立方体与对称性的几何演示

立方体与对称性的几何演示
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2017-09-08 21:40
本例通过GeoGebra动态演示了一个带对称性的立方体及其重心(重心)位置。用户可以通过滑块调整长宽高,观察立方体在不同比例下的几何性质,并利用Mod函数和LaTeX标注实现精确的尺寸计算。核心数学概念包括立体几何、三角函数(正弦函数)、对称变换与重心坐标。作图中使用了Polygon工具、Mod函数、LaTeX文本、Slider控件以及一系列交互式对象(如Border、Gear、Toggle等)来构建和展示图形。适合高中及以上学生学习空间几何与动态数学软件的应用。

GeoGebra 命令及参数

  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 绘图提示语参考

绘制一个动态几何演示界面,主体为一个可调节长、宽、高的长方体及其对称与质心示意,包含一个由四个顶点构成的多边形底面、用于改变比例的滑块、显示尺寸与质心坐标的数学文本标注,以及边框、齿轮和切换控件等交互元素;同时呈现一段关于等差数列与汽车折旧的说明文字、步骤计数、定义框和取模计算结果,整体适合高中以上学生探索立体几何与动态数学。
以上提示语为根据原始绘图命令整理而来,仅供参考。