Articles containing proofs | Mathematical identities | Integer sequences | Proof without words | Elementary mathematics | Number theory
In number theory, the sum of the first n cubes is the square of the nth triangular number. That is, The same equation may be written more compactly using the mathematical notation for summation: This identity is sometimes called Nicomachus's theorem, after Nicomachus of Gerasa (c. 60 – c. 120 CE). (Wikipedia).
[ANT08b] Square triangular numbers
Another application of Pell's equation.
From playlist [ANT] An unorthodox introduction to algebraic number theory
Squaring Numbers with Digits of 1
#shorts This video shows a pattern when squaring number with digits of 1.
From playlist Math Shorts
Triangular numbers, Venn diagrams and probability.
From playlist PIXL PPE Paper 2 June 2016 Higher Tier AQA Style Worked Solutions
Square Numbers | Numbers | Maths | FuseSchool
Understand and learn how to use square numbers and cube numbers!
From playlist MATHS: Numbers
Powered by https://www.numerise.com/ Square numbers
From playlist Indices, powers & roots
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 ℕumber Theory
Visualising irrationality with triangular squares
NEW (Christmas 2019). Two ways to support Mathologer Mathologer Patreon: https://www.patreon.com/mathologer Mathologer PayPal: paypal.me/mathologer (see the Patreon page for details) Get ready for some brand new and very pretty visual proofs of the fact that root 2, root 3, root 5 and r
From playlist Recent videos
Square, Cube & Triangular Numbers | Numbers | Maths | FuseSchool
In this video we are going to look at square, cube and triangular numbers, what they are, how they can be useful and some of the patterns they form CREDITS Animation & Design: Jean -Pierre Louw (Behance.net/Jean-Pierre_Louw) Narration: Dale Bennett Script: Joe Lewis VISIT US Website: www
From playlist MATHS: Numbers
Products of Odd Squares and Triangular Numbers (visual proof - updated version)
This is a short, animated visual proof demonstrating that the product of an odd square and a triangular number is the difference of two triangular numbers. #mathshorts #mathvideo #math #squares #mtbos #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof #iteach
From playlist Algebra
Sum of odd integers: a generalization (visual proof)
This short animated proof demonstrates the classic sum of odds visual proof and then shows one way to extend the idea to finding sums in other polygonal arrays. Surprisingly, the natural extension to finding sums of certain entries in a triangular array yields the sequence of squares. We l
From playlist Finite Sums
Mod-01 Lec-19 Cholesky decomposition
Elementary Numerical Analysis by Prof. Rekha P. Kulkarni,Department of Mathematics,IIT Bombay.For more details on NPTEL visit http://nptel.ac.in
From playlist NPTEL: Elementary Numerical Analysis | CosmoLearning Mathematics
3D Shapes - Faces, Edges, and Vertices - Euler's Formula - Geometry
This geometry video tutorial provides a basic introduction into 3d shapes. It covers 3-dimensional figures such as cylinders, cones, rectangular prisms, triangular prisms, square pyramids, and cubes. It provides the equations and formulas needed to calculate the surface area and volume o
From playlist Geometry Video Playlist
Odd squares mod 8 and the Sum of Positive Integers (two facts from eight triangles; visual proof)
This is a short, animated visual proof demonstrating how to use eight triangular arrays to find the congruence class of odd squares modulo 8 AND how to use the same diagram to produce a formula for the sum of the first n positive integers. #mathshorts #mathvideo #math #numbertheory #mtb
From playlist 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
Triangular Prism - Volume, Surface Area, Base and Lateral Area Formula, Basic Geometry
This basic geometry video tutorial explains how to find the volume and surface area of a triangular prism. It explains how to derive the formulas in addition to provide examples and practice problems for you to work on. The volume of a triangular prism is half of the volume of a rectangu
From playlist Pre-Algebra Video Playlist
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
Paola Boito: Topics in structured linear algebra - lecture 1
CIRM VIRTUAL EVENT Recorded during the meeting "French Computer Algebra Days" the March 01, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audio
From playlist Virtual Conference