等距多边形路径演示
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①本范例演示了等距多边形及其路径的构造与动态变化;②涉及的核心数学概念包括多边形、复数、圆、整数、正弦函数等;③作图要点提炼自 GeoGebra 命令:Mod(模运算)、Vector(向量)、Rotate(旋转)、If(条件判断)、Translate(平移)、AngularBisector(角平分线)、Circle(画圆)、Intersect(交点)、Segment(线段)、Distance(距离)、Line(直线)、Mirror(镜像)、Point(点)、Polygon(多边形);④适合高中及以上数学学习者,用于理解等距多边形的几何性质和路径生成。
GeoGebra 命令及参数
Mod(t, 0.62832) → tmMod(t, 1.0472) → tmod1Mod(t, 2.0944) → tmod2Mod(t, 0.62832) → tmod3Mod(t, 1.25664) → tmod4Vector((0, 0), (-12.56637, 0)) → uRotate(A1, (-tmod1), A2) → B1Rotate(A2, (-tmod1), A1) → B2Rotate(A3, (-tmod1), A1) → B3Rotate(A4, (-tmod1), A2) → B4If(flag1, CircleArc[A1, B2, B3], CircleArc[A2, B1, B4]) → C1If(flag1, CircleArc[B3, A1, B2], CircleArc[B4, A2, B1]) → C2If(flag1, CircleArc[B2, B3, A1], CircleArc[B1, B4, A2]) → C3If(flag1, Polygon[A1, B2, B3], Polygon[A2, B1, B4]) → C4Translate(C1, u) → D1Translate(C2, u) → D2Translate(C3, u) → D3Translate(C4, u) → D4AngularBisector(B1, A2, B4) → eAngularBisector(A2, B4, B1) → fAngularBisector(B3, B2, A1) → gAngularBisector(B2, A1, B3) → hIf(flag1, Intersect[g, h], Intersect[e, f]) → ATranslate(A, u) → A'Circle(C, radius) → cTranslate(C, u) → C'Translate(c, u) → c'Intersect(c, xAxis, 2) → FRotate(F, (-t), C) → F'Rotate(F, π - t, C) → F_1'Segment(F_1', F') → dTranslate(F_1', u) → GTranslate(F', u) → F''Segment(G, F'') → d'Distance(A8, A7) → di1Rotate(A7, -1.8849555921538759, A8) → A9Rotate(A8, -1.88495559215388, A9) → A10Rotate(A9, -1.88495559215388, A10) → A11Line(A11, A9) → lMirror(A10, l) → A12Mirror(A7, l) → A13Mirror(A8, l) → A14Rotate(A7, (-tm), $A$9) → B7Rotate(A8, (-tm), $A$9) → B8Rotate(A10, (-tm), $A$9) → B10Rotate(A11, (-tm), $A$9) → B11Rotate(A9, (-tm), $A$11) → C9Rotate(A12, (-tm), $A$11) → C12Rotate(A13, (-tm), $A$11) → C13Rotate(A14, (-tm), $A$11) → C14If(flag2, CircleArc[A9, B11, B7], CircleArc[A11, C9, C14]) → D7If(flag2, CircleArc[B8, B10, B11], CircleArc[C13, C12, C9]) → D8If(flag2, CircleArc[B7, A9, B10], CircleArc[C14, A11, C12]) → D9If(flag2, CircleArc[B11, B8, A9], CircleArc[C9, C13, A11]) → D10If(flag2, CircleArc[B10, B7, B8], CircleArc[C12, C14, C13]) → D11If(flag2, Polygon[B10, B11, 5], Polygon[C14, C13, 5]) → D12Translate(D7, u) → E7Translate(D8, u) → E8Translate(D9, u) → E9Translate(D10, u) → E10Translate(D11, u) → E11Translate(D12, u) → E12AngularBisector(C13, C14, C9) → mAngularBisector(C14, C9, C12) → nAngularBisector(B8, B7, B11) → pAngularBisector(B7, B11, B10) → qIf(flag2, Intersect[p, q], Intersect[m, n]) → BPoint(b) → DPoint(b) → EPolygon(D, E, 4) → poly1, i, j, k, r, H, IPoint(a) → JPoint(a) → KPolygon(J, K, 4) → poly2, s, a_1, b_1, c_1, L, MTranslate(B, u) → B'
AI 绘图提示语参考
绘制一个动态的雷奥劳斯多边形路径演示,展示多边形的构造和运动轨迹,包含多个圆弧和折线段,通过旋转和镜像操作生成复杂的几何图案,并标注关键点的位置和路径,体现三角函数和复数在几何构造中的应用。
以上提示语为根据原始绘图命令整理而来,仅供参考。