Pentagonal orthocupolarotunda

Orthocenters exist! | Universal Hyperbolic Geometry 10 | NJ Wildberger

In classical hyperbolic geometry, orthocenters of triangles do not in general exist. Here in universal hyperbolic geometry, they do. This is a crucial building block for triangle geometry in this subject. The dual of an orthocenter is called an ortholine---also not seen in classical hyperb

From playlist Universal Hyperbolic Geometry

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

The Chaos Game in Pentagon, Octagon, and Square (math visualization)

To buy me a coffee, head over to https://www.buymeacoffee.com/VisualProofs Thanks! In this video, we explore the differences between starting with a random dot in a regular pentagon, octagon, and square and iterating the procedure of choosing a vertex (or midpoint for square) at random a

From playlist Fractals

What's a Pentagon? Geometry Terms and Definitions

An introduction to the pentagon, a fundamental geometric shape. Geometer: Louise McCartney Artwork: Kelly Vivanco Director: Michael Harrison Written & Produced by Kimberly Hatch Harrison and Michael Harrison ♦♦♦♦♦♦♦♦♦♦ Ways to support our channel: ► Join our Patreon : https://www.patr

From playlist Socratica: The Geometry Glossary Series

Incenter, Circumcenter, Orthocenter & Centroid of a Triangle - Geometry

This geometry video tutorial explains how to identify the location of the incenter, circumcenter, orthocenter and centroid of a triangle. The incenter can be found be drawing the 3 angle bisectors of a triangle and identifying the point of intersection. The incenter always lie inside of

From playlist Geometry Video Playlist

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

How to determine if a set of points makes up a rectangle using the distance formula

👉 Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr

From playlist Quadrilaterals on a Coordinate Plane

Using a set of points determine if the figure is a parallelogram using the midpoint formula

👉 Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr

From playlist Quadrilaterals on a Coordinate Plane

Orthogonality and Orthonormality

We know that the word orthogonal is kind of like the word perpendicular. It implies that two vectors have an angle of ninety degrees or half pi radians between them. But this term means much more than this, as we can have orthogonal matrices, or entire subspaces that are orthogonal to one

From playlist Mathematics (All Of It)

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

Doris Schattschneider - The Story of Marjorie Rice - G4G13 Apr 2018

From playlist G4G13 Videos

Glen Whitney - Convex Pintegon Tilings - CoM Oct 2021

Tiling the plane with convex pentagons has a rich mathematical history in which Martin Gardner and a diverse cast of other participants play key roles. Broad audiences can appreciate the associated questions, and enjoy the beautiful images that the answers yield. All of these characteristi

From playlist Celebration of Mind 2021

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

Do Facts Matter in Storytelling?

From the mediaX Seminar, Science Storytelling & the Contagion of Ideas, journalist Jamie McIntyre shares how his reporting of the Pentagon attack on 9-11 was taken out of context, and how this event lead him on a decade long journey to try to better understand the limits of factual informa

From playlist Science Storytelling and the Contagion of Ideas

Diana Davis: Billiards on regular polygons

HYBRID EVENT Recorded during the meeting "Differential Geometry, Billiards, and Geometric Optics" the October 04, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathemat

From playlist Dynamical Systems and Ordinary Differential Equations

Laura Taalman - Printing Perfect Pentagons - G4G13 Apr 2018

So we know there are 15 families of pentagonal tessellations… how do we 3D print models based on those tessellations?

From playlist G4G13 Videos

Bob Hearn - There Are Only 15 - G4G13 Apr 2018

Notes on the proof that there are only 15 convex pentagons that tile the plane.

From playlist G4G13 Videos

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

A 100 YEAR OLD PROBLEM AND ITS 15 SOLUTIONS: Pentagons and Tiling | ND

Today we look at a 100+ year old problem and its 15 solutions. The 100 year old math problem being the convex monohedral pentagonal tiling problem the only open case of the convex monohedral tiling problem. Pentagons have been a point of interest in the study of tiling for a while due to t

From playlist The New CHALKboard

Determine if a set of points is a trapezoid or not

👉 Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr

From playlist Quadrilaterals on a Coordinate Plane