Fields of geometry | Symmetry | Geometry education
In mathematics, transformation geometry (or transformational geometry) is the name of a mathematical and pedagogic take on the study of geometry by focusing on groups of geometric transformations, and properties that are invariant under them. It is opposed to the classical synthetic geometry approach of Euclidean geometry, that focuses on proving theorems. For example, within transformation geometry, the properties of an isosceles triangle are deduced from the fact that it is mapped to itself by a reflection about a certain line. This contrasts with the classical proofs by the criteria for congruence of triangles. The first systematic effort to use transformations as the foundation of geometry was made by Felix Klein in the 19th century, under the name Erlangen programme. For nearly a century this approach remained confined to mathematics research circles. In the 20th century efforts were made to exploit it for mathematical education. Andrei Kolmogorov included this approach (together with set theory) as part of a proposal for geometry teaching reform in Russia. These efforts culminated in the 1960s with the general reform of mathematics teaching known as the New Math movement. (Wikipedia).
What is a transformation vector
👉 Learn how to apply transformations of a figure and on a plane. We will do this by sliding the figure based on the transformation vector or directions of translations. When performing a translation we are sliding a given figure up, down, left or right. The orientation and size of the fi
From playlist Transformations
Geometry - Determine the transformation vector for two triangles
👉 Learn how to apply transformations of a figure and on a plane. We will do this by sliding the figure based on the transformation vector or directions of translations. When performing a translation we are sliding a given figure up, down, left or right. The orientation and size of the fi
From playlist Transformations
From playlist Transformations of the Number Line
From playlist Transformations of the Number Line
Sketch a Linear Transformation of a Unit Square Given the Transformation Matrix (Shear)
This video explains 2 ways to graph a linear transformation of a unit square on the coordinate plane.
From playlist Matrix (Linear) Transformations
Shifting a triangle using a transformation vector
👉 Learn how to apply transformations of a figure and on a plane. We will do this by sliding the figure based on the transformation vector or directions of translations. When performing a translation we are sliding a given figure up, down, left or right. The orientation and size of the fi
From playlist Transformations
How to apply a transformation vector to translate a figure
👉 Learn how to apply transformations of a figure and on a plane. We will do this by sliding the figure based on the transformation vector or directions of translations. When performing a translation we are sliding a given figure up, down, left or right. The orientation and size of the fi
From playlist Transformations
Introduction to transformations | Transformations | Geometry | Khan Academy
Introduction to transformations Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/geometry/transformations/rigid-transformations-intro/e/performing-translations-on-the-coordinate-plane?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry Watch t
From playlist High School Geometry | High School Math | Khan Academy
Generalized Geometry for String Theory - B. Zwiebach - 12/10/2013
A conference celebrating the 50th anniversary of quarks honoring Murray Gell-Mann was held at Caltech on December 9-10, 2013. For more information, visit: http://hep.caltech.edu/gm/
From playlist String Theory - Prof. Zwiebach & Susskind
Linear Algebra Vignette 1a: Matrix Representation of a Linear Transformation
This course is on Lemma: http://lem.ma Lemma looking for developers: http://lem.ma/jobs Other than http://lem.ma, I recommend Strang http://bit.ly/StrangYT, Gelfand http://bit.ly/GelfandYT, and my short book of essays http://bit.ly/HALAYT Questions and comments below will be prompt
From playlist Linear Algebra Vignettes
Possible transformations example | Transformations | Geometry | Khan Academy
Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/geometry/transformations/properties-definitions-of-translations/e/qualitatively-defining-rigid-transformations?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry Watch the next lesson: https://w
From playlist High School Geometry | High School Math | Khan Academy
Translation example | Transformations | Geometry | Khan Academy
Translation example Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/geometry/transformations/rigid-transformations-intro/e/performing-translations-on-the-coordinate-plane?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry Watch the next less
From playlist High School Geometry | High School Math | Khan Academy
From playlist Wolfram Technology Conference 2021
Reflecting line across another line example | Transformations | Geometry | Khan Academy
Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/geometry-home/transformations/old-transformations-videos/v/reflecting-line-across-another-line-example Watch the next lesson: https://www.khanacademy.org/math/geo
From playlist Transformations | Geometry | Khan Academy
Using rotation widget | Transformations | Geometry | Khan Academy
Using rotation widget Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/geometry/transformations/rigid-transformations-intro/e/performing-rotations-on-the-coordinate-plane?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry Watch the next lesso
From playlist High School Geometry | High School Math | Khan Academy
Another congruence by transformation example | Congruence | Geometry | Khan Academy
Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/geometry/congruent-triangles/transformations-congruence/e/exploring-rigid-transformations-and-congruence?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry Watch the next lesson: https://www.kha
From playlist Mathematics I | 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