Is the Transformation f Orientation Preserving or Reversing?

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Homework Help Overview

The discussion revolves around the transformation defined by reflections across three great circles on a sphere, specifically whether this transformation is orientation preserving or reversing. The subject area includes concepts from geometry and linear algebra related to transformations and their properties.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster considers using a matrix derived from the normals of the great circles to determine the orientation of the transformation by calculating the determinant. There is uncertainty about whether this approach is valid without a given matrix. Participants also question the notation used, particularly the meaning of "Rc3Rc2Rc1" and the implications of reflections in this context.

Discussion Status

Some participants have provided clarifications regarding the notation and the nature of reflections. There is an exploration of how the number of reflections affects orientation, with a suggestion that three reflections may lead to orientation reversing. However, there is no explicit consensus on the method or final determination of the transformation's orientation.

Contextual Notes

Participants are navigating the definitions and implications of reflections in relation to the great circles, and there is a noted confusion regarding the notation and its application in the context of the problem.

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consider the 3 great circles C1,C2,C3 with respective normals
(0,-1,1) (1,0,1) (1,1,0), and let f = Rc3Rc2Rc1

is f orientation preserving or orientation reversing.

can i make a matrix using the normals... then calculate the determinate of A. and if its negative then its reversing and if its positive then its preserving... or can i only calculate the matrix when its givin to me...
 
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Pearce_09 said:
consider the 3 great circles C1,C2,C3 with respective normals
(0,-1,1) (1,0,1) (1,1,0), and let f = Rc3Rc2Rc1
is f orientation preserving or orientation reversing.
can i make a matrix using the normals... then calculate the determinate of A. and if its negative then its reversing and if its positive then its preserving... or can i only calculate the matrix when its givin to me...

I don't understand your notation. What does "Rc3Rc2Rc1" mean? I assume that the c3, c2, c1 should really be C3, C2, C1, but what is R?
 
R means reflection, sorry i should have stated that
so reflection in C3 Reflection in C2 and Reflection in C1
 
"Reflection in C3"? C1, C2, C3 are great circles on a sphere? And reflection is to the other hemisphere?
Reflection, generally, is orientation reversing. Two reflections would be orientation preserving and 3, as you have here, orientation reversing.
 

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