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Cuboid with Symmetry and Centroid – GeoGebra Dynamic Demonstration

Cuboid with Symmetry and Centroid – GeoGebra Dynamic Demonstration
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2017-09-08 21:40
TrigonometrySolid GeometryTransformationGeometric ConstructionSlider Animation
This example uses GeoGebra to dynamically demonstrate a cuboid with symmetry and its centroid (center of mass). Users can adjust length, width, and height via sliders to explore the shape's geometric properties under different proportions, employing the Mod function and LaTeX labeling for precise dimension calculations. Core mathematical concepts include solid geometry, trigonometry (sine function), symmetry transformations, and centroid coordinates. The construction leverages the Polygon tool, Mod function, LaTeX text, Slider controls, and interactive objects (e.g., Border, Gear, Toggle) to build and visualize the figure. It is suitable for high‑school and above students learning spatial geometry and the application of dynamic mathematics software.

GeoGebra Commands & Parameters

  1. Mod(b, 1000) → g2
  2. LaTeX("\text{Initial value of the car.}") → text2_1
  3. LaTeX((("\text{At year 1, the car has lost \textcolor{#000099}{\textdollar{" * s2) * "},750} from it’s \\initial value.}")) → text2_2
  4. LaTeX("\text{*Note: the common difference is negative since \\the car is losing value each year*}") → text2_4
  5. LaTeX("\text{Write the explicit formula.}") → text2_3
  6. LaTeX("\text{Explicit formula for any given \\arithmetic sequence.}") → text2_6
  7. LaTeX("\text{Substitute values for and d}") → text2_5
  8. Mod(d3, 1000) → g4
  9. LaTeX("\text{Simplify the explicit formula}") → text10
  10. Mod(d4, 1000) → g6
  11. LaTeX((((("\text{Distribute \textcolor{#000099}{– {" * g3) * "}{") * g4) * "}} over \textcolor{#000099}{(n – 1)}")) → text10_2
  12. LaTeX("\text{Combine like terms}") → text10_1
  13. LaTeX("\text{Substitute for the value \textcolor{#000099}{n = 8.} Solve.}") → text10_3
  14. Mod(e, 1000) → g8
  15. LaTeX("\text{Substitute}") → text10_4
  16. LaTeX("\text{Evaluate}") → text10_5
  17. LaTeX((((("\text{Kellen’s car will be worth \textcolor{#000099}{\textdollar\;{" * g7) * "},{") * g8) * "}} after \textcolor{#000099}{8} years of ownership.}")) → text10_6
  18. LaTeX("\text{\mathbf{Sequence:} A particular order in which related things follow each other.}") → text19
  19. LaTeX("\text{\mathbf{Depreciate:} Diminish in value over a period of time.}") → text18
  20. LaTeX((("\text{Step {" * count) * "} of 14}")) → text17
  21. LaTeX("\text{Identify the first term and common difference\textcolor{#000099}{(d).}") → text2
  22. LaTeX((((("\text{Depreciate\; value\;\\\;\;\;\;\;\;\;\textcolor{#000099}{\;\;{" * g3) * "},{") * g4) * "}}")) → text15
  23. LaTeX((((("\text{Initial\; value \;of \;Car\\\;\;\;\;\;\;\;\textcolor{#000099}{\;{" * g5) * "},{") * g6) * "}}}")) → text16
  24. LaTeX((((("\text{After graduating college, Kellen purchased a new car for \textcolor{#000099}{ \textdollar {" * s1) * "},400.} The value of the car depreciates, \\or loses value, by \textcolor{#000099}{\textdollar{") * s2) * "},750} each year she owns it. What will be the value of Kellen’s car after \textcolor{#000099}{ 8 } years of ownership?\\Write an explicit formula to describe the scenario.}")) → text1
  25. LaTeX("\text{\mathbf{Note:}“Use the (Data Kit) \\to return to the original \\problem or randomly generate\\a similar practice problem.\\and “Use the (Definition) \\to review words to know.}") → text20
  26. Polygon(A, B, C, D) → poly1, a, b_1, c_1, d
  27. LaTeX("\text{“}") → text21_1
  28. LaTeX("\text{“}") → text21_2
  29. LaTeX("\text{Click the Button to solve the problem.}") → text21

AI Drawing Prompt Reference

Create a dynamic geometry demonstration page showing a cuboid with adjustable length, width, and height, symmetry and centroid indicators, a four-vertex polygon base, sliders for proportions, mathematical text labels for dimensions and centroid coordinates, and interactive border, gear, and toggle controls. Include a narrative panel about an arithmetic sequence and car depreciation, with step counting, definitions, and modulo-based computed values, suitable for high-school and above students exploring solid geometry and dynamic mathematics.
The prompt above was compiled from the original drawing commands and is for reference only.