A centered (or centred) triangular number is a centered figurate number that represents an equilateral triangle with a dot in the center and all its other dots surrounding the center in successive equilateral triangular layers. The following image shows the building of the centered triangular numbers by using the associated figures: at each step, the previous triangle (shown in red) is surrounded by a triangular layer of new dots (in blue). (Wikipedia).
[ANT08b] Square triangular numbers
Another application of Pell's equation.
From playlist [ANT] An unorthodox introduction to algebraic number theory
Learn how to determine the surface area of a triangular 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
02 Cubic Meters in a Right Triangular Prism #46
volume in a right triangular prism
From playlist Skill 16 Attempt 1
Learn how to determine the surface area of a triangular prism
👉 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
👉 Learn the essential definitions of triangles. A triangle is a polygon with three sides. Triangles are classified on the basis of their angles or on the basis of their side lengths. The classification of triangles on the bases of their angles are: acute, right and obtuse triangles. The cl
From playlist Types of Triangles and Their Properties
Odd Squares as Difference of Triangular Numbers (visual proof)
This is a short, animated visual proof demonstrating how to visualize odd squares as the difference of two triangular numbers. #mathshorts​ #mathvideo​ #math​ #numbertheory #mtbos​ #manim​ #animation​ #theorem​ #pww​ #proofwithoutwords​ #visualproof​ #proof​ #iteachmath #squares #triangula
From playlist Triangular Numbers
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 â„•umber Theory
Determining the volume of rectangular 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
This geometry video tutorial explains how to calculate the volume of a triangular prism using a simple formula. The volume is equal to the product of the area of the base and the height of the prism. The base is the area of a triangle - it could be a right triangle, an isosceles triangle
From playlist Geometry Video Playlist
A Dozen Proofs: Sum of Integers Formula (visual proofs) #SoME2
In this video, we explore the famous formula for the sum of the first n positive integers. In particular, we present twelve proofs of the sum formula using induction, area-based techniques, combinatorial techniques, physical techniques, and by using a couple of deep theorems. All of the pr
From playlist Finite Sums
The Collapse of Viruses: Graph-Based Percolation Theory in the Wolfram Language
Graph-based percolation theory may be done in the Wolfram Language, here to aid in the understanding of viruses, their disassembly and eventual collapse. Capsids are protein nanocontainers that store and protect a virus’s genetic material in transit between hosts. Capsids consist of hundre
From playlist Wolfram Technology Conference 2020
Matrices: Determinants of 2x2 and 3x3 Matrices
This is the fifth video of a series from the Worldwide Center of Mathematics explaining the basics of matrices. This video deals with finding the determinant of square 2x2 and 3x3 matrices. For more math videos, visit our channel or go to www.centerofmath.org
From playlist Basics: Matrices
19. Baroque Extravaganzas: Rock Tombs, Fountains, and Sanctuaries in Jordan, Lebanon, and Libya
Roman Architecture (HSAR 252) Professor Kleiner features the baroque phenomenon in Roman architecture, in which the traditional vocabulary of architecture, consisting of columns and other conventional architectural elements, is manipulated to enliven building façades and inject them wit
From playlist Roman Architecture with Diana E. E. Kleiner
This lecture is part of an online graduate course on Lie groups. We give an introductory survey of Lie groups theory by describing some examples of Lie groups in low dimensions. Some recommended books: Lie algebras and Lie groups by Serre (anything by Serre is well worth reading) Repre
From playlist Lie groups
2020 Theory Winter School: Oskar Vafek (pt 2)
Topic: Topology and interactions in twisted bilayer graphene narrow bands Part 2 For more information on the 2020 Theory Winter School: https://nationalmaglab.org/news-events/events/for-scientists/winter-theory-school
From playlist 2020 Theory Winter School
James Propp - Conjectural Enumerations of Trimer Covers of Finite Subgraphs of the Triangular (...)
The work of Conway and Lagarias applying combinatorial group theory to packing problems suggests what we might mean by “domain-wall boundary conditions” for the trimer model on the infinite triangular lattice in which the permitted trimers are triangle trimers and three-in-a-line trimers.
From playlist Combinatorics and Arithmetic for Physics: special days
From superconductors to Coulomb gases: crystallization questions - Sylvia Serfaty
Ruth and Irving Adler Expository Lecture in Mathematics Topic: From superconductors to Coulomb gases: crystallization questions Speaker: Sylvia Serfaty Affiliation: New York University Date: March 5, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
Electric Flux and Gauss' Law - Review for AP Physics C: Electricity and Magnetism
AP Physics C: Electricity and Magnetism review of Electric Flux and Gauss’ Law including: Electric flux for a constant electric field, an example of the flux through a closed rectangular box, the electric flux from a point charge, a basic introduction to Gauss’ law, an example of Gauss’ la
From playlist AP Physics C: Electricity & Magnetism Review
Studies of Magnetic Quantum Disorder on Jeff=1/2 Triangular Lattices by Stephen Wilson
PROGRAM FRUSTRATED METALS AND INSULATORS (HYBRID) ORGANIZERS Federico Becca (University of Trieste, Italy), Subhro Bhattacharjee (ICTS-TIFR, India), Yasir Iqbal (IIT Madras, India), Bella Lake (Helmholtz-Zentrum Berlin fĂĽr Materialien und Energie, Germany), Yogesh Singh (IISER Mohali, In
From playlist FRUSTRATED METALS AND INSULATORS (HYBRID, 2022)
What are the trigonometric definitions of a right triangle
👉 Learn all about the trigonometry of right triangles. A right triangle is a triangle that has 90 degrees as one of its angles. The trigonometric identities of right triangles give us the relationship between the angles of a right triangle and the side lengths of the right triangle. These
From playlist Right Triangle Trigonometry | Learn About