韦恩图绘制 by Steve Phelps
几何画板及绘图内容加载中,请稍等……
①本范例演示如何使用 GeoGebra 绘制韦恩图;②涉及核心数学概念包括集合运算、逻辑关系、解析几何;③作图要点:使用 Point, Circle, Intersect, Integral, IntegralBetween, Polygon, PolyLine, LaTeX, Random 等命令和对象;④适合高中及以上学生学习和理解集合论及几何作图。
GeoGebra 命令及参数
Point(xAxis) → ACircle(A, 2) → cIntersect(c, xAxis, 2) → BCircle(B, 2) → dIntersect(c, d, 2) → CCircle(C, 2) → eIntersect(c, d, 1) → DIntersect(d, e, 1) → EIntersect(c, e, 2) → FIntersect(c, xAxis, 1) → GIntersect(d, xAxis, 2) → HIntegral(h, -3, -1) → aIntegralBetween(h, g, -1, 0) → bIntegral(hh, -3, -2) → iIntegral(p, -2, -1) → jIntegralBetween(g, p, -1, 0) → kIntegralBetween(h, p, 0, 1) → lIntegralBetween(g, h, 0, 1) → mIntegral(g, 1, 3) → nIntegral(gg, 2, 3) → oIntegral(p, 1, 2) → qIntegralBetween(hh, pp, -2, 0) → rIntegralBetween(gg, pp, 0, 2) → sIntegralBetween(p, hh, -2, -1) → tIntegralBetween(gg, hh, -1, 0) → uIntegralBetween(hh, gg, 0, 1) → vIntegralBetween(p, gg, 1, 2) → wIntegral(p, -1, 1) → a_1Integral(gg, -1, 0) → b_1Polygon((-4.5, 2.5), (4.5, 2.5), (4.5, -5), (-4.5, -5)) → poly1, f_1, g_1, h_1, i_1PolyLine((-4.5, 2.5), (4.5, 2.5), (4.5, -5), (-4.5, -5), (-4.5, 2.5)) → j_1Integral(hh, 0, 1) → cccLaTeX("A \cap \left( B' \cup C' \right)") → B1LaTeX("A \cap C' ") → B2LaTeX("\left(A \cup B \right) \cap C' ") → B3LaTeX("A") → B4LaTeX("A \cap B") → B5LaTeX("A \cap B \cap C") → B6LaTeX("A \cap C") → B8LaTeX("B \cap C") → B9LaTeX("B \cap \left( A' \cup C' \right)") → B10LaTeX("C \cap \left( A' \cup B' \right)") → B11LaTeX("A \cap B \cap C'") → B12LaTeX("A \cap B' \cap C") → B13LaTeX("A' \cap B \cap C") → B14LaTeX("\left( B \cup C \right)' ") → B15LaTeX("\left( A \cup C \right)' ") → B16LaTeX("\left( A \cup B \right)' ") → B17LaTeX("A' ") → B18LaTeX("B' ") → B19LaTeX("C' ") → B20LaTeX("\left(B \cup C \right) \cap A' ") → B21LaTeX("\left(A \cup C \right) \cap B' ") → B22LaTeX("\left( A \cup B \cup C \right)' ") → B7Random(1, 22) → pick
AI 绘图提示语参考
画一个包含两个相交圆的维恩图,展示集合的交集和并集关系。首先绘制两个半径为2的圆,使它们在x轴上相交。接着,在圆内和圆外添加多个点,并用线条连接这些点,形成封闭的多边形区域。最后,在图的周围添加LaTeX公式,标注不同的集合运算结果,如A∩B、A∪B等。
以上提示语为根据原始绘图命令整理而来,仅供参考。