Euclidean solid geometry | Analytic geometry | Multi-dimensional geometry | Three-dimensional coordinate systems
Three-dimensional space (also: 3D space, 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called parameters) are required to determine the position of an element (i.e., point). This is the informal meaning of the term dimension. In mathematics, a tuple of n numbers can be understood as the Cartesian coordinates of a location in a n-dimensional Euclidean space. The set of these n-tuples is commonly denoted and can be identified to the n-dimensional Euclidean space.When n = 3, this space is called three-dimensional Euclidean space (or simply Euclidean space when the context is clear). It serves as a model of the physical universe (when relativity theory is not considered), in which all known matter exists. While this space remains the most compelling and useful way to model the world as it is experienced, it is only one example of a large variety of spaces in three dimensions called 3-manifolds. In this classical example, when the three values refer to measurements in different directions (coordinates), any three directions can be chosen, provided that vectors in these directions do not all lie in the same 2-space (plane). Furthermore, in this case, these three values can be labeled by any combination of three chosen from the terms width/breadth, height/depth, and length. (Wikipedia).
From playlist Dimensions Deutsch
Multivariable Calculus | Three equations for a line.
We present three equations that represent the same line in three dimensions: the vector equation, the parametric equations, and the symmetric equation. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Lines and Planes in Three Dimensions
From playlist Dimensions Russian / Pусский
Do physicists describe the world in 4D?
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From playlist Science Unplugged: Physics
This video is about Three-Dimensional Figures
From playlist Surface Area and Volume
Have you ever wondered why we live in 3 dimensions or what 3D means? In this fun and nontechnical video, I give the mathematical definition of dimension and explain why this notion makes sense. Enjoy! Link to Replacement Theorem video: https://www.youtube.com/watch?v=lIkzgaHwQHY&list=PLJ
From playlist Vector Spaces
Space Coordinates Plotting Points in 3 Dimensions
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Space Coordinates Plotting Points in 3 Dimensions
From playlist Calculus 3
Calculus 3: Vector Calculus in 3-D (1 of 35) Vector Representation in 3-D
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain the various ways to represent vectors and unit vectors in 3 dimensional space. Next video in the series can be seen at: https://youtu.be/1EYceUjvvjQ
From playlist CALCULUS 3 CH 3.3 VECTOR CALCULUS IN 3-D
WildLinAlg17: Rank and Nullity of a Linear Transformation
We begin to discuss linear transformations involving higher dimensions (ie more than three). The kernel and the image are important spaces, or properties of vectors, associated to a linear transformation. The corresponding dimensions are the nullity and the rank, and they satisfy a simple
From playlist A first course in Linear Algebra - N J Wildberger
The Poincaré Conjecture (special lecture) John W. Morgan [ICM 2006]
slides for this talk: https://www.mathunion.org/fileadmin/IMU/Videos/ICM2006/tars/morgan2006.pdf The Poincaré Conjecture (special lecture) John W. Morgan Columbia University, USA https://www.mathunion.org/icm/icm-videos/icm-2006-videos-madrid-spain/icm-madrid-videos-24082006
From playlist Mathematics
History of Geometry IV: The emergence of higher dimensions | Sociology and Pure Maths| NJ Wildberger
In this history of mathematics, the 19th century stands out as an especially important chapter in the story of geometry. One of the key developments here is the move to understanding and studying higher dimensions. Here we touch on some of these advances, with an aim to explaining: where d
From playlist Sociology and Pure Mathematics
Steve Trettel - Visiting the Thurston Geometries: Computer Graphics in Curved Space - CoM Feb 2021
A beautiful observation of classical physics is that “light travels in straight lines” is only an approximation to reality. More precisely, light always takes a geodesic – a path between two points minimizing its time of travel. While this is often used to explain physical phenomena mathe
From playlist Celebration of Mind 2021
S.A.Robertson, How to see objects in four dimensions, LMS 1993
Based on the 1993 London Mathematical Society Popular Lectures, this special 'television lecture' is entitled "How to see objects in four dimensions" by Professor S.A.Robertson. The London Mathematical Society is one of the oldest mathematical societies, founded in 1865. Despite it's name
From playlist Mathematics
Sergei Gukov - Fivebranes and 4-manifolds
Sergei GUKOV (Caltech, Pasadena, USA)
From playlist Algèbre, Géométrie et Physique : une conférence en l'honneur
The distance in the n-dimensional space -- Elementary Linear Algebra
This lecture is on Elementary Linear Algebra. For more see http://calculus123.com.
From playlist Elementary Linear Algebra
WildLinAlg16: Applications of row reduction II
This video looks at various applications of row reduction to working with vectors and linear transformations in 2 and 3 dimensional space. We look at transformations given by 2x3 and by 3x2 matrices, along with the important notions of spanning sets and linearly independent sets of vector
From playlist A first course in Linear Algebra - N J Wildberger
What is General Relativity? Lesson 59: Scalar Curvature Part 8: Interpretation of Scalar Curvature.
What is General Relativity? Lesson 59: Scalar Curvature Part 8: Interpretation of Scalar Curvature (note: this is a re-post of a video that was posted at 2x playback speed. Sorry!) We begin our examination of Section 4.4.6 of "A Simple Introduction to Particle Physics Part II - Geometric
From playlist What is General Relativity?
Minkowski Space-Time: Spacetime in Special Relativity
Includes discussion of the space-time invariant interval and how the axes for time and space transform in Special Relativity.
From playlist Physics
(January 28, 2013) Leonard Susskind presents three possible geometries of homogeneous space: flat, spherical, and hyperbolic, and develops the metric for these spatial geometries in spherical coordinates. Originally presented in the Stanford Continuing Studies Program. Stanford Universit
From playlist Lecture Collection | Cosmology