A centered pentagonal number is a centered figurate number that represents a pentagon with a dot in the center and all other dots surrounding the center in successive pentagonal layers. The centered pentagonal number for n is given by the formula The first few centered pentagonal numbers are 1, 6, 16, 31, 51, 76,106, 141, 181, 226, 276,331, 391, 456, 526, 601,681, 766, 856, 951, 1051, 1156, 1266, 1381, 1501, 1626, 1756, 1891, 2031, 2176, 2326, 2481, 2641, 2806, 2976 (sequence in the OEIS). (Wikipedia).
Golden Ratio ϕ hidden in Pentagon!
The ratio of a common diagonal and side of regular pentagon is equal to golden ratio. Golden ratio is an irrational constant in mathematics, ϕ = 1.618033... Mathematicians since Euclid have studied the properties of the golden ratio, including its appearance in the dimensions of a regula
From playlist Summer of Math Exposition Youtube Videos
How to find the volume of a pentagonal pyramid
👉 Learn how to find the volume and the surface area of a pyramid. A pyramid is a 3-dimensional object having a polygon as its base and triangular surfaces converging at a single point called its apex. A pyramid derives its name from the shape of its base, i.e. a pyramid with a triangular b
From playlist Volume and Surface Area
Geometry: Ch 4 - Geometric Figures (8 of 18) The Regular Pentagon
Visit http://ilectureonline.com for more math and science lectures! In this video I will find the 3 angles of the regular pentagon and its parameter and area. Next video in this series can be seen at: https://youtu.be/3G_jjW1d280
From playlist GEOMETRY 4 - GEOMETRIC FIGURES
How to Construct a Dodecahedron
How the greeks constructed the Dodecahedron. Euclids Elements Book 13, Proposition 17. In geometry, a dodecahedron is any polyhedron with twelve flat faces. The most familiar dodecahedron is the regular dodecahedron with regular pentagons as faces, which is a Platonic solid. A regular dode
From playlist Platonic Solids
Find the Area of a Pentagon on the Coordinate Plane
This video explains how to determine the area of a pentagon on the coordinate plane.
From playlist Mathematics General Interest
To construct a PENTAGON with ruler (straightedge) and compass
Geometrical construction of a pentagon with Euclidean Tools Follow me: http://www.twitter.com/dantecardoso
From playlist Math
Geometry: Ch 4 - Geometric Figures (9 of 18) The Regular Pentagon Analyzed with Trig
Visit http://ilectureonline.com for more math and science lectures! In this video I will further explain the regular pentagon using trigonometry the details of the regular pentagon. Next video in this series can be seen at: https://youtu.be/68gZJwZJeZ0
From playlist GEOMETRY 4 - GEOMETRIC FIGURES
More patterns with algebra | Arithmetic and Geometry Math Foundations 51 | N J Wildberger
The patterns formed by triangular numbers and square numbers have generalizations in different directions. One is to three dimensional tetrahedral numbers, and three dimensional pyramidal numbers. Another is to pentagonal numbers, which have a number of interesting features. This video be
From playlist Math Foundations
What is sin(π/5)? #SoME1 #SummerofMathExposition #3blue1Brown
This is a re-upload of yesterday's entry into 3Blue1Brown's Summer of Math Exposition, as the last few minutes were cut off...now the actual answer is included! Patreon: https://www.patreon.com/whatthehectogon Instagram: https://www.instagram.com/whatthehectogon/ Doggo: https://www.inst
From playlist Trigonometry
D. Davis - Periodic paths on the pentagon
Mathematicians have long understood periodic trajectories on the square billiard table. In the present work, we describe periodic trajectories on the regular pentagon – their geometry, symbolic dynamics, and group structure. Some of the periodic trajectories exhibit a surprising
From playlist Ecole d'été 2018 - Teichmüller dynamics, mapping class groups and applications
A more accurate way of drawing a pentagon based curve of pursuit, using the Clone tool.
From playlist Inkscape for teachers
Math Mornings at Yale: Asher Auel - Wallpaper, Platonic Solids, and Symmetry
The Platonic solids-the tetrahedron, cube, octahedron, dodecahedron, and icosahedron-are some of the most beautiful and symmetric geometrical objects in 3-dimensional space. Their mysteries started to be unraveled by the ancient Greeks and still fascinate us today. In 1872, the German geom
From playlist Math Mornings at Yale
Interior and Exterior Angles of a Polygon
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From playlist Geometry Basics
Frank Morgan - Optimal Pentagonal Tilings - CoM May 2021
In 2001 Thomas Hales proved that hexagons provide the least-perimeter way to tile the plane with unit areas. Of course, among hexagons, the regular one is best. Similarly, the best quadrilateral is square and the best triangle is equilateral. But what is the best pentagonal tile? Unfortuna
From playlist Celebration of Mind 2021
Roger Penrose - Forbidden crystal symmetry in mathematics and architecture
Sir Roger Penrose provides a unique insight into the "forbidden symmetry" of his famous penrose tiles and the use of non-repeating patterns in design and architecture. It is a rigorous mathematical theorem that the only crystallographic symmetries are 2-fold, 3-fold, 4-fold, and 6-fold s
From playlist Mathematics
Computer History RCA 3301, Spectra, PENTAGON 1960's-early '70's Underground Data Center IBM STRATCOM
Computer History: RCA 3301 REALCOM Real-Time Computer at the PENTAGON’s underground Data Center (1963-1971). Rare Color Film of the RCA 3301, IBM 360 Computer and the Army’s STRATCOM telecommunications center and underground computer data center beneath the Pentagon. Government film giv
From playlist Computers of the 1960's
Area of Regular Polygons - Hexagons, Pentagons, & Equilateral Triangles With Inscribed Circles
This geometry video tutorial explains how to calculate the area of a regular polygon using a simple formula. The first two problem explains how to calculate the area of a pentagon and a hexagon given the apothem and a side length. The next two problems explain how to calculate the area o
From playlist GED Math Playlist
Ayliean MacDonald - The Pentagon: A User’s Guide - CoM Oct 2021
Regular pentagons throw a spanner in the works when it comes to tessellation but don’t let that one case tarnish the good name of the pentagon! Come along as we explore the 15 irregular pentagons which do tile the plane, journey through five fold symmetry, make a quick pit stop to look at
From playlist Celebration of Mind 2021
Geometry - Ch. 1: Basic Concepts (38 of 49) Review Problem 4: Perimeter=? of a Pentagon
Visit http://ilectureonline.com for more math and science lectures! In this video I will calculate the perimeter of the regular pentagon give one side=(8x-3)m and the other side=(4x+9)m. Next video in this series can be seen at: https://youtu.be/gfGqD1YzMFU
From playlist GEOMETRY CH 1 BASIC CONCEPTS
Mathematics as Metaphor - Curtis McMullen (Harvard University)
Public lecture
From playlist Mathematics Research Center