In mathematical logic, Craig's interpolation theorem is a result about the relationship between different logical theories. Roughly stated, the theorem says that if a formula φ implies a formula ψ, and the two have at least one atomic variable symbol in common, then there is a formula ρ, called an interpolant, such that every non-logical symbol in ρ occurs both in φ and ψ, φ implies ρ, and ρ implies ψ. The theorem was first proved for first-order logic by William Craig in 1957. Variants of the theorem hold for other logics, such as propositional logic. A stronger form of Craig's interpolation theorem for first-order logic was proved by Roger Lyndon in 1959; the overall result is sometimes called the Craig–Lyndon theorem. (Wikipedia).
Geometric Algebra - Linear and Spherical Interpolation (LERP, SLERP, NLERP)
In this video, I'll derive the formulas for doing linear and spherical interpolations between two vectors. In deriving the latter formula, we will use rotors, an object used in geometric algebra. We will also discuss normalized linear interpolation and contrast it with spherical interpolat
From playlist Geometric Algebra
Programming Terms: String Interpolation
In this programming terms video, we will be going over string interpolation. String interpolation is the process of evaluating a string containing one or more placeholders and yielding a result in which the placeholders are replaced with their corresponding values. Let's take a look at thi
From playlist Programming Terms
Solving a trigonometric equation with applying pythagorean identity
👉 Learn how to solve trigonometric equations. There are various methods that can be used to evaluate trigonometric equations, they include factoring out the GCF and simplifying the factored equation. Another method is to use a trigonometric identity to reduce and then simplify the given eq
From playlist Solve Trigonometric Equations by Factoring
Interpolation | Lecture 43 | Numerical Methods for Engineers
An explanation of interpolation and how to perform piecewise linear interpolation. Join me on Coursera: https://www.coursera.org/learn/numerical-methods-engineers Lecture notes at http://www.math.ust.hk/~machas/numerical-methods-for-engineers.pdf Subscribe to my channel: http://www.yout
From playlist Numerical Methods for Engineers
Craig Kaplan - Parquet Deformations: the tiles, they are a-changin - CoM Apr 2021
A Parquet Deformation is a tessellation that evolves gradually in space, a kind of animation expressed in a single drawing. William Huff developed Parquet Deformations and used them as an exercise for architecture and design students for decades. For a computer scientist, they also represe
From playlist Celebration of Mind 2021
Solve for all of the solutions of an equation when you have to factor
👉 Learn how to solve trigonometric equations. There are various methods that can be used to evaluate trigonometric equations, they include factoring out the GCF and simplifying the factored equation. Another method is to use a trigonometric identity to reduce and then simplify the given eq
From playlist Solve Trigonometric Equations by Factoring
How to use factoring to solve a trigonometric equation
👉 Learn how to solve trigonometric equations. There are various methods that can be used to evaluate trigonometric equations, they include factoring out the GCF and simplifying the factored equation. Another method is to use a trigonometric identity to reduce and then simplify the given eq
From playlist Solve Trigonometric Equations by Factoring
Live CEOing Ep 494: Design Review of Spatial Statistics
In this episode of Live CEOing, Stephen Wolfram discusses upcoming improvements and features to the Wolfram Language. If you'd like to contribute to the discussion in future episodes, you can participate through this YouTube channel or through the official Twitch channel of Stephen Wolfram
From playlist Behind the Scenes in Real-Life Software Design
Felix Otto - 23 September 2016
Otto, Felix "The thresholding scheme for mean curvature flow"
From playlist A Mathematical Tribute to Ennio De Giorgi
6.6: Steering Behaviors: Path Following - The Nature of Code
This video covers Craig Reynolds' steering behavior: path following. Read along: http://natureofcode.com/book/chapter-6-autonomous-agents/#chapter06_section8 http://www.red3d.com/cwr/steer/PathFollow.html Code: https://github.com/shiffman/The-Nature-of-Code-Examples/tree/master/chp06_ag
From playlist 6: Autonomous Agents - The Nature of Code
The Vandermonde Matrix and Polynomial Interpolation
The Vandermonde matrix is a used in the calculation of interpolating polynomials but is more often encountered in the proof that such polynomial interpolates exist. It is also often encountered in the study of determinants since it has a really nice determinant formula. Chapters 0:00 - In
From playlist Interpolation
Guido Kings: Motivic Eisenstein cohomology, p-adic interpolation and applications
The lecture was held within the framework of the Hausdorff Trimester Program: K-Theory and Related Fields. Guido Kings: Motivic Eisenstein cohomology, p-adic interpolation and applications Abstract: Motivic Eisenstein classes have been defined in various situations, for example for G =
From playlist HIM Lectures: Trimester Program "K-Theory and Related Fields"
Solve a trig equation by factoring a perfect square trinomial
👉 Learn how to solve trigonometric equations. There are various methods that can be used to evaluate trigonometric equations, they include factoring out the GCF and simplifying the factored equation. Another method is to use a trigonometric identity to reduce and then simplify the given eq
From playlist Solve Trigonometric Equations by Factoring
RubyConf 2016 - A Look at Hooks by Craig Buchek
RubyConf 2016 - A Look at Hooks by Craig Buchek Ruby has several methods that are invoked implicitly under certain circumstances. These methods are called "hooks", and they provide points to extend behavior. While hooks might seem like "spooky action at a distance", they can be really pow
From playlist RubyConf 2016
The thresholding scheme for mean curvature flow as minimizing movement scheme - 1
Speaker: Felix Otto (Max Planck Institute for Mathematics in the Sciences in Leipzig) International School on Extrinsic Curvature Flows | (smr 3209) 2018_06_12-15_45-smr3209
From playlist Felix Otto: "The thresholding scheme for mean curvature flow as minimizing movement scheme", ICTP, 2018
Least Squares Regression Lines on a Casio Graphical Calculator (AS / A Level / IB)
Find Least Squares or Linear Regression Lines using a Casio graphical calculator, Revise AS level (7356) and A level (7357) Maths L: Data Presentation and Interpretation, Statistics and Probability S1 and IB Mathematics SL Statistics and Biology. Choose between y-on-x or x-on-y regression
From playlist 2017 AS Level Further Mathematics Statistics 2 New Specification Revision (AQA Edexcel OCR MEI)
How to solve a trigonometric equation
👉 Learn how to solve trigonometric equations. There are various methods that can be used to evaluate trigonometric equations, they include factoring out the GCF and simplifying the factored equation. Another method is to use a trigonometric identity to reduce and then simplify the given eq
From playlist Solve Trigonometric Equations by Factoring
Solid mechanics deals with the deformation of objects under applied forces. This talk will describe how to create solid mechanics models in the Wolfram Language. The resulting partial differential equations (PDEs) can be solved numerically using NDSolve and NDEigensystem. Techniques will b
From playlist Wolfram Technology Conference 2021
A Converse to a Theorem of Gross-Zaqier-Kolyvagin - Christopher Skinner
Christopher Skinner Princeton University; Member, School of Mathematics April 4, 2013 The theorem of the title is that if the L-function L(E,s) of an elliptic curve E over the rationals vanishes to order r=0 or 1 at s=1 then the rank of the group of rational rational points of E equals r a
From playlist Mathematics
Learn how to write all of the solutions to a trigonometric equation
👉 Learn how to solve trigonometric equations. There are various methods that can be used to evaluate trigonometric equations, they include factoring out the GCF and simplifying the factored equation. Another method is to use a trigonometric identity to reduce and then simplify the given eq
From playlist Solve Trigonometric Equations by Factoring