and provides several examples of where the Fibonacci sequence appear in nature. http:mathispower4u.com
From playlist Mathematics General Interest
Cassini's identity | Lecture 7 | Fibonacci Numbers and the Golden Ratio
Derivation of Cassini's identity, which is a relationship between separated Fibonacci numbers. The identity is derived using the Fibonacci Q-matrix and determinants. Join me on Coursera: https://www.coursera.org/learn/fibonacci Lecture notes at http://www.math.ust.hk/~machas/fibonacci.pd
From playlist Fibonacci Numbers and the Golden Ratio
A nice Fibonacci sum done two ways!!
We find the infinite sum of f_n/2^n, where f_n is the nth Fibonacci number. As a tool, we construct the generating function for the Fibonacci sequence. We also find the sum using the "double summation trick" which was new to me!! This could also probably be done with summation by parts f
From playlist Identities involving Fibonacci numbers
Generating Functions and Combinatorial Identities
We describe one method of manipulating generating function to produce new combinatorial sum identities. We include an application of finding the value of a certain sum involving Fibonacci numbers. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Identities involving Fibonacci numbers
STAIRS reveal the relationship between Fibonacci and combinatorics
Part I: https://youtu.be/Hl61mJxILA4 Source of the beautiful thumbnail: https://www.videoblocks.com/video/winter-stargate-deep-space-fibonacci-spiral-infinite-zoom-scl2tvcpliylych5s I am still surprised at why I have not thought of this more direct linkage between Fibonacci numbers and c
From playlist Fibonacci
The golden ratio | Lecture 3 | Fibonacci Numbers and the Golden Ratio
The classical definition of the golden ratio. Two positive numbers are said to be in the golden ratio if the ratio between the larger number and the smaller number is the same as the ratio between their sum and the larger number. Phi=(1+sqrt(5))/2 approx 1.618. Join me on Coursera: http
From playlist Fibonacci Numbers and the Golden Ratio
Florian Luca: Fibonacci numbers and repdigits
CIRM VIRTUAL CONFERENCE Recorded during the meeting " Diophantine Problems, Determinism and Randomness" the November 26, 2020 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide
From playlist Virtual Conference
Continued Fraction Expansions, Pt. III
A fascinating generalization linking sequences, continued fractions, and polynomials. Email: allLogarithmsWereCreatedEqual@gmail.com Subscribe! https://www.youtube.com/AllLogarithmsEqual
From playlist Number Theory
Complexity problems in enumerative combinatorics – Igor Pak – ICM2018
Combinatorics Invited Lecture 13.9 Complexity problems in enumerative combinatorics Igor Pak Abstract: We give a broad survey of recent results in enumerative combinatorics and their complexity aspects. © International Congress of Mathematicians – ICM www.icm2018.org Os direitos s
From playlist Combinatorics
The Magical Fraction 1/999,999,999,999,999,999,999,998,999,999,999,999,999,999,999,999
The number 1/999,999,999,999,999,999,999,998,999,999,999,999,999,999,999,999 has the Fibonacci numbers in order for every group of 24 decimals. This video explains why the pattern emerges. (sources, proofs, and links below) Via Futility Closet: http://www.futilitycloset.com/2015/06/28/mad
From playlist Everyday Math
15. Dynamic Programming, Part 1: SRTBOT, Fib, DAGs, Bowling
MIT 6.006 Introduction to Algorithms, Spring 2020 Instructor: Erik Demaine View the complete course: https://ocw.mit.edu/6-006S20 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP63EdVPNLG3ToM6LaEUuStEY This is the first of four lectures on dynamic programing. This begin
From playlist MIT 6.006 Introduction to Algorithms, Spring 2020
Lec 3 | MIT 6.046J / 18.410J Introduction to Algorithms (SMA 5503), Fall 2005
Lecture 03: Divide-and-Conquer: Strassen, Fibonacci, Polynomial Multiplication View the complete course at: http://ocw.mit.edu/6-046JF05 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 6.046J / 18.410J Introduction to Algorithms (SMA 5503),
Secrets of the lost number walls
This video is about number walls a very beautiful corner of mathematics that hardly anybody seems to be aware of. Time for a thorough Mathologerization :) Overall a very natural follow-on to the very popular video on difference tables from a couple of months ago ("Why don't they teach Newt
From playlist Recent videos
Why don't they teach Newton's calculus of 'What comes next?'
Another long one. Obviously not for the faint of heart :) Anyway, this one is about the beautiful discrete counterpart of calculus, the calculus of sequences or the calculus of differences. Pretty much like in Alice's Wonderland things are strangely familiar and yet very different in this
From playlist Recent videos
Diagonalization Solutions (Fibonacci formula)
In which your daring math professor works out the 413th Fibonacci number using linear transformations, eigenstuff, and diagonalization. (PS: I didn't check my result in the video, but you can verify it here: https://www.wolframalpha.com/input/?i=413+fibonacci+number)
From playlist Linear Algebra
The Fibonacci bamboozlement | Lecture 8 | Fibonacci Numbers and the Golden Ratio
Explanation of the Fibonacci bamboozlement. The Fibonacci bamboozlement is a dissection fallacy where the rearrangement of pieces in a square can be used to construct a rectangle with one unit of area larger or smaller than that of the square. The square and rectangle have side lengths gi
From playlist Fibonacci Numbers and the Golden Ratio
Darij Grinberg - The one-sided cycle shuffles in the symmetric group algebra
We study a new family of elements in the group ring of a symmetric group – or, equivalently, a class of ways to shuffle a deck of cards. Fix a positive integer n. Consider the symmetric group S_n. For each 1 ≤ ℓ ≤ n, we define an element t_ℓ := cyc_ℓ + cyc{ℓ,ℓ+1} + cyc_{ℓ,ℓ+1,ℓ+2} + · · ·
From playlist Combinatorics and Arithmetic for Physics: Special Days 2022