Mapping wave forms to sphere, does wave form y=0 have a reflection?

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Discussion Overview

The discussion revolves around the concept of whether the wave form represented by y=0 has a reflection, particularly in the context of mapping wave forms to a sphere. Participants explore the conditions for inverses and reflections of wave forms, as well as the implications of these concepts in relation to antipodean pairs on a sphere.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant asserts that y=0 does not have an inverse, questioning if the wave form y=0 for all x can have an inverse.
  • Another participant asks about the conditions that an inverse of a wave form should fulfill.
  • A participant suggests that inverse polarity might be a consideration, but notes that if the inverse wave form consists of -y values, then y=0 would not have a corresponding -y, leading to potential issues with continuity.
  • This same participant clarifies that they are actually referring to reflection about the x-axis (y -> -y) rather than inversion, and connects this to the concept of antipodean pairs on the sphere.
  • A later reply indicates that further investigation suggests that zero may indeed have a reflection.

Areas of Agreement / Disagreement

Participants express differing views on the nature of inverses and reflections, with some uncertainty about the implications of y=0 in this context. The discussion remains unresolved regarding the specific conditions and characteristics of reflections for wave forms.

Contextual Notes

There are limitations in the discussion regarding the definitions of terms like "inverse" and "reflection," as well as the continuity of wave forms. The relationship between these concepts and their application to the sphere is not fully explored.

bahamagreen
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TL;DR
Continuous mapping of all continuous wave forms to the surface of a sphere
Zero does not have an inverse.
And y=0 does not have an inverse.
Does the wave form y=0 for all x have an inverse?
 
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What conditions should an inverse of a 'wave form' fulfil ?
:wideeyed:

##\ ##
 
BvU said:
What conditions should an inverse of a 'wave form' fulfil ?
:wideeyed:

##\ ##
My first thought is inverse polarity, but if the inverse wave form comprises -y values, any y=0 wouldn't have an inverse -y, so maybe the inverse wave form would not be strictly continuous? That seems asymmetric with respect to inversion...

edit-- I'm using the wrong term, inversion swaps the range and domain, what I am asking about is reflection about the x axis... y -> -y
This is in the context of antipodean pairs on the sphere
 
Last edited:
More checking, but it looks like zero does have reflection...
 

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