几何概率
几何画板及绘图内容加载中,请稍等……
所属专题
Selected Examples
该范例演示了几何概率的基本概念。通过构造几何图形,学生可以直观地理解概率与几何形状之间的关系。使用了If, Segment, Polygon, CountIf等命令,涉及的核心数学概念包括几何概率、条件概率等。适合高中数学教学,特别是概率统计课程。
GeoGebra 命令及参数
If(abs(A3 - B3) ≤ w, 1, 0) → C3If(abs(A4 - B4) ≤ w, 1, 0) → C4If(abs(A5 - B5) ≤ w, 1, 0) → C5If(abs(A6 - B6) ≤ w, 1, 0) → C6If(abs(A7 - B7) ≤ w, 1, 0) → C7If(abs(A8 - B8) ≤ w, 1, 0) → C8If(abs(A9 - B9) ≤ w, 1, 0) → C9If(abs(A10 - B10) ≤ w, 1, 0) → C10If(abs(A11 - B11) ≤ w, 1, 0) → C11If(abs(A12 - B12) ≤ w, 1, 0) → C12If(abs(A13 - B13) ≤ w, 1, 0) → C13If(abs(A14 - B14) ≤ w, 1, 0) → C14If(abs(A15 - B15) ≤ w, 1, 0) → C15If(abs(A16 - B16) ≤ w, 1, 0) → C16If(abs(A17 - B17) ≤ w, 1, 0) → C17If(abs(A18 - B18) ≤ w, 1, 0) → C18If(abs(A19 - B19) ≤ w, 1, 0) → C19If(abs(A20 - B20) ≤ w, 1, 0) → C20If(abs(A21 - B21) ≤ w, 1, 0) → C21If(abs(A22 - B22) ≤ w, 1, 0) → C22If(abs(A23 - B23) ≤ w, 1, 0) → C23If(abs(A24 - B24) ≤ w, 1, 0) → C24If(abs(A25 - B25) ≤ w, 1, 0) → C25If(abs(A26 - B26) ≤ w, 1, 0) → C26If(abs(A27 - B27) ≤ w, 1, 0) → C27If(abs(A28 - B28) ≤ w, 1, 0) → C28If(abs(A29 - B29) ≤ w, 1, 0) → C29If(abs(A30 - B30) ≤ w, 1, 0) → C30If(abs(A31 - B31) ≤ w, 1, 0) → C31If(abs(A32 - B32) ≤ w, 1, 0) → C32If(abs(A33 - B33) ≤ w, 1, 0) → C33If(abs(A34 - B34) ≤ w, 1, 0) → C34If(abs(A35 - B35) ≤ w, 1, 0) → C35If(abs(A36 - B36) ≤ w, 1, 0) → C36If(abs(A37 - B37) ≤ w, 1, 0) → C37If(abs(A38 - B38) ≤ w, 1, 0) → C38If(abs(A39 - B39) ≤ w, 1, 0) → C39If(abs(A40 - B40) ≤ w, 1, 0) → C40If(abs(A41 - B41) ≤ w, 1, 0) → C41If(abs(A42 - B42) ≤ w, 1, 0) → C42If(abs(A43 - B43) ≤ w, 1, 0) → C43If(abs(A44 - B44) ≤ w, 1, 0) → C44If(abs(A45 - B45) ≤ w, 1, 0) → C45If(abs(A46 - B46) ≤ w, 1, 0) → C46If(abs(A47 - B47) ≤ w, 1, 0) → C47If(abs(A48 - B48) ≤ w, 1, 0) → C48If(abs(A49 - B49) ≤ w, 1, 0) → C49If(abs(A50 - B50) ≤ w, 1, 0) → C50If(abs(A51 - B51) ≤ w, 1, 0) → C51If(abs(A52 - B52) ≤ w, 1, 0) → C52If(abs(A53 - B53) ≤ w, 1, 0) → C53If(abs(A54 - B54) ≤ w, 1, 0) → C54If(abs(A55 - B55) ≤ w, 1, 0) → C55If(abs(A56 - B56) ≤ w, 1, 0) → C56If(abs(A57 - B57) ≤ w, 1, 0) → C57If(abs(A58 - B58) ≤ w, 1, 0) → C58If(abs(A59 - B59) ≤ w, 1, 0) → C59If(abs(A60 - B60) ≤ w, 1, 0) → C60If(abs(A61 - B61) ≤ w, 1, 0) → C61If(abs(A62 - B62) ≤ w, 1, 0) → C62If(abs(A63 - B63) ≤ w, 1, 0) → C63If(abs(A64 - B64) ≤ w, 1, 0) → C64If(abs(A65 - B65) ≤ w, 1, 0) → C65If(abs(A66 - B66) ≤ w, 1, 0) → C66If(abs(A67 - B67) ≤ w, 1, 0) → C67If(abs(A68 - B68) ≤ w, 1, 0) → C68If(abs(A69 - B69) ≤ w, 1, 0) → C69If(abs(A70 - B70) ≤ w, 1, 0) → C70If(abs(A71 - B71) ≤ w, 1, 0) → C71If(abs(A72 - B72) ≤ w, 1, 0) → C72If(abs(A73 - B73) ≤ w, 1, 0) → C73If(abs(A74 - B74) ≤ w, 1, 0) → C74If(abs(A75 - B75) ≤ w, 1, 0) → C75If(abs(A76 - B76) ≤ w, 1, 0) → C76If(abs(A77 - B77) ≤ w, 1, 0) → C77If(abs(A78 - B78) ≤ w, 1, 0) → C78If(abs(A79 - B79) ≤ w, 1, 0) → C79If(abs(A80 - B80) ≤ w, 1, 0) → C80If(abs(A81 - B81) ≤ w, 1, 0) → C81If(abs(A82 - B82) ≤ w, 1, 0) → C82If(abs(A83 - B83) ≤ w, 1, 0) → C83If(abs(A84 - B84) ≤ w, 1, 0) → C84If(abs(A85 - B85) ≤ w, 1, 0) → C85If(abs(A86 - B86) ≤ w, 1, 0) → C86If(abs(A87 - B87) ≤ w, 1, 0) → C87If(abs(A88 - B88) ≤ w, 1, 0) → C88If(abs(A89 - B89) ≤ w, 1, 0) → C89If(abs(A90 - B90) ≤ w, 1, 0) → C90If(abs(A91 - B91) ≤ w, 1, 0) → C91If(abs(A92 - B92) ≤ w, 1, 0) → C92If(abs(A93 - B93) ≤ w, 1, 0) → C93If(abs(A94 - B94) ≤ w, 1, 0) → C94If(abs(A95 - B95) ≤ w, 1, 0) → C95If(abs(A96 - B96) ≤ w, 1, 0) → C96If(abs(A97 - B97) ≤ w, 1, 0) → C97If(abs(A98 - B98) ≤ w, 1, 0) → C98If(abs(A99 - B99) ≤ w, 1, 0) → C99If(abs(A100 - B100) ≤ w, 1, 0) → C100If(abs(A2 - B2) ≤ w, 1, 0) → C2If(abs(A101 - B101) ≤ w, 1, 0) → C101Segment(A, C) → fPolygon(A, B, C, D) → Vieleck1, a, b, c, dPolygon(A, I_4, K_4, C, L_4, J_4) → Vieleck2, e, g, h, i, j, kCountIf(x ≟ 1, C2:C101) → D2
AI 绘图提示语参考
画一个正方形ABCD,然后在正方形内部随机选取一个点P。接着,画出以P为圆心、半径为w的圆。最后,计算圆与正方形重叠部分的面积,并与正方形总面积进行比较,以直观理解几何概率的概念。
以上提示语为根据原始绘图命令整理而来,仅供参考。