# Geometry

Geometry (from Ancient Greek γεωμετρία (geōmetría) 'land measurement'; from γῆ (gê) 'earth, land', and μέτρον (métron) 'a measure') is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is called a geometer. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point, line, plane, distance, angle, surface, and curve, as fundamental concepts. During the 19th century several discoveries enlarged dramatically the scope of geometry. One of the oldest such discoveries is Gauss' Theorema Egregium ("remarkable theorem") that asserts roughly that the Gaussian curvature of a surface is independent from any specific embedding in a Euclidean space. This implies that surfaces can be studied intrinsically, that is, as stand-alone spaces, and has been expanded into the theory of manifolds and Riemannian geometry. Later in the 19th century, it appeared that geometries without the parallel postulate (non-Euclidean geometries) can be developed without introducing any contradiction. The geometry that underlies general relativity is a famous application of non-Euclidean geometry. Since then, the scope of geometry has been greatly expanded, and the field has been split in many subfields that depend on the underlying methods—differential geometry, algebraic geometry, computational geometry, algebraic topology, discrete geometry (also known as combinatorial geometry), etc.—or on the properties of Euclidean spaces that are disregarded—projective geometry that consider only alignment of points but not distance and parallelism, affine geometry that omits the concept of angle and distance, finite geometry that omits continuity, and others. Originally developed to model the physical world, geometry has applications in almost all sciences, and also in art, architecture, and other activities that are related to graphics. Geometry also has applications in areas of mathematics that are apparently unrelated. For example, methods of algebraic geometry are fundamental in Wiles's proof of Fermat's Last Theorem, a problem that was stated in terms of elementary arithmetic, and remained unsolved for several centuries. (Wikipedia).

Geometry: Ch 5 - Proofs in Geometry (2 of 58) Definitions

Visit http://ilectureonline.com for more math and science lectures! In this video I will explain and give examples of definitions. Next video in this series can be seen at: https://youtu.be/-Pmkhgec704

From playlist GEOMETRY 5 - PROOFS IN GEOMETRY

Geometry (1-1) First Terms

Geometry lecture on points, lines, and planes.

From playlist Geometry

Geometry for Kids - Definitions

This is a series of videos on Geometry, with kids in mind (~ 9 or 10 years old). In this video we start with some basic definitions: point, plane, segment, line, ray, secant, parallel, circle, radius, and diameter. Click "show more" for links and more details. You can find our Algebra for

From playlist Geometry for Kids

Geometry for Kids - Introduction

This is a series of videos on Geometry, with kids in mind (~ 9 or 10 years old). We will start from some basic definitions, and then work on some elementary plane geometry: lines, angles, polygons, triangles, etc, and work our way up to proving some theorems! In this first video, we introd

From playlist Geometry for Kids

Geometry - Basic Terminology (1 of 34) Definition of Points and Lines

Visit http://ilectureonline.com for more math and science lectures! In this video I will define and give examples of points and lines. Next video in the Basic Terminology series can be seen at: http://youtu.be/kziFbJMWjUY

From playlist GEOMETRY 1 - BASIC TERMINOLOGY

Geometry - Basic Terminology (5 of 34) Definition of Angles, Sides, and Vertex

Visit http://ilectureonline.com for more math and science lectures! In this video I will define and give examples of angles, sides, and vertex. Next video in the Basic Terminology series can be seen at: http://youtu.be/Q-SlfOC2a3Y

From playlist GEOMETRY 1 - BASIC TERMINOLOGY

Introduction to Projective Geometry (Part 1)

The first video in a series on projective geometry. We discuss the motivation for studying projective planes, and list the axioms of affine planes.

From playlist Introduction to Projective Geometry

What is a geometric mean

Learn about the geometric mean of numbers. The geometric mean of n numbers is the nth root of the product of the numbers. To find the geometric mean of n numbers, we first multiply the numbers and then take the nth root of the product.

From playlist Geometry - GEOMETRIC MEAN

Geometry - Basic Terminology (2 of 34) Definition of Planes

Visit http://ilectureonline.com for more math and science lectures! In this video I will define and give examples of planes. Next video in the Basic Terminology series can be seen at: http://youtu.be/Bly11gCPOao

From playlist GEOMETRY 1 - BASIC TERMINOLOGY

Homeschool Geometry - What Every Homeschool Parent Needs to Know

TabletClass Math Homeschool: https://tabletclass.com/ How to homeschool Geometry successfully. Need help with homeschooling Pre-Algebra, Algebra 1, Geometry, Algebra 2 and Pre-Calculus? Check out TabletClass Math for all your homeschooling needs: https://tabletclass.com/ .

From playlist Homeschool Geometry

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

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

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

SGP 2020 Graduate School: Geometric computing in geometry-central

This talk gives a basic introduction to geometry-central (http://geometry-central.net), a C++ library with data structures and algorithms for geometry processing. We cover the basic motivations and design of the library, as well as some examples of it in action. Part of the SGP 2020 Grad

From playlist Research

What is Mathematics, Really? #SoME2

"What is mathematics?" and "What do mathematicians do?" Mathematics seems daunting or deeply nerdy. In my view, it's another way to look at the world, the same as art or science. Let's do some mathematics ourselves, speeding through the process from asking a question to telling others what

From playlist Summer of Math Exposition 2 videos

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

Geometry: Introduction to the Polygon (quadrilateral, pentagon, hexagon and more)

Learn the definition of polygon - a very important shape in geometry. When a polygon has a small number of sides, there is a word you use instead of "polygon". We teach you the names of polygons with 3 to 10 sides. To learn more Geometry, you can watch our playlist from the beginning:

From playlist Euclidean Geometry

Walter Neumann: Lipschitz embedding of complex surfaces

Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b

From playlist Algebraic and Complex Geometry