Non-Euclidean geometry | Quaternions
In elliptic geometry, two lines are Clifford parallel or paratactic lines if the perpendicular distance between them is constant from point to point. The concept was first studied by William Kingdon Clifford in elliptic space and appears only in spaces of at least three dimensions. Since parallel lines have the property of equidistance, the term "parallel" was appropriated from Euclidean geometry, although the "lines" of elliptic geometry are geodesic curves and, unlike the lines of Euclidean geometry, are of finite length. The algebra of quaternions provides a descriptive geometry of elliptic space in which Clifford parallelism is made explicit. (Wikipedia).
What is an example of lines that are a linear pair
π Learn how to define angle relationships. Knowledge of the relationships between angles can help in determining the value of a given angle. The various angle relationships include: vertical angles, adjacent angles, complementary angles, supplementary angles, linear pairs, etc. Vertical a
From playlist Angle Relationships
Proving Parallel Lines with Angle Relationships
π Learn about converse theorems of parallel lines and a transversal. Two lines are said to be parallel when they have the same slope and are drawn straight to each other such that they cannot meet. In geometry, parallel lines are identified by two arrow heads or two small lines indicated i
From playlist Parallel Lines and a Transversal
What are parallel lines and a transversal
π Learn about converse theorems of parallel lines and a transversal. Two lines are said to be parallel when they have the same slope and are drawn straight to each other such that they cannot meet. In geometry, parallel lines are identified by two arrow heads or two small lines indicated i
From playlist Parallel Lines and a Transversal
What are the Angle Relationships for Parallel Lines and a Transversal
π Learn about converse theorems of parallel lines and a transversal. Two lines are said to be parallel when they have the same slope and are drawn straight to each other such that they cannot meet. In geometry, parallel lines are identified by two arrow heads or two small lines indicated i
From playlist Parallel Lines and a Transversal
What is the Corresponding Angle Converse Theorem
π Learn about converse theorems of parallel lines and a transversal. Two lines are said to be parallel when they have the same slope and are drawn straight to each other such that they cannot meet. In geometry, parallel lines are identified by two arrow heads or two small lines indicated i
From playlist Parallel Lines and a Transversal
What is the Consecutive Interior Angle Converse Theorem
π Learn about converse theorems of parallel lines and a transversal. Two lines are said to be parallel when they have the same slope and are drawn straight to each other such that they cannot meet. In geometry, parallel lines are identified by two arrow heads or two small lines indicated i
From playlist Parallel Lines and a Transversal
G. Molino - The Horizontal Einstein Property for H-Type sub-Riemannian Manifolds
We generalize the notion of H-type sub-Riemannian manifolds introduced by Baudoin and Kim, and then introduce a notion of parallel Clifford structure related to a recent work of Moroianu and Semmelmann. On those structures, we prove an Einstein property for the horizontal distribution usin
From playlist JournΓ©es Sous-Riemanniennes 2018
Geometric Algebra in 2D: complex numbers without the square root of minus one - Russell Goyder
Russell Goyder introduces geometric algebra from scratch, explaining how you can *multiply* vectors in a sensible way, that is deeply related to the geometry of rotations and reflections in space. After walking us through the basics, he shows how rotors represent rotations in the setting o
From playlist metauni festival 2023
QED Prerequisites Geometric Algebra 10: Bivector-vector products
In this lesson we cover the spacetime product of a Bivector and a vector as presented in section 3.3.1 of our topic paper. Our topic paper can be found at: https://arxiv.org/abs/1411.5002 Please consider supporting this channel on Patreon: https://www.patreon.com/XYLYXYLYX The software
From playlist QED- Prerequisite Topics
Rob Kusner: Willmore stability and conformal rigidity of minimal surfaces in S^n
A minimal surface M in the round sphere S^n is critical for area, as well as for the Willmore bending energy W=β«β«(1+H^2)da. Willmore stability of M is equivalent to a gap between β2 and 0 in its area-Jacobi operator spectrum. We show the W-stability of M persists in all higher dimensional
From playlist Geometry
Twisted matrix factorizations and loop groups - Daniel Freed
Daniel Freed University of Texas, Austin; Member, School of Mathematics and Natural Sciences February 9, 2015 The data of a compact Lie group GG and a degree 4 cohomology class on its classifying space leads to invariants in low-dimensional topology as well as important representations of
From playlist Mathematics
Consecutive Angles Theorem with Parallel Lines
π Learn about parallel lines and a transversal theorems. Two lines are said to be parallel when they have the same slope and are drawn straight to each other such that they cannot meet. In geometry, parallel lines are identified by two arrow heads or two small lines indicated in both lines
From playlist Parallel Lines and a Transversal Theorems
Rudolf Zeidler - Scalar and mean curvature comparison via the Dirac operator
I will explain a spinorial approach towards a comparison and rigidity principle involving scalar and mean curvature for certain warped products over intervals. This is motivated by recent scalar curvature comparison questions of Gromov, in particular distance estimates under lower scalar c
From playlist Talks of Mathematics MΓΌnster's reseachers
Jean-Pierre Bourguignon: Revisiting the question of dependence of spinor fields and Dirac [...]
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 Geometry
QED Prerequisites Geometric Algebra 5- Multivectors
In this lesson we introduce the idea of multivectors and emphasize the need to understand how to take the spacetime product of any two multivectors in the Spacetime Algebra. We demonstrate how this is done for the product between a vector and a bivector and we interpret the meaning of each
From playlist QED- Prerequisite Topics
This shows an interactive illustration that explains that parallel vectors can have either the same or opposite directions. The clip is from the book "Immersive Linear Algebra" at http://www.immersivemath.com
From playlist Chapter 2 - Vectors
What are adjacent angles and linear pairs
π Learn how to define angle relationships. Knowledge of the relationships between angles can help in determining the value of a given angle. The various angle relationships include: vertical angles, adjacent angles, complementary angles, supplementary angles, linear pairs, etc. Vertical a
From playlist Angle Relationships
A Geometric and topological view of classical optics by Rajaram Nityananda
DISCUSSION MEETING : GEOMETRIC PHASES IN OPTICS AND TOPOLOGICAL MATTER ORGANIZERS : Subhro Bhattacharjee, Joseph Samuel and Supurna Sinha DATE : 21 January 2020 to 24 January 2020 VENUE : Madhava Lecture Hall, ICTS, Bangalore This is a joint ICTS-RRI Discussion Meeting on the geometric
From playlist Geometric Phases in Optics and Topological Matter 2020
Multiplicities and the Equivariant Index - Jochen Bruening
Jochen Bruening Humboldt University September 30, 2011 For more videos, visit http://video.ias.edu
From playlist Mathematics
What is an angle and it's parts
π Learn how to define angle relationships. Knowledge of the relationships between angles can help in determining the value of a given angle. The various angle relationships include: vertical angles, adjacent angles, complementary angles, supplementary angles, linear pairs, etc. Vertical a
From playlist Angle Relationships