Centered pentagonal number

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

Pentagon pursuit using clones

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

http://mathispower4u.wordpress.com/

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