In affine geometry, uniform scaling (or isotropic scaling) is a linear transformation that enlarges (increases) or shrinks (diminishes) objects by a scale factor that is the same in all directions. The result of uniform scaling is similar (in the geometric sense) to the original. A scale factor of 1 is normally allowed, so that congruent shapes are also classed as similar. Uniform scaling happens, for example, when enlarging or reducing a photograph, or when creating a scale model of a building, car, airplane, etc. More general is scaling with a separate scale factor for each axis direction. Non-uniform scaling (anisotropic scaling) is obtained when at least one of the scaling factors is different from the others; a special case is directional scaling or stretching (in one direction). Non-uniform scaling changes the shape of the object; e.g. a square may change into a rectangle, or into a parallelogram if the sides of the square are not parallel to the scaling axes (the angles between lines parallel to the axes are preserved, but not all angles). It occurs, for example, when a faraway billboard is viewed from an oblique angle, or when the shadow of a flat object falls on a surface that is not parallel to it. When the scale factor is larger than 1, (uniform or non-uniform) scaling is sometimes also called dilation or enlargement. When the scale factor is a positive number smaller than 1, scaling is sometimes also called contraction or reduction. In the most general sense, a scaling includes the case in which the directions of scaling are not perpendicular. It also includes the case in which one or more scale factors are equal to zero (projection), and the case of one or more negative scale factors (a directional scaling by -1 is equivalent to a reflection). Scaling is a linear transformation, and a special case of homothetic transformation (scaling about a point). In most cases, the homothetic transformations are non-linear transformations. (Wikipedia).
Dimensions (1 of 3: The Traditional Definition - Directions)
More resources available at www.misterwootube.com
From playlist Exploring Mathematics: Fractals
Chapter 1 of the Dimensions series. See http://www.dimensions-math.org for more information. Press the 'CC' button for subtitles.
From playlist Dimensions
This video shows how to use scale to determine the dimensions of a proportional model. http://mathispower4u.yolasite.com/
From playlist Unit Scale and Scale Factor
Proportions and Similar Polygons / Similar Figures
I work through 5 examples of solving for missing sides of similar polygons. Similar polygons have linear sides, the corresponding angles are congruent, and the corresponding sides are proportional. The equal proportions, or constant ratios of the side lengths, are called the Scale Factor
From playlist Geometry
Chapter 5 of the Dimensions series. See http://www.dimensions-math.org for more information. Press the 'CC' button for subtitles.
From playlist Dimensions
Chapter 2 of the Dimensions series. See http://www.dimensions-math.org for more information. Press the 'CC' button for subtitles.
From playlist Dimensions
Physical Science 1.4e - The Slope of a Line
The slope of a line. The concept if explained: slope is rise over run, and is a number that represents the steepness of a line. A simple example is worked and explained.
From playlist Physical Science Chapter 1 (Complete chapter)
3D Trigonometry Example (1 of 2: Setting up the triangles)
More resources available at www.misterwootube.com
From playlist Trigonometry and Measure of Angles
Chapter 6 of the Dimensions series. See http://www.dimensions-math.org for more information. Press the 'CC' button for subtitles.
From playlist Dimensions
Similar triangle basics | Similarity | Geometry | Khan Academy
Introduction to what it means for triangles to be similar Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/geometry/similarity/triangle_similarlity/e/similar_triangles_1?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry Watch the next lesson
From playlist High School Geometry | High School Math | Khan Academy
Symposium on Geometry Processing 2017 Graduate School Lecture by Keenan Crane https://www.cs.cmu.edu/~kmcrane/ http://geometry.cs.ucl.ac.uk/SGP2017/?p=gradschool#abs_conformal_geometry Digital geometry processing is the natural extension of traditional signal processing to three-dimensi
From playlist Tutorials and Lectures
Dilating one line onto another | Transformations | Geometry | Khan Academy
Watch the next lesson: https://www.khanacademy.org/math/geometry/transformations/dilations-scaling/v/comparing-side-lengths-after-dilation?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry Missed the previous lesson? https://www.khanacademy.org/math/geometry/transformations/dilations-s
From playlist High School Geometry | High School Math | Khan Academy
Mod-01 Lec-06 Introduction to Nanomaterials
Nanostructures and Nanomaterials: Characterization and Properties by Characterization and Properties by Dr. Kantesh Balani & Dr. Anandh Subramaniam,Department of Nanotechnology,IIT Kanpur.For more details on NPTEL visit http://nptel.ac.in.
From playlist IIT Kanpur: Nanostructures and Nanomaterials | CosmoLearning.org
Ginestra Bianconi: Emergent Network Geometry
The lecture was held within the framework of the Hausdorff Trimester Program : Applied and Computational Algebraic Topology
From playlist HIM Lectures: Special Program "Applied and Computational Algebraic Topology"
Scaling down a triangle by half | Transformations | Geometry | Khan Academy
Watch the next lesson: https://www.khanacademy.org/math/geometry/transformations/dilations-scaling/v/dilating-one-line-onto-another?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry Missed the previous lesson? https://www.khanacademy.org/math/geometry/transformations/transformations-sy
From playlist High School Geometry | High School Math | Khan Academy
Another example of rigid transformations for congruence | Congruence | Geometry | Khan Academy
Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/geometry/congruent-triangles/transformations-congruence/e/defining-congruence-through-rigid-transformations?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry Watch the next lesson: https://www.
From playlist High School Geometry | High School Math | Khan Academy
Rod Gover - An introduction to conformal geometry and tractor calculus (Part 3)
After recalling some features (and the value of) the invariant « Ricci calculus » of pseudo‐Riemannian geometry, we look at conformal rescaling from an elementary perspective. The idea of conformal covariance is visited and some covariant/invariant equations from physics are recovered in
From playlist Ecole d'été 2014 - Analyse asymptotique en relativité générale
Lecture 1 of Leonard Susskind's Modern Physics concentrating on Cosmology. Recorded January 13, 2009 at Stanford University. This Stanford Continuing Studies course is the fifth of a six-quarter sequence of classes exploring the essential theoretical foundations of modern physics. The t
From playlist Lecture Collection | Modern Physics: Cosmology
Geometry: Ch 5 - Proofs in Geometry (2 of 58) Definitions
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain and give examples of definitions. Next video in this series can be seen at: https://youtu.be/-Pmkhgec704
From playlist GEOMETRY 5 - PROOFS IN GEOMETRY
Livine Etera : The Geometry of Loop Quantum Gravity
Recording during the thematic meeting : "Geometrical and Topological Structures of Information" the August 31, 2017 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent
From playlist Geometry