Triangle inequality, parallelogram equality

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Homework Help Overview

The discussion revolves around the concepts of triangle inequality and parallelogram equality, exploring their definitions and implications in geometry and vector spaces.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants express confusion regarding the relationship between the triangle inequality and the properties of triangles, as well as the connection to parallelogram equality. There are inquiries about the implications of the inequalities when applied to vectors.

Discussion Status

Some participants are seeking clarification on the definitions and applications of the inequalities, while others are attempting to relate these concepts to vector addition and geometric interpretations. There is an ongoing exploration of the assumptions underlying these inequalities.

Contextual Notes

One participant references the triangle inequality in the context of vectors, suggesting a geometric interpretation that may not be universally accepted. The discussion reflects a need for deeper understanding of the foundational principles involved.

asdf1
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what does a triangle have to do with triangle inequality, and what does a paralllelogram have to do with parallelogram equality?
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i'm still confused:
"triangle inequality is the theorem stating that for any triangle, the measure of a given side must be less than the sum of the other two sides but greater than the difference between the two sides."
yet "|x+y| ≤ |x|+|y| " shouldn't mean "|z|≤ |x|+|y| "?
 
asdf1 said:
i'm still confused:
"triangle inequality is the theorem stating that for any triangle, the measure of a given side must be less than the sum of the other two sides but greater than the difference between the two sides."
yet "|x+y| ≤ |x|+|y| " shouldn't mean "|z|≤ |x|+|y| "?

If you think of x and y as vectors in space they will form a triangle with a third vector that is the vector sum x+y so the inequality makes sense.
 
thank you very much!
 

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