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System of Equations in Three Variables

System of Equations in Three Variables
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2015-06-22 00:01
FunctionCoordinate GeometrySolid Geometry
This example demonstrates the geometric representation of a system of equations in three variables. Key mathematical concepts include linear equations in three-dimensional space and their solution sets. Using GeoGebra commands such as Polygon, Prism, and PointIn, the example constructs geometric figures in three-dimensional space. Suitable for high school mathematics education and learning the relationship between geometry and algebra in three-dimensional space.

GeoGebra Commands & Parameters

  1. Polygon(A, B, D, C) → poly1, a, b, d, c
  2. Polygon(A, B, F, E) → poly2, a_1, b_1, f, e_1
  3. Prism(poly2, J) → g, K, edgeBK, edgeFL, edgeEM, edgeJK, edgeKL, edgeLM, edgeJM, L, M, faceABKJ, faceBFLK, faceEFLM, faceAEMJ, faceJKLM, edgeAJ
  4. Prism(poly1, N) → e, G, edgeBG, edgeDH, edgeCI, edgeGN, edgeGH, edgeHI, edgeIN, H, I, faceABGN, faceBDHG, faceCDHI, faceACIN, faceGHIN, edgeAN
  5. PointIn(P3) → O

AI Drawing Prompt Reference

Draw the geometric representation of a system of equations in three-dimensional space. First, draw two quadrilaterals poly1 and poly2, then construct two prisms g and e with poly2 and poly1 as their bases, respectively. Finally, add a point O on prism g. The entire figure illustrates the geometric relationship of linear equations in three-dimensional space.
The prompt above was compiled from the original drawing commands and is for reference only.