Analytic geometry | Mathematical concepts | Elementary geometry
In geometry, a line is an infinitely long object with no width, depth, or curvature. Thus, lines are one-dimensional objects, though they may exist in two, three, or higher dimension spaces. The word line may also refer to a line segment in everyday life, which has two points to denote its ends. Lines can be referred by two points that lay on it (e.g., ) or by a single letter (e.g., ). Euclid described a line as "breadthless length" which "lies equally with respect to the points on itself"; he introduced several postulates as basic unprovable properties from which he constructed all of geometry, which is now called Euclidean geometry to avoid confusion with other geometries which have been introduced since the end of the 19th century (such as non-Euclidean, projective and affine geometry). In modern mathematics, given the multitude of geometries, the concept of a line is closely tied to the way the geometry is described. For instance, in analytic geometry, a line in the plane is often defined as the set of points whose coordinates satisfy a given linear equation, but in a more abstract setting, such as incidence geometry, a line may be an independent object, distinct from the set of points which lie on it. When a geometry is described by a set of axioms, the notion of a line is usually left undefined (a so-called primitive object). The properties of lines are then determined by the axioms which refer to them. One advantage to this approach is the flexibility it gives to users of the geometry. Thus in differential geometry, a line may be interpreted as a geodesic (shortest path between points), while in some projective geometries, a line is a 2-dimensional vector space (all linear combinations of two independent vectors). This flexibility also extends beyond mathematics and, for example, permits physicists to think of the path of a light ray as being a line. (Wikipedia).
What is a line segment and ray
π Learn essential definitions of points, lines, and planes. A point defines a position in space. A line is a set of points. A line can be created by a minimum of two points. A plane is a flat surface made up of at least three points. A plane contains infinite number of lines. A ray is a li
From playlist Points Lines and Planes
π Learn essential definitions of points, lines, and planes. A point defines a position in space. A line is a set of points. A line can be created by a minimum of two points. A plane is a flat surface made up of at least three points. A plane contains infinite number of lines. A ray is a li
From playlist Points Lines and Planes
π Learn essential definitions of points, lines, and planes. A point defines a position in space. A line is a set of points. A line can be created by a minimum of two points. A plane is a flat surface made up of at least three points. A plane contains infinite number of lines. A ray is a li
From playlist Points Lines and Planes
Identify and Name a Point, Line, Ray, Segment, and Angle
This video defines a point, line, segment, ray, and angle. Once identified each is properly named.
From playlist Introduction to Geometry Basics: Points, Lines, Segments, Planes, Angles, and Polygons
What is a point a line and a plane
π Learn essential definitions of points, lines, and planes. A point defines a position in space. A line is a set of points. A line can be created by a minimum of two points. A plane is a flat surface made up of at least three points. A plane contains infinite number of lines. A ray is a li
From playlist Points Lines and Planes
π Learn essential definitions of points, lines, and planes. A point defines a position in space. A line is a set of points. A line can be created by a minimum of two points. A plane is a flat surface made up of at least three points. A plane contains infinite number of lines. A ray is a li
From playlist Points Lines and Planes
π Learn essential definitions of points, lines, and planes. A point defines a position in space. A line is a set of points. A line can be created by a minimum of two points. A plane is a flat surface made up of at least three points. A plane contains infinite number of lines. A ray is a li
From playlist Points Lines and Planes
π Learn essential definitions of points, lines, and planes. A point defines a position in space. A line is a set of points. A line can be created by a minimum of two points. A plane is a flat surface made up of at least three points. A plane contains infinite number of lines. A ray is a li
From playlist Points Lines and Planes
A brief history of Geometry III: The 19th century | Sociology and Pure Mathematics | N J Wildberger
The 19th century was a pivotal time in the development of modern geometry, actually a golden age for the subject, which then saw a precipitous decline in the 20th century. Why was that? To find out, let's first overview some of the main developments in geometry during the 1800's, includin
From playlist Sociology and Pure Mathematics
Perspectives in Math and Art by Supurna Sinha
KAAPI WITH KURIOSITY PERSPECTIVES IN MATH AND ART SPEAKER: Supurna Sinha (Raman Research Institute, Bengaluru) WHEN: 4:00 pm to 5:30 pm Sunday, 24 April 2022 WHERE: Jawaharlal Nehru Planetarium, Bengaluru Abstract: The European renaissance saw the merging of mathematics and art in th
From playlist Kaapi With Kuriosity (A Monthly Public Lecture Series)
The Beautiful Story of Non-Euclidean Geometry
Visit https://brilliant.org/TreforBazett/ to get started learning STEM for free, and the first 200 people will get 20% off their annual premium subscription. Check out my MATH MERCH line in collaboration with Beautiful Equations βΊhttps://www.beautifulequation.com/pages/trefor In this vi
From playlist Cool Math Series
An Intuitive Introduction to Projective Geometry Using Linear Algebra
This is an area of math that I've wanted to talk about for a long time, especially since I have found how projective geometry can be used to formulate Euclidean, spherical, and hyperbolic geometries, and a possible (and hopefully plausible) way projective geometry (specifically the model t
From playlist Summer of Math Exposition 2 videos
Geometry Course β Chapter 1 (Foundations) Letβs Start!
Learn Geometry - chapter 1 full Geometry course, Foundations to Geometry. For more in-depth math help check out my catalog of courses. Every course includes over 275 videos of easy to follow and understand math instruction, with fully explained practice problems and printable worksheets
From playlist GED Prep Videos
A brief history of geometry II: The European epoch | Sociology and Pure Mathematics | N J Wildberger
Let's have a quick overview of some of the developments in the European story of geometry -- at least up to the 19th century. We'll discuss Cartesian geometry, Projective geometry, Descriptive geometry, Algebraic geometry and Differential geometry. This is meant for people from outside m
From playlist Sociology and Pure Mathematics
AlgTop20: The geometry of surfaces
This lecture relates the two dimensional surfaces we have just classified with the three classical geometries- Euclidean, spherical and hyperbolic. Our approach to these geometries is non-standard (the usual formulations are in fact deeply flawed) and we concentrate on isometries, avoiding
From playlist Algebraic Topology: a beginner's course - N J Wildberger
Homeschool Geometry Curriculum β TabletClass Math
Homeschooling Geometry can be a big challenge however with TabletClass Math you will have a great and proven math curriculum to help you. In this video I will go over a basic geometry problem that your child should be able to do in high school level Geometry. Check out our Homeschool Geo
From playlist Homeschool Math
Washington Geometry EOC (End of Course Exam) β PRACTICE PROBLEM!
Passing the Washington Geometry EOC (End of Course Exam) will require your ability to increase your focus and commitment on what you learned in Geometry. The Washington Geometry EOC exam is not easy and most students donβt appreciate the amount of geometry concepts and skills they need to
From playlist Test Prep Math
What is a point line and plane
π Learn essential definitions of points, lines, and planes. A point defines a position in space. A line is a set of points. A line can be created by a minimum of two points. A plane is a flat surface made up of at least three points. A plane contains infinite number of lines. A ray is a li
From playlist Points Lines and Planes