Geometry: Planes, x+y+z=0 - How Does It Work?

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SUMMARY

The equation x+y+z=0 represents a plane in three-dimensional space, despite being a two-dimensional object. A plane can be defined using two coordinates, but it exists within a three-dimensional context where additional variables may be necessary for representation. This understanding clarifies the relationship between dimensions and how planes can be visualized and manipulated within higher-dimensional spaces.

PREREQUISITES
  • Understanding of basic geometry concepts, specifically planes and dimensions.
  • Familiarity with three-dimensional coordinate systems.
  • Knowledge of mathematical equations and their graphical representations.
  • Basic skills in visualizing geometric objects in higher dimensions.
NEXT STEPS
  • Study the properties of planes in three-dimensional geometry.
  • Explore the concept of embedding lower-dimensional objects in higher-dimensional spaces.
  • Learn about the graphical representation of equations in three dimensions.
  • Investigate the implications of dimensionality in mathematical modeling.
USEFUL FOR

Students of mathematics, educators teaching geometry, and anyone interested in understanding the relationship between dimensions and geometric representations.

binbagsss
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I do not understnad how x+y+z=0 can be a plane, I thought a plane has 2 dimensions, this is all :) thanks.
 
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A plane is a two dimensional object, but it can be rotated into three dimensions. Another way of looking at it is that you only need two coordinates to express a point on the plane (hence it being 2-dimensional), but it can be embedded in a space consisting of an arbitrary amount of dimensions, in which case you could need more variables to express it.
 
Vorde said:
A plane is a two dimensional object, but it can be rotated into three dimensions. Another way of looking at it is that you only need two coordinates to express a point on the plane (hence it being 2-dimensional), but it can be embedded in a space consisting of an arbitrary amount of dimensions, in which case you could need more variables to express it.

Ahh of course - cheers !
 

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