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GeoGebra Sequence Command with Geometric Applications

GeoGebra Sequence Command with Geometric Applications
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2020-10-20 16:13
FunctionTrigonometrySequenceSlider AnimationGraphing
This example demonstrates how to use GeoGebra's Sequence command to generate dynamic sequences combined with geometric mean, unit circle, and other mathematical concepts. The construction uses variable n to control the number of terms, with list objects l1, l2 to store data and text objects for annotation. Core mathematical concepts include sequences and series, geometric mean, compound interest calculations, orthocenter properties, Poisson distribution, and unit circle trigonometry. Construction highlights: Sequence command generates numerical series, slider n adjusts term count, list objects l1-l6 store different data series, text objects text1-text9 display calculations and results. Suitable for high school mathematics sequence teaching and university-level probability & statistics for Poisson distribution sequence demonstration.

GeoGebra Commands & Parameters

  1. Sequence(Sequence[Polygon[(a, b), (a + 2, b + 2), 4], a, 1, n, 1], b, 1, n, 1) → l1
  2. Sequence(Sequence[Circle[(a, b), 1], a, 1, n, 2], b, 1, n, 2) → l2
  3. Sequence(Sequence[Polygon[(a, b), (a + 2, b + 2), 4], a, 1, n, 2], b, 1, n, 2) → l3
  4. Sequence(Sequence[Polygon[(a, b), (a + 2, b), 3], a, 1, n, 3], b, 2, n, 2) → l4
  5. Sequence(Sequence[(a, b), a, 1, n, 1], b, 1, n, 1) → l5
  6. Sequence(Sequence[Segment[(a, b), (b, a)], a, 1, n, 1], b, 1, n, 1) → l6

AI Drawing Prompt Reference

Create a dynamic geometric array controlled by a slider. On a coordinate plane, arrange multiple squares in rows and columns, each with side length 2, starting from the top-left and extending right and down. Intersperse circles of radius 1 at every other unit position, alternating with the squares. Additionally, place triangles and points at specific intervals, and connect symmetric coordinate points with line segments. The overall layout is grid-like, containing squares, circles, triangles, points, and segments, with the count increasing or decreasing based on the slider, visually demonstrating the combination of sequences and geometry.
The prompt above was compiled from the original drawing commands and is for reference only.