In physics and mathematics, a sequence of n numbers can specify a location in n-dimensional space. When n = 1, the set of all such locations is called a one-dimensional space. An example of a one-dimensional space is the number line, where the position of each point on it can be described by a single number. In algebraic geometry there are several structures that are technically one-dimensional spaces but referred to in other terms. A field k is a one-dimensional vector space over itself. Similarly, the projective line over k is a one-dimensional space. In particular, if k = ℂ, the complex numbers, then the complex projective line P1(ℂ) is one-dimensional with respect to ℂ, even though it is also known as the Riemann sphere. More generally, a ring is a length-one module over itself. Similarly, the projective line over a ring is a one-dimensional space over the ring. In case the ring is an algebra over a field, these spaces are one-dimensional with respect to the algebra, even if the algebra is of higher dimensionality. (Wikipedia).
What exactly is space? Brian Greene explains what the "stuff" around us is. Subscribe to our YouTube Channel for all the latest from World Science U. Visit our Website: http://www.worldscienceu.com/ Like us on Facebook: https://www.facebook.com/worldscienceu Follow us on Twitter: https:
From playlist Science Unplugged: Physics
What is (a) Space? From Zero to Geo 1.5
What is space? In this video, we learn about the many different things that we might call "space". We come up with both a geometric and an algebraic definition, and the discussion also leads us to the important concept of subspaces. Sorry for how long this video took to make! I mention
From playlist From Zero to Geo
This video explains the definition of a vector space and provides examples of vector spaces.
From playlist Vector Spaces
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From playlist Science Unplugged: Special Relativity
This lecture is on Introduction to Higher Mathematics (Proofs). For more see http://calculus123.com.
From playlist Proofs
Do physicists describe the world in 4D?
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From playlist Science Unplugged: Physics
Spacetime and the Twins Paradox
An explanation of spacetime, the twins paradox which results from a moving clock running slow, and the possibility of forward time travel - but no return journey!
From playlist Special and General Relativity
Worldwide Calculus: Euclidean Space
Lecture on 'Euclidean Space' from 'Worldwide Multivariable Calculus'. For more lecture videos and $10 digital textbooks, visit www.centerofmath.org.
From playlist Multivariable Spaces and Functions
Dimensions (1 of 3: The Traditional Definition - Directions)
More resources available at www.misterwootube.com
From playlist Exploring Mathematics: Fractals
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
Introduction to Projective Geometry (Part 3)
At long last! I'm rambling on about projective space again. Will it last? Who knows!?
From playlist Introduction to Projective Geometry
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
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
Daniel Friedan - Where does quantum field theory come from?
Daniel Friedan (Rutgers Univ.) Where does quantum field theory come from? This will be an interim report on a long-running project to construct a mechanism that produces spacetime quantum field theory; to indentify possible exotic, non-canonical low- energy phenomena in SU(2) and SU(3) gau
From playlist Conférence à la mémoire de Vadim Knizhnik
An introduction to persistent homology
Title: An introduction to persistent homology Venue: Webinar for DELTA (Descriptors of Energy Landscape by Topological Analysis Abstract: This talk is an introduction to applied and computational topology, in particular as related to the study of energy landscapes arising in chemistry. W
From playlist Tutorials
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?
Applied topology 6: Homology Abstract: We give a visual introduction to homology groups. Roughly speaking, i-dimensional homology "counts the number of i-dimensional holes" in a space. This video accompanies the class "Topological Data Analysis" at Colorado State University: https://www.
From playlist Applied Topology - Henry Adams - 2021
What is an i-dimensional hole in a space?
What is an i-dimensional hole in a space? I describe how topology provides (at least) two answers to this question --- both the homotopy groups and the homology groups of that space. I give some intuition for what an i-dimensional hole is, and I give some intuition for how homotopy groups
From playlist Topology - Henry Adams - 2022
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
What is a dimension? In 3D...and 2D... and 1D
1D - it's the new 3D! Tweet it - http://bit.ly/mP3FFo Facebook it - http://on.fb.me/qtTraR minutephysics is now on Google+ - http://bit.ly/qzEwc6 And facebook - http://facebook.com/minutephysics Minute Physics provides an energetic and entertaining view of old and new problems
From playlist MinutePhysics