In mathematics, specifically abstract algebra, a square class of a field is an element of the square class group, the quotient group of the multiplicative group of nonzero elements in the field modulo the square elements of the field. Each square class is a subset of the nonzero elements (a coset of the multiplicative group) consisting of the elements of the form xy2 where x is some particular fixed element and y ranges over all nonzero field elements. For instance, if , the field of real numbers, then is just the group of all nonzero real numbers (with the multiplication operation) and is the subgroup of positive numbers (as every positive number has a real square root). The quotient of these two groups is a group with two elements, corresponding to two cosets: the set of positive numbers and the set of negative numbers. Thus, the real numbers have two square classes, the positive numbers and the negative numbers. Square classes are frequently studied in relation to the theory of quadratic forms. The reason is that if is an -vector space and is a quadratic form and is an element of such that , then for all , and thus it is sometimes more convenient to talk about the square classes which the quadratic form represents. Every element of the square class group is an involution. It follows that, if the number of square classes of a field is finite, it must be a power of two. (Wikipedia).
👉 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
Classifying triangles by the measure of their sides
👉 Learn all about classifying triangles. A triangle is a closed figure with three sides. A triangle can be classified based on the length of the sides or based on the measure of the angles. To classify a triangle based on the length of the sides, we have: equilateral (3 sides are equal), i
From playlist Triangles
👉 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
👉 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
What is an equiangular triangle
👉 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
What is an equilateral triangle
👉 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
How to classify polygons by the measure of their angles
👉 Learn all about classifying triangles. A triangle is a closed figure with three sides. A triangle can be classified based on the length of the sides or based on the measure of the angles. To classify a triangle based on the length of the sides, we have: equilateral (3 sides are equal), i
From playlist Triangles
👉 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
What are four types of polygons
👉 Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
In JavaScript you can use the OOP (Object-Oriented-Programming) feature of "classes" to construct objects which are then useful resources for your script/application. Learn all about classes in JavaScript in this video. ⭐️ Course Contents ⭐️ ⌨️ (00:00) The Basics ⌨️ (14:40) Getters and S
From playlist Tutorials
CTNT 2018 - "Arithmetic Statistics" (Lecture 2) by Álvaro Lozano-Robledo
This is lecture 2 of a mini-course on "Arithmetic Statistics", taught by Álvaro Lozano-Robledo, during CTNT 2018, the Connecticut Summer School in Number Theory. For more information about CTNT and other resources and notes, see https://ctnt-summer.math.uconn.edu/
From playlist CTNT 2018 - "Arithmetic Statistics" by Álvaro Lozano-Robledo
16.17: Inheritance in JavaScript - Topics of JavaScript/ES6
In this video, I discuss the concept of inheritance in Object-Oriented Programming (OOP) with JavaScript and using ES6 classes. https://thecodingtrain.com/Tutorials/16-javascript-es6/16.17-inheritance.html 🕹️ p5.js Web Editor Sketch: https://editor.p5js.org/codingtrain/sketches/52LIIRRCa
From playlist 16: Topics of JavaScript/ES6-ES8 - p5.js Tutorial
Representation theory: Examples D8, A4, S4, S5, A5
In this talk we calculate the character tables of several small groups: the dihedral group of order 8, and the alternating and symmetric groups on 4 and 5 points. We do this by first finding the 1-dimensional characters, then finding a few other characters by looking at permutation repres
From playlist Representation theory
Multiclass Classification : Data Science Concepts
How do we predict MORE than 2 classes??? My Patreon : https://www.patreon.com/user?u=49277905
From playlist Data Science Concepts
F. Polizzi - Classification of surfaces via Mori theory (Part 2)
Abstract - We give a summary of the Minimal Model Program (namely, Mori Theory) in the case of surfaces.
From playlist Ecole d'été 2019 - Foliations and algebraic geometry
Year 12/AS Statistics Chapter 2.3 (Measures of Location & Spread)
The third lesson on measures of location and spread focuses heavily on practicing the methods for interpolating data, and then finishes with introducing the concept of standard deviation along with its formulae and some worked examples. This lesson is meant as preparation for Exercise 2D
From playlist Year 12/AS Edexcel (8MA0) Mathematics: FULL COURSE
All Formulae for CBSE Class 10- Sutra - Math || Board Brahmastra || Misbah Sir || Infinity Learn
Don’t Memorise brings learning to life through its captivating educational videos. To Know More, visit https://infinitylearn.com/ ✅ Please Join Our Telegram Channel ►https://t.me/InfinityLearn9_10 New videos every week. To stay updated, subscribe to our YouTube channel: http://bit.ly/Don
From playlist Board Brahmastra || CBSE Class 10 Crash Course
Hannah Alpert (4/15/22): Homology of sliding-squares configuration spaces
The configuration space of n ordered points in the plane is homotopy equivalent to that of n ordered unit squares sliding in the plane. How does the rank of its degree-j homology group change if the squares are confined to the p by q rectangle? This rank turns out to be much bigger, grow
From playlist Vietoris-Rips Seminar
Year 12/AS Statistics Chapter 2.4 (Measures of Location & Spread)
This lesson looks at how to calculate standard deviation and variance for tabulated data, including how to calculate estimates of standard deviation and variance for grouped continuous data. Later on, we explore what is meant by summary data and how this is used in questions. This lesson
From playlist Year 12/AS Edexcel (8MA0) Mathematics: FULL COURSE
👉 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