Algebraic curves | Plane curves
In mathematics, a polynomial lemniscate or polynomial level curve is a plane algebraic curve of degree 2n, constructed from a polynomial p with complex coefficients of degree n. For any such polynomial p and positive real number c, we may define a set of complex numbers by This set of numbers may be equated to points in the real Cartesian plane, leading to an algebraic curve Ζ(x, y) = c2 of degree 2n, which results from expanding out in terms of z = x + iy. When p is a polynomial of degree 1 then the resulting curve is simply a circle whose center is the zero of p. When p is a polynomial of degree 2 then the curve is a Cassini oval. (Wikipedia).
Curves in Modern Times | Algebraic Calculus One | Wild Egg
This video introduces some key objects, and also challenges, when we move beyond the Greek tradition to the more modern view of "curves". This rests crucially on the development of analytic geometry, or Cartesian coordinates, by Fermat and Descartes in the 17th century. They, along with Jo
From playlist Algebraic Calculus One from Wild Egg
Newton's method and algebraic curves | Real numbers and limits Math Foundations 86 | N J Wildberger
Newton's method can be extended to meets of algebraic curves. We show how, using the examples of the Fermat curve and the Lemniscate of Bernoulli. We start by finding the Taylor expansions of the associated polynomials (polynumbers) at a fixed point (r,s) in the plane. The first tangents
From playlist Math Foundations
Nicholas Katz: Life Over Finite Fields
Abstract: We will discuss some of Deligne's work and its diophantine applications. This lecture was given at The University of Oslo, May 22, 2013 and was part of the Abel Prize Lectures in connection with the Abel Prize Week celebrations. Program for the Abel Lectures 2013 1."Hidden s
From playlist Abel Lectures
PreCalculus - Polar Coordinates (21 of 35) Graphing Polar Epns: r^2=(2^2)[sin2(theta)], Lemniscate
Visit http://ilectureonline.com for more math and science lectures! In this video I will graph polar equation r^2=(2^2)[sin2(theta)], the lemniscate. Next video in the polar coordinates series can be seen at: http://youtu.be/lbdYN9S9aPs
From playlist Michel van Biezen: PRECALCULUS 10 - POLAR COORDINATES
Learn how to classify a polynomial based on the degree
π Learn how to classify polynomials. A polynomial is an expression of the sums/differences of two or more terms having different interger exponents of the same variable. A polynomial can be classified in two ways: by the number of terms and by its degree. A monomial is an expression of 1
From playlist Classify Polynomials
PreCalculus - Polar Coordinates (20 of 35) Graphing Polar Eqns: r^2=(2^2)[cos2(theta)], Lemniscate
Visit http://ilectureonline.com for more math and science lectures! In this video I will graph polar equation r^2=(2^2)[cos2(theta)], the lemniscate. Next video in the polar coordinates series can be seen at: http://youtu.be/WzlQjURlikE
From playlist Michel van Biezen: PRECALCULUS 10 - POLAR COORDINATES
Summary for classifying polynomials
π Learn how to classify polynomials. A polynomial is an expression of the sums/differences of two or more terms having different interger exponents of the same variable. A polynomial can be classified in two ways: by the number of terms and by its degree. A monomial is an expression of 1
From playlist Classify Polynomials
Some minimal submanifolds generalizing the Clifford torus -Jaigyoung Choe
Workshop on Mean Curvature and Regularity Topic: Some minimal submanifolds generalizing the Clifford torus Speaker: Jaigyoung Choe Affiliation: KIAS Date: November 5, 2018 For more video please visit http://video.ias.edu
From playlist Workshop on Mean Curvature and Regularity
Motion, Time and Change | Algebraic Calculus One | Wild Egg
In this video we introduce basic physical ideas that are important in calculus, particularly with regard to motion, time and change. We illustrate the ideas with projectile motion as understood by Galileo. An important notion here is the idea of the rate of change of a quantity with respe
From playlist Algebraic Calculus One from Wild Egg
Curves we (mostly) don't learn in high school (and applications)
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From playlist Applied Math
Is it a polynomial with two variables
π Learn how to determine whether a given equation is a polynomial or not. A polynomial function or equation is the sum of one or more terms where each term is either a number, or a number times the independent variable raised to a positive integer exponent. A polynomial equation of functio
From playlist Is it a polynomial or not?
How to reorder and classify a polynomial based on it's degree and number of terms
π Learn how to classify polynomials. A polynomial is an expression of the sums/differences of two or more terms having different integer exponents of the same variable. A polynomial can be classified in two ways: by the number of terms and by its degree. A monomial is an expression of 1
From playlist Classify Polynomials | Equations
π Learn how to classify polynomials. A polynomial is an expression of the sums/differences of two or more terms having different interger exponents of the same variable. A polynomial can be classified in two ways: by the number of terms and by its degree. A monomial is an expression of 1
From playlist Classify Polynomials
Classifying a polynomial expression by subtraction
π Learn how to classify polynomials. A polynomial is an expression of the sums/differences of two or more terms having different interger exponents of the same variable. A polynomial can be classified in two ways: by the number of terms and by its degree. A monomial is an expression of 1
From playlist Classify Polynomials | Simplify First
The differential calculus for curves (II) | Differential Geometry 8 | NJ Wildberger
In this video we extend Lagrange's approach to the differential calculus to the case of algebraic curves. This means we can study tangent lines, tangent conics and so on to a general curve of the form p(x,y)=0; this includes the situation y=f(x) as a special case. It also allows us to deal
From playlist Differential Geometry
Learn how to write a polynomial in standard form and classify
π Learn how to classify polynomials. A polynomial is an expression of the sums/differences of two or more terms having different integer exponents of the same variable. A polynomial can be classified in two ways: by the number of terms and by its degree. A monomial is an expression of 1
From playlist Classify Polynomials | Equations
How to classify a polynomial by expanding
π Learn how to classify polynomials. A polynomial is an expression of the sums/differences of two or more terms having different interger exponents of the same variable. A polynomial can be classified in two ways: by the number of terms and by its degree. A monomial is an expression of 1
From playlist Classify Polynomials | Simplify First
Classify a polynomial then determining if it is a polynomial or not
π Learn how to determine whether a given equation is a polynomial or not. A polynomial function or equation is the sum of one or more terms where each term is either a number, or a number times the independent variable raised to a positive integer exponent. A polynomial equation of functio
From playlist Is it a polynomial or not?
Labeling a polynomial based on the degree and number of terms
π Learn how to classify polynomials. A polynomial is an expression of the sums/differences of two or more terms having different integer exponents of the same variable. A polynomial can be classified in two ways: by the number of terms and by its degree. A monomial is an expression of 1
From playlist Classify Polynomials | Equations
Graphing Polar Equations, Test for Symmetry & 4 Examples Corrected
This lesson first starts with how to test for symmetry in a polar graph. Symmetry to the Polar Axis at 1:34 Symmetry to the line Theta=pi/2 at 8:13 Symmetry to the Pole at 10:38 Special Types of Graphs Circles at 13:13 Limacons at 16:16 I explain how to recognize
From playlist PreCalculus