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Big Tree Branch Diagram

Big Tree Branch Diagram
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2020-06-02 06:29
SequenceProbability & StatisticsGeometric Construction
This example demonstrates the geometric construction of a big tree's branches. Key mathematical concepts include geometric construction, probability and statistics, and sequences. Using GeoGebra commands like Sequence, it dynamically shows the spatial layout and probability distribution of branches.

GeoGebra Commands & Parameters

  1. Sequence(((BranchWidth + LabelGap) * (k - 1)), k, 1, 5) → BaseLocs
  2. Sequence(Sequence[(BranchLocs(n), (((2^(5 - n) * ((2 * k) - 1)) + 1) / 2 * BranchSpace)), k, 1, 2^(n)], n, 1, 5) → BranchEnds
  3. Sequence(Sequence[(BaseLocs(n), (((2^(6 - n) * ((2 * k) - 1)) + 1) / 2 * BranchSpace)), k, 1, 2^(n - 1)], n, 1, 5) → BasePoints
  4. Sequence(Sequence[Text[(1 + (-1)^(k)) / 2, (BranchLocs(n), (((2^(5 - n) * ((2 * k) - 1)) + 1) / 2 * BranchSpace)) + TextPosOffset], k, 1, 2^(n)], n, 1, Trials) → EndLabels
  5. Sequence(Sequence[Segment[BranchEnds(n, (2 * k) - 1), BasePoints(n, k)], k, 1, 2^(n - 1)], n, 1, Trials) → DownBranches
  6. Sequence(Sequence[Segment[BasePoints(n, k), BranchEnds(n, (2 * k))], k, 1, 2^(n - 1)], n, 1, Trials) → UpBranches
  7. Sequence(Sequence[Text[ProbSuccess, (BasePoints(n, k) * (1 - BranchLabelLoc)) + (BranchEnds(n, (2 * k)) * BranchLabelLoc) + (0, 0.2)], k, 1, 2^(n - 1)], n, 1, Trials) → UpLabels
  8. Sequence(Sequence[Text[1 - ProbSuccess, (BasePoints(n, k) * (1 - BranchLabelLoc)) + (BranchEnds(n, (2 * k) - 1) * BranchLabelLoc) + (0, -0.7)], k, 1, 2^(n - 1)], n, 1, Trials) → DownLabels