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Connectivity Matrix by chris cambré (2)

Connectivity Matrix by chris cambré (2)
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2017-11-17 16:42
MatrixGeometric ConstructionGraphing
This example illustrates the concept of a connectivity matrix, involving core mathematical concepts of matrices and graph theory. Using GeoGebra commands such as Circle, Intersect, and Rotate, a visual model of a connectivity matrix is constructed. This example is suitable for high school mathematics education, particularly in matrix and graph theory courses.

GeoGebra Commands & Parameters

  1. Circle(OO, 1, xOyPlane) → c
  2. Intersect(xAxis, c, 1) → A
  3. Rotate(A, 60°) → B
  4. TableText({{"A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L", "M", "N", "P", "Q", "R", "S", "T", "U"}}) → tekst2
  5. TableText({{"A"}, {"B"}, {"C"}, {"D"}, {"E"}, {"F"}, {"G"}, {"H"}, {"I"}, {"J"}, {"K"}, {"L"}, {"M"}, {"N"}, {"P"}, {"Q"}, {"R"}, {"S"}, {"T"}, {"U"}}) → tekst3
  6. Point(Circle[((A * (1 - sqrt(5))) + (B * (3 + sqrt(5)))) / 4, (Distance[A, B] * sqrt(10 + (2 * sqrt(5))) / 4), Segment[A, B]]) → C
  7. Dodecahedron(A, B, C) → a, D, M, N, O, P, Q, R, S, T, zijvlakABCDE, zijvlakAEIOJ, E, zijvlakABFKJ, zijvlakBCGLF, zijvlakCDHMG, zijvlakDEINH, zijvlakINSTO, zijvlakJKPTO, zijvlakFKPQL, zijvlakGLQRM, zijvlakHMRSN, zijvlakPQRST, F, RibbeAE, RibbeAB, RibbeBC, RibbeCD, RibbeDE, RibbeAJ, RibbeEI, RibbeIO, RibbeJO, RibbeJK, G, RibbeFK, RibbeBF, RibbeFL, RibbeGL, RibbeCG, RibbeGM, RibbeHM, RibbeDH, RibbeHN, RibbeIN, H, RibbeNS, RibbeST, RibbeOT, RibbePT, RibbeKP, RibbePQ, RibbeLQ, RibbeQR, RibbeMR, RibbeRS, I, J, K, L
  8. Join({{"A"}, Sequence[Element[MMM, 1, nn], nn, 1, 20]}) → RijAA
  9. Join({{"B"}, Sequence[Element[MMM, 2, nn], nn, 1, 20]}) → RijBB
  10. Join({{"C"}, Sequence[Element[MMM, 3, nn], nn, 1, 20]}) → RijCC
  11. Join({{"D"}, Sequence[Element[MMM, 4, nn], nn, 1, 20]}) → RijDD
  12. Join({{"E"}, Sequence[Element[MMM, 5, nn], nn, 1, 20]}) → RijEE
  13. Join({{"F"}, Sequence[Element[MMM, 6, nn], nn, 1, 20]}) → RijFF
  14. Join({{"G"}, Sequence[Element[MMM, 7, nn], nn, 1, 20]}) → RijGG
  15. Join({{"H"}, Sequence[Element[MMM, 8, nn], nn, 1, 20]}) → RijHH
  16. Join({{"I"}, Sequence[Element[MMM, 9, nn], nn, 1, 20]}) → RijII
  17. Join({{"J"}, Sequence[Element[MMM, 10, nn], nn, 1, 20]}) → RijJJ
  18. Join({{"K"}, Sequence[Element[MMM, 11, nn], nn, 1, 20]}) → RijKK
  19. Join({{"L"}, Sequence[Element[MMM, 12, nn], nn, 1, 20]}) → RijLL
  20. Join({{"M"}, Sequence[Element[MMM, 13, nn], nn, 1, 20]}) → RijMM
  21. Join({{"N"}, Sequence[Element[MMM, 14, nn], nn, 1, 20]}) → RijNN
  22. Join({{"O"}, Sequence[Element[MMM, 15, nn], nn, 1, 20]}) → RijOO
  23. Join({{"P"}, Sequence[Element[MMM, 16, nn], nn, 1, 20]}) → RijPP
  24. Join({{"Q"}, Sequence[Element[MMM, 17, nn], nn, 1, 20]}) → RijQQ
  25. Join({{"R"}, Sequence[Element[MMM, 18, nn], nn, 1, 20]}) → RijRR
  26. Join({{"S"}, Sequence[Element[MMM, 19, nn], nn, 1, 20]}) → RijSS
  27. Join({{"T"}, Sequence[Element[MMM, 20, nn], nn, 1, 20]}) → RijTT
  28. TableText({rij0, RijAA, RijBB, RijCC, RijDD, RijEE, RijFF, RijGG, RijHH, RijII, RijJJ, RijKK, RijLL, RijMM, RijNN, RijOO, RijPP, RijQQ, RijRR, RijSS, RijTT}, "c") → tekst5
  29. Point(ribben) → PP

AI Drawing Prompt Reference

Draw a regular dodecahedron with its vertices evenly distributed on a unit circle centered at the origin, starting from the intersection of the circle with the positive x-axis and rotating by 60 degrees each time to generate 20 vertices. Next to the dodecahedron, display a 20x20 connectivity matrix as a table, with rows and columns labeled by letters A through T, where the matrix entries indicate whether corresponding vertices are connected by an edge. Additionally, mark a point at the midpoint of each edge of the dodecahedron to highlight the edge structure. The overall composition should clearly show the three-dimensional shape of the dodecahedron and its correspondence with the matrix.
The prompt above was compiled from the original drawing commands and is for reference only.