Find Area of Triangle (-1 2 -1 2), (-1 2 -1 1) & (2 -1 2 2)

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Discussion Overview

The discussion revolves around finding the area of a triangle defined by three points in a four-dimensional space. Participants explore the implications of the fourth coordinate and the methodology for calculating the area in this context.

Discussion Character

  • Exploratory
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant expresses confusion about the nature of the triangle's coordinates in four-dimensional space.
  • Another participant questions whether the fourth dimension refers to time, suggesting a connection to Minkowski space.
  • Several participants discuss the need to define the fourth coordinate and its significance, with one noting it may represent an axis rather than a true fourth dimension.
  • A participant suggests finding the lengths of each side in four dimensions to approach the problem as an ordinary triangle.
  • Another participant proposes a formula for calculating the length between points in four-dimensional space, indicating a potential method for further analysis.
  • One participant argues that the fourth coordinate does not imply a fourth dimension but rather follows specific conventions for coordinate representation.
  • A later reply highlights the orthogonality of the vectors formed by the triangle's sides, suggesting a geometric property that may be relevant to the area calculation.

Areas of Agreement / Disagreement

Participants express varying interpretations of the fourth coordinate and its implications for the triangle's area. There is no consensus on the correct approach or understanding of the problem.

Contextual Notes

Participants note the potential semantic issues surrounding the fourth coordinate and its representation, indicating that assumptions about dimensionality may affect the interpretation of the problem.

kingkong69
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find the area of the triangle with vertices (-1 2 -1 2) (-1 2 -1 1) and (2 -1 2 2)
its 4 d

Im confused
thanks in advance
 
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OMG! i have never seen something like this before.

Where did you find this question?
You will have to define the 4d space first.

Is the 4th dimension time? Like the Minkowski space.

A google search on area of triangle in 4d yields nothing.
 


Its stated in that webpage.

the fourth co-ordinate is n which signifies the axis.

I cannot elaborate much on how you will attempt the problem as I have no experience regarding maplesoft.

I hope the link helps you with what the four co-ordinates signify
 


I would say, that you just need to find length of each side in 4D. From there it is just ordinary triangle.
 
minio said:
I would say, that you just need to find length of each side in 4D. From there it is just ordinary triangle.


How do we find length of each side in 4d?
I think I am learning something new here :-)
 


I am definitely no expert so I might be wrong, but I would say that the length would be

\left|AB\right|=\sqrt{(a_{w}-b_{w})^{2}+(a_{x}-b_{x})^{2}+(a_{y}-b_{y})^{2}+(a_{z}-b_{z})^{2}}
 
  • #10


Ok.I think its right by symmetricity.

But my opinion is that its not valid on this question.
Here the 4th coordinate doesn't signify the presence of a 4th dimension. It just represents some co-ordinate axis which the website states.
It is actually stating the coordinates based on some conventions.
 
  • #11


If you call your three points A=(-1 2 -1 2), B=(-1 2 -1 1) and C=(2 -1 2 2), try to think in terms of the vectors AB and AC (as two of the sides of your triangle). The first thing you may notice is that these two vectors are orthogonal.
 

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