Diophantine equations | Theorems in number theory
In mathematics, a Thue equation is a Diophantine equation of the form ƒ(x,y) = r, where ƒ is an irreducible bivariate form of degree at least 3 over the rational numbers, and r is a nonzero rational number. It is named after Axel Thue who in 1909 proved a theorem, now called Thue's theorem, that a Thue equation has finitely many solutions in integers x and y. The Thue equation is solvable effectively: there is an explicit bound on the solutions x, y of the form where constants C1 and C2 depend only on the form ƒ. A stronger result holds, that if K is the field generated by the roots of ƒ then the equation has only finitely many solutions with x and y integers of K and again these may be effectively determined. (Wikipedia).
Summary for graph an equation in Standard form
👉 Learn about graphing linear equations. A linear equation is an equation whose highest exponent on its variable(s) is 1. i.e. linear equations has no exponents on their variables. The graph of a linear equation is a straight line. To graph a linear equation, we identify two values (x-valu
From playlist ⚡️Graph Linear Equations | Learn About
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
The Infinite Game of Chess (with Outray Chess)
An infinite game of chess with the Thue-Morse sequence. To avoid an infinite game of chess there was a rule that declared that a game would end if any sequence of moves were repeated three times in a row. However Dutch mathematician Max Euwe showed that the Thue-Morse sequence can define
From playlist My Maths Videos
Arne Martin Aurlien: Implement an Esoteric Programming Language for Fun | JSConf EU 2014
Inside most of us there’s a befunge programmer who wants to come out. When doing day-to-day “serious” programming it is usually a good idea to keep them as firmly locked up as possible. Let’s ignore that instinct for a little while. In this talk I’ll try to convince you why you should try
From playlist JSConf EU 2014
Koch Curve from Thue-Morse Turtle Graphics
This video shows the first 65536 steps of the turtle graphics construction of the Koch curve using the Thue-Morse sequence. To learn more about some of the amazing properties of Thue-Morse sequence, see this longer video: https://youtu.be/yqEIhdnfJxE.. #numbertheory #turtlegraphics ______
From playlist Fractals
The Thue-Morse Sequence (with visualizations)
In this video, we introduce the Prouhet-Thue-Morse sequence, which is a binary sequence. We discuss three methods to construct the sequence and then investigate some of the sequence's properties (including why it is the "fair sharing" sequence, the overlap-free property, its connection to
From playlist Fractals
Hugh Montgomery: Moments of a Thue-Morse generating function
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 Number Theory
👉 Learn about graphing linear equations. A linear equation is an equation whose highest exponent on its variable(s) is 1. i.e. linear equations has no exponents on their variables. The graph of a linear equation is a straight line. To graph a linear equation, we identify two values (x-valu
From playlist ⚡️Graph Linear Equations | Learn About
#MegaFavNumbers: 258,474,216. See https://www.youtube.com/watch?v=R2eQVqdUQLI&list=PLar4u0v66vIodqt3KSZPsYyuULD5meoAo. Further reading: The OEIS for the sequence: https://oeis.org/A001219 Another relevant sequence: https://oeis.org/A097571 S. P. Mohanty, Which triangular numbers are prod
From playlist MegaFavNumbers
What do I need to know to graph an equation in standard form
👉 Learn about graphing linear equations. A linear equation is an equation whose highest exponent on its variable(s) is 1. i.e. linear equations has no exponents on their variables. The graph of a linear equation is a straight line. To graph a linear equation, we identify two values (x-valu
From playlist ⚡️Graph Linear Equations | Learn About
Learn how to graph a quadratic equation
👉 Learn how to graph quadratics in standard form. A quadratic equation is an equation whose highest exponent in the variable(s) is 2. To graph a quadratic equation, we make use of a table of values and the fact that the graph of a quadratic is a parabola which has an axis of symmetry, to p
From playlist Graph a Quadratic in Standard Form | ax^2
Writing the equation of a line parallel to another given and equation and a point
👉 Learn how to write the equation of a line that is parallel to a given line. The equation of a line is such that its highest exponent on its variable(s) is 1. (i.e. there are no exponents in its variable(s)). There are various forms which we can write the equation of a line: the point-slo
From playlist Write Linear Equations
Michael Drmota: Automatic sequences along squares and primes
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 Number Theory
Walking the Dragon and Koch Curves with a Turtle (131072 steps each!)
In this video, we describe two how to draw two amazing curves - the Dragon curve and the Koch curve - using the simple process of Turtle graphics. For both curves, we draw 131072 line segments (this is 2 to the 17th power). It is amazing that such a simple process can draw these complex cu
From playlist Fractals
What do I need to know to graph an equation in slope intercept form
👉 Learn about graphing linear equations. A linear equation is an equation whose highest exponent on its variable(s) is 1. i.e. linear equations has no exponents on their variables. The graph of a linear equation is a straight line. To graph a linear equation, we identify two values (x-valu
From playlist ⚡️Graph Linear Equations | Learn About
Graphing a quadratic using a table
👉 Learn how to graph quadratics in standard form. A quadratic equation is an equation whose highest exponent in the variable(s) is 2. To graph a quadratic equation, we make use of a table of values and the fact that the graph of a quadratic is a parabola which has an axis of symmetry, to p
From playlist Graph a Quadratic in Standard Form | ax^2
Graphing a quadratic using a table
👉 Learn how to graph quadratics in standard form. A quadratic equation is an equation whose highest exponent in the variable(s) is 2. To graph a quadratic equation, we make use of a table of values and the fact that the graph of a quadratic is a parabola which has an axis of symmetry, to p
From playlist Graph a Quadratic in Standard Form | ax^2
What is everything you need to know to graph an equation in slope intercept form
👉 Learn about graphing linear equations. A linear equation is an equation whose highest exponent on its variable(s) is 1. i.e. linear equations has no exponents on their variables. The graph of a linear equation is a straight line. To graph a linear equation, we identify two values (x-valu
From playlist ⚡️Graph Linear Equations | Learn About
Gary Walsh: On binary quartic Thue equations and related topics
CIRM VIRTUAL CONFERENCE Recorded during the meeting " Diophantine Problems, Determinism and Randomness" the November 25, 2020 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide
From playlist Virtual Conference
Find a line parallel to another line through a point
👉 Learn how to write the equation of a line that is parallel to a given line. The equation of a line is such that its highest exponent on its variable(s) is 1. (i.e. there are no exponents in its variable(s)). There are various forms which we can write the equation of a line: the point-slo
From playlist Write Linear Equations