A hexagonal number is a figurate number. The nth hexagonal number hn is the number of distinct dots in a pattern of dots consisting of the outlines of regular hexagons with sides up to n dots, when the hexagons are overlaid so that they share one vertex. The formula for the nth hexagonal number The first few hexagonal numbers (sequence in the OEIS) are: 1, 6, 15, 28, 45, 66, 91, 120, 153, 190, 231, 276, 325, 378, 435, 496, 561, 630, 703, 780, 861, 946... Every hexagonal number is a triangular number, but only every other triangular number (the 1st, 3rd, 5th, 7th, etc.) is a hexagonal number. Like a triangular number, the digital root in base 10 of a hexagonal number can only be 1, 3, 6, or 9. The digital root pattern, repeating every nine terms, is "1 6 6 1 9 3 1 3 9". Every even perfect number is hexagonal, given by the formula where Mp is a Mersenne prime. No odd perfect numbers are known, hence all known perfect numbers are hexagonal.For example, the 2nd hexagonal number is 2×3 = 6; the 4th is 4×7 = 28; the 16th is 16×31 = 496; and the 64th is 64×127 = 8128. The largest number that cannot be written as a sum of at most four hexagonal numbers is 130. Adrien-Marie Legendre proved in 1830 that any integer greater than 1791 can be expressed in this way. Hexagonal numbers should not be confused with centered hexagonal numbers, which model the standard packaging of Vienna sausages. To avoid ambiguity, hexagonal numbers are sometimes called "cornered hexagonal numbers". (Wikipedia).
Counting: Number of Hexadecimal Numbers with Restrictions (And/Or)
This video explains how to determine how many hexadecimals are possible with given conditions.
From playlist Counting (Discrete Math)
Geometry: Ch 4 - Geometric Figures (11 of 18) The Regular Hexagon Analyzed with Trig
Visit http://ilectureonline.com for more math and science lectures! In this video I will further explain the regular hexagon using trigonometry the details of the regular hexagon. Next video in this series can be seen at: https://youtu.be/oaT0pSYDVZI
From playlist GEOMETRY 4 - GEOMETRIC FIGURES
Powered by https://www.numerise.com/ Cube numbers
From playlist Indices, powers & roots
Powered by https://www.numerise.com/ Square numbers
From playlist Indices, powers & roots
Counting: Number of Hexadecimal Strings with Restrictions (And/Or)
This video explains how to determine how many hexadecimal strings are possible with given conditions.
From playlist Counting (Discrete Math)
Hexadecimal to Octal Conversion
This number systems tutorial explains how to do a hexadecimal to octal conversion. Subscribe: https://www.youtube.com/channel/UCEWpbFLzoYGPfuWUMFPSaoA?sub_confirmation=1 Access to Premium Videos: https://www.patreon.com/MathScienceTutor https://www.facebook.com/MathScienceTutoring/
From playlist Number Systems
Polygonal Numbers - Geometric Approach & Fermat's Polygonal Number Theorem
I created this video with the YouTube Video Editor (http://www.youtube.com/editor)
From playlist ℕumber Theory
Geometry: Ch 4 - Geometric Figures (10 of 18) The Regular Hexagon
Visit http://ilectureonline.com for more math and science lectures! In this video I will find the 3 angles of the regular hexagon and its parameter and area. Next video in this series can be seen at: https://youtu.be/1-bs5CvLQik
From playlist GEOMETRY 4 - GEOMETRIC FIGURES
How Many Faces, Edges And Vertices Does A Hexagonal Prism Have?
How Many Faces, Edges And Vertices Does A Hexagonal Prism Have? Here we’ll look at how to work out the faces, edges and vertices of a hexagonal prism. We’ll start by counting the faces, these are the flat surfaces that make the shape. A hexagonal prism has 8 faces altogether - 2 hexagon
From playlist Faces, edges and Vertices of 3D shapes
Dr James Grime talking Magic Hexagons (and magic squares). More links & stuff in full description below ↓↓↓ Support us on Patreon and get extra stuff: http://www.patreon.com/numberphile James Grime: http://singingbanana.com Support us on Patreon: http://www.patreon.com/numberphile NUMB
From playlist James Grime on Numberphile
Exotic patterns in Faraday waves by Laurette Tuckerman (Sorbonne University, France)
ICTS Special Colloquium Title: Exotic patterns in Faraday waves Speaker: Laurette Tuckerman (Sorbonne University, France) Date & Time: Thu, 20 February 2020, 11:30 to 13:00 Venue: Emmy Noether Seminar Room, ICTS Campus, Bangalore Abstract: For the Faraday instability, by which stand
From playlist ICTS Colloquia
Live demo https://codepen.io/thebabydino/pen/ExWrbqj If the work I've been putting out since early 2012 has helped you in any way or you just like it, please consider supporting it to help me continue and stay afloat. You can do so in one of the following ways: * you can be a cool cat 😼🎩
From playlist CSS variables
Venn Diagrams (1 of 2: Calculating probabilities)
More resources available at www.misterwootube.com
From playlist Probability and Discrete Probability Distributions
AlgTop21: The two-holed torus and 3-crosscaps surface
We describe how the two-holed torus and the 3-crosscaps surface can be given hyperbolic geometric structure. For the two-holed torus we cut it into 4 hexagons and then describe a tesselation of the hyperbolic plane (using the Beltrami Poincare model described in the previous lecture) compo
From playlist Algebraic Topology: a beginner's course - N J Wildberger
There is more than one way to tile the plane. In this video we'll explore hexagonal tiling. Hexagonal tiling can be used to make many cool effects. Twitter: @The_ArtOfCode Facebook: https://www.facebook.com/groups/theartofcode/ Patreon: https://www.patreon.com/TheArtOfCode PayPal Donation
From playlist Tools
How many panels on a soccer ball? - Numberphile
Applying the Euler Characteristic to a soccer ball (football). More links & stuff in full description below ↓↓↓ See the Brussels Sprouts video: http://youtu.be/OAss481FfAQ Truncated Icosahedron: http://youtu.be/4mEk7d8oRho An extra bit: http://youtu.be/QwfPTE7lEbE Featuring Teena Gerhard
From playlist Football (soccer) on Numberphile
More important than knowing a bunch of digits in the decimal approximation of Pi is to understand what Pi means. Pi is the ratio of the Circumference to the Diameter of any circle. Multiply the diameter by Pi to get the circumference or divide the circumference by pi to get the diameter.
From playlist Lessons of Interest on Assorted Topics
Rigidity of the hexagonal triangulation of the plane and its applications - Feng Luo
Feng Luo, Rutgers October 5, 2015 http://www.math.ias.edu/wgso3m/agenda 015-2016 Monday, October 5, 2015 - 08:00 to Friday, October 9, 2015 - 12:00 This workshop is part of the topical program "Geometric Structures on 3-Manifolds" which will take place during the 2015-2016 academic year
From playlist Workshop on Geometric Structures on 3-Manifolds
Powered by https://www.numerise.com/ What are prime numbers. What are composite numbers. www.hegartymaths.com http://www.hegartymaths.com/
From playlist Basic Arithmetic & Numeracy
Understanding spin-1 kagome antiferromagnet through Hida model by Brijesh Kumar
Program The 2nd Asia Pacific Workshop on Quantum Magnetism ORGANIZERS: Subhro Bhattacharjee, Gang Chen, Zenji Hiroi, Ying-Jer Kao, SungBin Lee, Arnab Sen and Nic Shannon DATE: 29 November 2018 to 07 December 2018 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Frustrated quantum magne
From playlist The 2nd Asia Pacific Workshop on Quantum Magnetism