Homogeneous polynomials | Algebraic varieties | Algebraic geometry | Multilinear algebra
In mathematics, a cubic form is a homogeneous polynomial of degree 3, and a cubic hypersurface is the zero set of a cubic form. In the case of a cubic form in three variables, the zero set is a cubic plane curve. In, Boris Delone and Dmitry Faddeev showed that binary cubic forms with integer coefficients can be used to parametrize orders in cubic fields. Their work was generalized in to include all cubic rings (a cubic ring is a ring that is isomorphic to Z3 as a Z-module), giving a discriminant-preserving bijection between orbits of a GL(2, Z)-action on the space of integral binary cubic forms and cubic rings up to isomorphism. The classification of real cubic forms is linked to the classification of umbilical points of surfaces. The equivalence classes of such cubics form a three-dimensional real projective space and the subset of define a surface – the umbilic torus. (Wikipedia).
Solving a Cubic Equation Using a Triangle
There is this surprising fact about cubic equations with 3 real solutions where an equilateral triangle centered on the inflection point can always be scaled/rotated by some amount such that its vertices will line up with the roots of the equation. But is there any way that this can be us
From playlist Summer of Math Exposition Youtube Videos
What are Cubic Graphs? | Graph Theory
What are cubic graphs? We go over this bit of graph theory in today's math lesson! Recall that a regular graph is a graph in which all vertices have the same degree. The degree of a vertex v is the number of edges incident to v, or equivalently the number of vertices adjacent to v. If ever
From playlist Graph Theory
Chemistry - Liquids and Solids (26 of 59) Crystal Structure: Density of the Unit Cell: Simple Cubic
Visit http://ilectureonline.com for more math and science lectures! In this video I will calculate the % volume of the molecules in a simple cubic.
From playlist MOST POPULAR VIDEOS
Algebraic geometry 2 Two cubic curves.
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It discusses two examples of cubic curves: a nodal cubic, and an elliptic curve.
From playlist Algebraic geometry I: Varieties
Solving Cubic Inequalities (1 of 3: Interpreting the graph)
More resources available at www.misterwootube.com
From playlist Further Work with Functions
Unit Cell Chemistry Simple Cubic, Body Centered Cubic, Face Centered Cubic Crystal Lattice Structu
This chemistry video tutorial provides a basic introduction into unit cell and crystal lattice structures. It highlights the key differences between the simple cubic unit cell, the body centered cubic structure and the face centered cubic structure in table format. The full version of th
From playlist New AP & General Chemistry Video Playlist
"Find the volume of more complex compound 3D shapes."
From playlist Shape: Volume & Surface Area
Cubic Curves (2 of 4: Polynomial Division & the factors of a Polynomial)
More resources available at www.misterwootube.com
From playlist Further Polynomials
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
Asymptotics of number fields - Manjul Bhargava [2011]
Asymptotics of number fields Introductory Workshop: Arithmetic Statistics January 31, 2011 - February 04, 2011 January 31, 2011 (11:40 AM PST - 12:40 PM PST) Speaker(s): Manjul Bhargava (Princeton University) Location: MSRI: Simons Auditorium http://www.msri.org/workshops/566
From playlist Number Theory
Ari Shnidman: Monogenic cubic fields and local obstructions
Recording during the meeting "Zeta Functions" the December 05, 2019 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http:
From playlist Number Theory
What is General Relativity? Lesson 33: Math Break - The Cubic Equation
What is General Relativity? Lesson 33: Math Break-The Cubic Equation This is a lecture about the lesser known cousin of the quadratic equation: the cubic equation. The purpose of this lecture is to develop confidence regarding the roots of a cubic equation. All of the geodesics of the Sch
From playlist What is General Relativity?
Lattice Structures in Ionic Solids
We've learned a lot about covalent compounds, but we haven't talked quite as much about ionic compounds in their solid state. These will adopt a highly ordered and repeating lattice structure, but the geometry of the lattice depends entirely on the types of ions and their ratio in the chem
From playlist General Chemistry
Hodge theory and derived categories of cubic fourfolds - Richard Thomas
Richard Thomas Imperial College London September 16, 2014 Cubic fourfolds behave in many ways like K3 surfaces. Certain cubics - conjecturally, the ones that are rational - have specific K3s associated to them geometrically. Hassett has studied cubics with K3s associated to them at the le
From playlist Mathematics
Lec 19 | MIT 18.085 Computational Science and Engineering I, Fall 2008
Lecture 19: Quadratic/cubic elements License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 18.085 Computational Science & Engineering I, Fall 2008
Arul Shankar, Ordering elliptic curves by conductor
VaNTAGe seminar, on Oct 27, 2020 License: CC-BY-NC-SA. Closed captions provided by Rachana Madhukara.
From playlist Rational points on elliptic curves
500 years of NOT teaching THE CUBIC FORMULA. What is it they think you can't handle?
Why is it that, unlike with the quadratic formula, nobody teaches the cubic formula? After all, they do lots of polynomial torturing in schools and the discovery of the cubic formula is considered to be one of the milestones in the history of mathematics. It's all a bit of a mystery and ou
From playlist Recent videos