Euclidean geometry | Elementary geometry

Euclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry: the Elements. Euclid's approach consists in assuming a small set of intuitively appealing axioms (postulates) and deducing many other propositions (theorems) from these. Although many of Euclid's results had been stated earlier, Euclid was the first to organize these propositions into a logical system in which each result is proved from axioms and previously proved theorems. The Elements begins with plane geometry, still taught in secondary school (high school) as the first axiomatic system and the first examples of mathematical proofs. It goes on to the solid geometry of three dimensions. Much of the Elements states results of what are now called algebra and number theory, explained in geometrical language. For more than two thousand years, the adjective "Euclidean" was unnecessary because no other sort of geometry had been conceived. Euclid's axioms seemed so intuitively obvious (with the possible exception of the parallel postulate) that any theorem proved from them was deemed true in an absolute, often metaphysical, sense. Today, however, many other self-consistent non-Euclidean geometries are known, the first ones having been discovered in the early 19th century. An implication of Albert Einstein's theory of general relativity is that physical space itself is not Euclidean, and Euclidean space is a good approximation for it only over short distances (relative to the strength of the gravitational field). Euclidean geometry is an example of synthetic geometry, in that it proceeds logically from axioms describing basic properties of geometric objects such as points and lines, to propositions about those objects. This is in contrast to analytic geometry, introduced almost 2,000 years later by René Descartes, which uses coordinates to express geometric properties as algebraic formulas. (Wikipedia).

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

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

Geometry: Introduction to Triangles - Isosceles Triangle, Scalene Triangle, and more

A quick introduction to triangles. Triangles can be described by the lengths of their sides (equilateral, isosceles, and scalene) or by the sizes of their angles (acute angles, right angles, and obtuse angles). To learn more Geometry, you can watch our playlist from the beginning: https

From playlist Euclidean Geometry

What is a Quadrilateral? – Geometric Shapes – Geometry

Quadrilaterals all have four sides, but they all look a little different. How many kinds of quadrilaterals do you know? In this video we’ll talk about the different types of quadrilaterals. These geometric shapes include the square, rectangle, parallelogram, trapezoid and rhombus. Anot

From playlist Euclidean Geometry

Geometry: Sum of the angles in a triangle (a one-minute proof)

We prove that the sum of the angles of any triangle is 180°. It is important to develop the skill of proving things, because when you understand *why* something works, it reinforces your knowledge. To learn more Geometry, you can watch our playlist from the beginning: https://bit.ly/Geo

From playlist Euclidean Geometry

Introduction to Metric Spaces - Definition of a Metric. - The metric on R - The Euclidean Metric on R^n - A metric on the set of all bounded functions - The discrete metric

From playlist Topology

Euclidean and Algebraic Geometry, David Cox [2014]

Slides for this talk: https://drive.google.com/file/d/1s87shlFPPVolx1dV7H4CBc1DjDrh0piR/view?usp=sharing David Cox Amherst College This talk will survey some examples, mostly geometric questions about Euclidean space, where the methods of algebraic geometry can offer some insight. I wil

From playlist Mathematics

Geometry: Introduction to Circles - radius, diameter, circumference and area of a circle

We give a quick introduction to the circle. First we define the important parts of a circle: the radius, diameter and circumference. We then give the formulas for computing the circumference and area. To learn more Geometry, you can watch our playlist from the beginning: https://bit.ly

From playlist Euclidean Geometry

Would Alien (Non-Euclidean) Geometry Break Our Brains?

Author H. P. Lovecraft often described his fictional alien worlds as having 'Non-Euclidean Geometry', but what exactly is this? And would it really break our brains? Produced by Tom Rocks Maths intern Joe Double, with assistance from Dr Tom Crawford at the University of Oxford. Thanks to

From playlist Mathstars

CS224W: Machine Learning with Graphs | 2021 | Lecture 19.2 - Hyperbolic Graph Embeddings

For more information about Stanford’s Artificial Intelligence professional and graduate programs, visit: https://stanford.io/3Brc7vN Jure Leskovec Computer Science, PhD In previous lectures, we focused on graph representation learning in Euclidean embedding spaces. In this lecture, we in

From playlist Stanford CS224W: Machine Learning with Graphs

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

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

Colloquium MathAlp 2019 - Claude Lebrun

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From playlist Colloquiums MathAlp

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 ►https://www.beautifulequation.com/pages/trefor In this vi

From playlist Cool Math Series

From playlist Contributed talks One World Symposium 2020

Metric space definition and examples. Welcome to the beautiful world of topology and analysis! In this video, I present the important concept of a metric space, and give 10 examples. The idea of a metric space is to generalize the concept of absolute values and distances to sets more gener

From playlist Topology

11. Non-Euclidean Spaces: Closed Universes

MIT 8.286 The Early Universe, Fall 2013 View the complete course: http://ocw.mit.edu/8-286F13 Instructor: Alan Guth In this lecture, the professor reviewed Euclid's Postulates and talked about non-Euclidean geometry and a sphere in 4 Euclidean dimensions. License: Creative Commons BY-NC-

From playlist The Early Universe by Prof. Alan Guth