Ratios | Mathematical terminology
In mathematics, two sequences of numbers, often experimental data, are proportional or directly proportional if their corresponding elements have a constant ratio, which is called the coefficient of proportionality or proportionality constant. Two sequences are inversely proportional if corresponding elements have a constant product, also called the coefficient of proportionality. This definition is commonly extended to related varying quantities, which are often called variables. This meaning of variable is not the common meaning of the term in mathematics (see variable (mathematics)); these two different concepts share the same name for historical reasons. Two functions and are proportional if their ratio is a constant function. If several pairs of variables share the same direct proportionality constant, the equation expressing the equality of these ratios is called a proportion, e.g., a/b = x/y = ⋯ = k (for details see Ratio).Proportionality is closely related to linearity. (Wikipedia).
Any function proportional to a PMF or PDF uniquely determines it. Using proportionality is a extremely useful trick when doing Bayesian inference.
From playlist Machine Learning
How to use the LCD to help us solve a rational equation
👉 Learn how to solve proportions. Two ratios are said to be proportional when the two ratios are equal. Thus, proportion problems are problems involving the equality of two ratios. When given a proportion problem with an unknown, we usually cross-multiply the two ratios and then solve for
From playlist How to Solve Rational Equations
How to use proportionality of a triangle to determine if two lines are parallel
👉 Learn how to solve for the unknown in a triangle divided internally such that the division is parallel to one of the sides of the triangle. The triangle proportionality theorem states that if a line is parallel to one side of a triangle and it intersects the other two sides, then it divi
From playlist Similar Triangles within Triangles Solve for x
What is the triangle proportionality theorem
👉 Learn how to solve for the unknown in a triangle divided internally such that the division is parallel to one of the sides of the triangle. The triangle proportionality theorem states that if a line is parallel to one side of a triangle and it intersects the other two sides, then it divi
From playlist Similar Triangles within Triangles Solve for x
Tutorial lesson for solving a rational expression by multiplying by the LCD
👉 Learn how to solve proportions. Two ratios are said to be proportional when the two ratios are equal. Thus, proportion problems are problems involving the equality of two ratios. When given a proportion problem with an unknown, we usually cross-multiply the two ratios and then solve for
From playlist How to Solve Rational Equations
Unfolding Method and Homogenization (Lecture 4) by Daniel Onofrei
PROGRAM: MULTI-SCALE ANALYSIS AND THEORY OF HOMOGENIZATION ORGANIZERS: Patrizia Donato, Editha Jose, Akambadath Nandakumaran and Daniel Onofrei DATE: 26 August 2019 to 06 September 2019 VENUE: Madhava Lecture Hall, ICTS, Bangalore Homogenization is a mathematical procedure to understa
From playlist Multi-scale Analysis And Theory Of Homogenization 2019
Moon Duchin - Graphs, Geometry and Gerrymandering - CoM Oct 2021
Graphs, Geometry and Gerrymandering Co-sponsored by Georgia Tech's School of Mathematics What are all the ways to draw the lines, when you’re dividing up a state to get representation? If you can’t find them all, can you choose a good sample? I’ll discuss some surprisingly simple question
From playlist Celebration of Mind 2021
Mathematics Public Lecture Moon Duchin
Political Thicket, Mathematical Quagmire: How voting is and is not a math problem
From playlist Mathematics Research Center
Lecture 23 | The Fourier Transforms and its Applications
Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood lectures on linear systems, focusing on linear time and variance systems. The Fourier transform is a tool for solving physical problems. In thi
From playlist Lecture Collection | The Fourier Transforms and Its Applications
Algebra - Direct and Inverse Variation [i.e. y is proportional to -something-] (2 of 5)
Visit http://ilectureonline.com for more math and science lectures! One common way to describe a function is through proportionality, that is y is proportional to some algebraic statement. This five part lecture series covers methods of determining what that relationship describing y is.
From playlist ALGEBRA 19 - DIRECT AND INVERSE VARIATION
2021 I. E. Block Community Lecture: Jonathan Christopher Mattingly
Dr. Jonathan Christopher Mattingly of Duke University presented a talk titled 'Can You Hear the Will of the People in the Vote? Assessing Fairness in Redistricting via Monte Carlo Sampling' during the 2021 SIAM Annual Meeting on July 20, 2021. The U.S. political system chooses representa
From playlist Math 498 - Districting Playlist
Algebra - Direct and Inverse Variation [i.e. y is proportional to -something-] (1 of 5)
Visit http://ilectureonline.com for more math and science lectures! One common way to describe a function is through proportionality, that is y is proportional to some algebraic statement. This five part lecture series covers methods of determining what that relationship describing y is.
From playlist ALGEBRA 19 - DIRECT AND INVERSE VARIATION
Study and research paths: A model for inquiry – Marianna Bosch Casabò – ICM2018
Mathematics Education and Popularization of Mathematics Invited Lecture 18.2 Study and research paths: A model for inquiry Marianna Bosch Casabò Abstract: This paper presents a line of research in didactics of mathematics developed during the past decade within the Anthropological Theory
From playlist Mathematics Education and Popularization of Mathematics
Using triangle proportionality theorem to prove parallel lines
👉 Learn how to solve for the unknown in a triangle divided internally such that the division is parallel to one of the sides of the triangle. The triangle proportionality theorem states that if a line is parallel to one side of a triangle and it intersects the other two sides, then it divi
From playlist Similar Triangles within Triangles Solve for x
Understanding Wavelets, Part 1: What Are Wavelets
This introductory video covers what wavelets are and how you can use them to explore your data in MATLAB®. •Try Wavelet Toolbox: https://goo.gl/m0ms9d •Ready to Buy: https://goo.gl/sMfoDr The video focuses on two important wavelet transform concepts: scaling and shifting. The concepts ca
From playlist Understanding Wavelets
23.1 Capacitors and Capacitive Reactance
This video covers Section 23.1 of Cutnell & Johnson Physics 10e, by David Young and Shane Stadler, published by John Wiley and Sons. The lecture is part of the course General Physics - Life Sciences I and II, taught by Dr. Boyd F. Edwards at Utah State University. This video was produced
From playlist Lecture 23A. Alternating Current Circuits
PHYS 102 | The Inductor 2 - Defining the Inductance
Here are some mathematical thoughts about what an inductor will do to the potentials and EMF's in a circuit. It leads to a definition of L, the inductance, and its unit the "Henry". -----Inductors playlist - https://www.youtube.com/playlist?list=PL9_sR6Qqqcyn51rN4BaPhjckWWoMPvHJg -----Use
From playlist PHYS 102 | Inductors
Areas and volumes for a sphere | Universal Hyperbolic Geometry 35 | NJ Wildberger
The beautiful formulas for the surface area and volume of a sphere go back to Archimedes, who also discovered some other remarkable facts relating spheres to circumscribing cylinders. We describe these results. Then we introduce rational turn angles---a renormalization of the notion of an
From playlist Universal Hyperbolic Geometry
How to apply the triangle proportionality theorem to determine the missing side
👉 Learn how to solve for the unknown in a triangle divided internally such that the division is parallel to one of the sides of the triangle. The triangle proportionality theorem states that if a line is parallel to one side of a triangle and it intersects the other two sides, then it divi
From playlist Similar Triangles within Triangles Solve for x