Parametric families of graphs | Fibonacci numbers | Network topology

Fibonacci cube

In the mathematical field of graph theory, the Fibonacci cubes or Fibonacci networks are a family of undirected graphs with rich recursive properties derived from its origin in number theory. Mathematically they are similar to the hypercube graphs, but with a Fibonacci number of vertices. Fibonacci cubes were first explicitly defined in in the context of interconnection topologies for connecting parallel or distributed systems. They have also been applied in chemical graph theory. The Fibonacci cube may be defined in terms of Fibonacci codes and Hamming distance, independent sets of vertices in path graphs, or via distributive lattices. (Wikipedia).

Fibonacci cube
Video thumbnail

Fibonacci numbers and the golden ratio | Lecture 4 | Fibonacci Numbers and the Golden Ratio

Relationship between the Fibonacci numbers and the golden ratio. The ratio of consecutive Fibonacci numbers approaches the golden ratio. Join me on Coursera: https://www.coursera.org/learn/fibonacci Lecture notes at http://www.math.ust.hk/~machas/fibonacci.pdf Subscribe to my channel: h

From playlist Fibonacci Numbers and the Golden Ratio

Video thumbnail

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

Video thumbnail

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

Video thumbnail

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

Video thumbnail

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

Video thumbnail

The Fibonacci spiral | Lecture 15 | Fibonacci Numbers and the Golden Ratio

How to construct a Fibonacci spiral. Join me on Coursera: https://www.coursera.org/learn/fibonacci Lecture notes at http://www.math.ust.hk/~machas/fibonacci.pdf Subscribe to my channel: http://www.youtube.com/user/jchasnov?sub_confirmation=1

From playlist Fibonacci Numbers and the Golden Ratio

Video thumbnail

A Beautiful Visual Interpretation - The Sum of Squares of the Fibonacci Numbers.

Help me create more free content! =) https://www.patreon.com/mathable Merch :v - https://papaflammy.myteespring.co/ https://www.amazon.com/shop/flammablemaths https://shop.spreadshirt.de/papaflammy Become a Member of the Flammily! :0 https://www.youtub

From playlist Number Theory

Video thumbnail

Sum of Fibonacci Numbers.

Help me create more free content! =) https://www.patreon.com/mathable Merch :v - https://papaflammy.myteespring.co/ https://www.amazon.com/shop/flammablemaths https://shop.spreadshirt.de/papaflammy Become a Member of the Flammily! :0 https://www.youtub

From playlist Number Theory

Video thumbnail

Phi and the TRIBONACCI monster

NEW (Christmas 2019). Two ways to support Mathologer Mathologer Patreon: https://www.patreon.com/mathologer Mathologer PayPal: paypal.me/mathologer (see the Patreon page for details) Today's video is about explaining a lot of the miracles associated with the golden ratio phi, the Fibona

From playlist Recent videos

Video thumbnail

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

Video thumbnail

CMU Discrete Mathematics 3/12

Due to the COVID-19 pandemic, Carnegie Mellon University is protecting the health and safety of its community by holding all large classes online. People from outside Carnegie Mellon University are welcome to tune in to see how the class is taught, but unfortunately Prof. Loh will not be o

From playlist CMU 21-228 Discrete Mathematics

Video thumbnail

Exercise - Write a Fibonacci Function

Introduction to the Fibonacci Sequence and a programming challenge

From playlist Computer Science

Video thumbnail

How to discover new math

In this video I walk you through my process of exploring and tinkering with a piece of known mathematics to ultimately find a novel connection to Fibonacci numbers. Chapters: 0:00 - intro 2:51 - block demonstration 8:42 - use python to further explore our transformation and derive a se

From playlist Summer of Math Exposition Youtube Videos

Video thumbnail

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

Video thumbnail

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

Video thumbnail

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),

Video thumbnail

Golden Ratio BURN (Internet Beef) - Numberphile

Seriously? Matt Parker is talking about Fibonacci and Lucas numbers again. Part 2: https://youtu.be/z1THaBtc5RE More links & stuff in full description below ↓↓↓ See part 2 on Numberphile2: https://youtu.be/z1THaBtc5RE The original trilogy of videos where this all started: http://bit.ly/G

From playlist Matt Parker (standupmaths) on Numberphile

Video thumbnail

The Fibonacci Sequence

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

Video thumbnail

Introduction To Sequences | Algebra | Maths | FuseSchool

In this video we’re going to discover some key sequences terminology and how to recognise and generate some important sequences. We will come across all of these key sequences... Arithmetic, Linear, Triangular, Square, Cube, Fibonacci, Quadratic, Geometric. And these key words; Term, 1st t

From playlist MATHS

Related pages

Binary number | Resonance (chemistry) | Fibonacci number | Hamming distance | Perfect matching | Partially ordered set | Planar graph | Hamiltonian path | Discrete Mathematics (journal) | Hypercube graph | Network topology | Median graph | Fibbinary number | Complement graph | Distributive lattice | Path graph | Clique (graph theory) | Graph theory | Majority function | Simplex graph | Bipartite graph | Lucas number | Vertex (graph theory) | Symmetric difference | Birkhoff's representation theorem | Number theory | Independent set (graph theory) | Ars Combinatoria (journal) | Broadcasting (networking) | Chemical graph theory | Partial cube | Independence number