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Questions tagged [transformational-geometry]

In mathematics, transformation geometry (or transformational geometry) is the name of a mathematical and pedagogic approach to the study of geometry by focusing on groups of geometric transformations, and the properties of figures that are invariant under them.

In mathematics, transformation geometry (or transformational geometry) is the name of a mathematical and pedagogic approach to the study of geometry by focusing on groups of geometric transformations, and the properties of figures that are invariant under them. Reference: Wikipedia.

It is opposed to the classical synthetic geometry approach of Euclidean geometry, that focuses on geometric constructions.

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Understanding a Lemma from J. Aarts Plane and Solid Geometry

I read this recent question on proving that the identity is never the product of an odd number of reflections. After googling a bit, I found a Lemma in J. Aarts Plane and Solid Geometry, but I didn't fully understand the proof. I'll post the…
yunone
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Definition of collineation

In a book I am reading on transformational Euclidean geometry, the author defines a collineation as a bijection of the plane which takes lines to lines -- that is, for a collineation $F$, if $L$ is a line, then $F[L]$ is a line. A line is understood…
blargoner
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Calculate the slope of a line on an auto-scaled chart?

Let say, I have a line with two points A=(1, 10.09) and B=(3, 10.42) on an auto-scaled chart like this. I would like to calculate the slope of this line. Can I transform the y-coordinates (or the real slope) into a new system, provided that the…
alex555
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Is there any ongoing research in transformation geometry?

I'm a 3rd year undergrad Math student and totally confused right now on what field I'm gonna choose in my thesis next semester. We we're introduced in Transformation Geometry (Introduction to Symmetries by George Martin, used by our professor as a…
Crunchy
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vector analysis and co-ordinate transformation

Suppose one try to introduce a new product of two vectors as $C = A\operatorname{XX}B$, where $A,B,C$ are all vectors. Now it is defined as \begin{align} C_x &=A_y B_z + A_z B_y\\ C_y &= A_z B_x+A_x B_z\\ C_z &=A_x B_y+A_y…
rickriordan
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