Algebraic curves | Plane curves
In algebraic geometry, a quartic plane curve is a plane algebraic curve of the fourth degree. It can be defined by a bivariate quartic equation: with at least one of A, B, C, D, E not equal to zero. This equation has 15 constants. However, it can be multiplied by any non-zero constant without changing the curve; thus by the choice of an appropriate constant of multiplication, any one of the coefficients can be set to 1, leaving only 14 constants. Therefore, the space of quartic curves can be identified with the real projective space It also follows, from Cramer's theorem on algebraic curves, that there is exactly one quartic curve that passes through a set of 14 distinct points in general position, since a quartic has 14 degrees of freedom. A quartic curve can have a maximum of: * Four connected components * Twenty-eight bi-tangents * Three ordinary double points. One may also consider quartic curves over other fields (or even rings), for instance the complex numbers. In this way, one gets Riemann surfaces, which are one-dimensional objects over but are two-dimensional over An example is the Klein quartic. Additionally, one can look at curves in the projective plane, given by homogeneous polynomials. (Wikipedia).
The "tangent plane" of the graph of a function is, well, a two-dimensional plane that is tangent to this graph. Here you can see what that looks like.
From playlist Multivariable calculus
#Cycloid: A curve traced by a point on a circle rolling in a straight line. (A preview of this Sunday's video.)
From playlist Miscellaneous
👉 Learn essential definitions of points, lines, and planes. A point defines a position in space. A line is a set of points. A line can be created by a minimum of two points. A plane is a flat surface made up of at least three points. A plane contains infinite number of lines. A ray is a li
From playlist Points Lines and Planes
👉 Learn essential definitions of points, lines, and planes. A point defines a position in space. A line is a set of points. A line can be created by a minimum of two points. A plane is a flat surface made up of at least three points. A plane contains infinite number of lines. A ray is a li
From playlist Points Lines and Planes
👉 Learn essential definitions of points, lines, and planes. A point defines a position in space. A line is a set of points. A line can be created by a minimum of two points. A plane is a flat surface made up of at least three points. A plane contains infinite number of lines. A ray is a li
From playlist Points Lines and Planes
Bitangents to plane quartics - tropical, real and arithmetic count by Hannah Markwig
PROGRAM COMBINATORIAL ALGEBRAIC GEOMETRY: TROPICAL AND REAL (HYBRID) ORGANIZERS Arvind Ayyer (IISc, India), Madhusudan Manjunath (IITB, India) and Pranav Pandit (ICTS-TIFR, India) DATE: 27 June 2022 to 08 July 2022 VENUE: Madhava Lecture Hall and Online Algebraic geometry is the study of
From playlist Combinatorial Algebraic Geometry: Tropical and Real (HYBRID)
Determining if a set of points makes a parallelogram or not
👉 Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr
From playlist Quadrilaterals on a Coordinate Plane
Isabel Vogt - An enriched count of the bitangents to a smooth plane quartic curve - AGONIZE
Recent work of Kass–Wickelgren gives an enriched count of the 27 lines on a smooth cubic surface over arbitrary fields, generalizing Segre’s signed count count of elliptic and hyperbolic lines. Their approach using 𝔸1-enumerative geometry suggests that other classical enumerative problems
From playlist Arithmetic Geometry is ONline In Zoom, Everyone (AGONIZE)
Determine if a set of points is a trapezoid or not
👉 Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr
From playlist Quadrilaterals on a Coordinate Plane
Tropical Geometry - Lecture 2 - Curve Counting | Bernd Sturmfels
Twelve lectures on Tropical Geometry by Bernd Sturmfels (Max Planck Institute for Mathematics in the Sciences | Leipzig, Germany) We recommend supplementing these lectures by reading the book "Introduction to Tropical Geometry" (Maclagan, Sturmfels - 2015 - American Mathematical Society)
From playlist Twelve Lectures on Tropical Geometry by Bernd Sturmfels
A positive proportion of plane cubics fail the Hasse principle - Manjul Bhargava [2011]
Arithmetic Statistics April 11, 2011 - April 15, 2011 April 11, 2011 (02:10 PM PDT - 03:00 PM PDT) Speaker(s): Manjul Bhargava (Princeton University) Location: MSRI: Simons Auditorium http://www.msri.org/workshops/567/schedules/12761
From playlist Number Theory
Mirror symmetry for the mirror quartic, and other stories - Ivan Smith
Workshop on Homological Mirror Symmetry: Methods and Structures Speaker: Ivan Smith Topic: Mirror symmetry for the mirror quartic, and other stories Affiliation: University of Cambridge Date: November, 9, 2016 For more video, visit http://video.ias.edu
From playlist Workshop on Homological Mirror Symmetry: Methods and Structures
Artan Sheshmani : On the proof of S-duality modularity conjecture on quintic threefolds
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
Tropical Geometry - Lecture 8 - Surfaces | Bernd Sturmfels
Twelve lectures on Tropical Geometry by Bernd Sturmfels (Max Planck Institute for Mathematics in the Sciences | Leipzig, Germany) We recommend supplementing these lectures by reading the book "Introduction to Tropical Geometry" (Maclagan, Sturmfels - 2015 - American Mathematical Society)
From playlist Twelve Lectures on Tropical Geometry by Bernd Sturmfels
This talk is about the Riemann-Roch theorem for genus 3 curves. We show that any such curve is either hyperelliptic or a nonsingular plane quartic. We find the Weierstrass points and the holomorphic 1-forms and the canonical divisors of these curves. Finally we give a brief description of
From playlist Algebraic geometry: extra topics
VaNTAGe seminar, on Sep 15, 2020 License: CC-BY-NC-SA.
From playlist Rational points on elliptic curves
Determining the Unit Tangent Vector
This video explains how to determine the unit tangent vector to a curve defined by a vector valued function. http://mathispower4u.wordpress.com/
From playlist Vectors
Persistence of the Brauer-Manin obstruction under field extension - Viray - Workshop 2 - CEB T2 2019
Bianca Viray (University of Washington) / 27.06.2019 Persistence of the Brauer-Manin obstruction under field extension. We consider the question of when an empty Brauer set over the ground field gives rise to an empty Brauer set over an extension. We first consider the case of quartic d
From playlist 2019 - T2 - Reinventing rational points
👉 Learn essential definitions of points, lines, and planes. A point defines a position in space. A line is a set of points. A line can be created by a minimum of two points. A plane is a flat surface made up of at least three points. A plane contains infinite number of lines. A ray is a li
From playlist Points Lines and Planes