五分钟计时器
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①本范例演示如何通过 GeoGebra 构建一个五分钟计时器;②涉及的核心数学概念包括角度、时间计算、几何变换;③作图要点:使用了 Random, If, Circle, Rotate, Tangent, Intersect, Dilate, Polygon, Semicircle, Line, OrthogonalLine, Midpoint, Textfield, Ellipse, Sequence 等命令和对象;④适合初中数学教学,用于理解时间与角度的关系及几何作图技巧。
GeoGebra 命令及参数
Random(0, 11) → A16If(counterlevel < 6, (Random[0, 3] * 15), (Random[0, 11] * 5)) → B16Circle(A, 0.05) → r6Rotate(C, (-C17), A) → C'Tangent(C', r6) → t7, t1Intersect(r6, t7) → ZDilate(Z, 1.15, C') → FIntersect(r6, t1) → XDilate(X, 1.15, C') → ECircle(A, 0.15) → r7Rotate(D, (-B17), A) → D'Tangent(D', r7) → t3, t6Intersect(r7, t3) → JDilate(J, 1.1, D') → MIntersect(r7, t6) → HDilate(H, 1.1, D') → NCircle(A, 5) → r1Circle(A, 4.3) → r2Polygon(F, E, C') → tg1, d10, d11, d13Polygon(D', N, M) → tg2, d4, d6, d3Circle(A, 0.2) → r8Rotate(B, (-A17), A) → B'Tangent(B', r8) → t8, t2Intersect(r8, t8) → KIntersect(r8, t2) → LDilate(K, 1.12, B') → GDilate(L, 1.12, B') → IPolygon(I, G, B') → tg3, d7, d2, d1Rotate(D, 30°, A) → DARotate(DA, 30°, A) → DBRotate(DB, 30°, A) → DCRotate(DC, 30°, A) → DDRotate(DD, 30°, A) → DERotate(DE, 30°, A) → DFRotate(DF, 30°, A) → DGRotate(DG, 30°, A) → DHRotate(DH, 30°, A) → DIRotate(DI, 30°, A) → DJRotate(DJ, 30°, A) → DKCircle(A, 5.1) → r3Semicircle(I, G) → z1Semicircle(I, G) → z2Intersect(r3, r2) → O, , ,Line(D, DF) → t4Intersect(r3, t4) → P, QOrthogonalLine(Q, t4) → t5Midpoint(T, R) → VMidpoint(U, S) → WCircle(V, R) → r4Circle(W, S) → r5Polygon(T, R, S, U) → tg4, d9, d5, d8, d12Semicircle(T, R) → z3Semicircle(S, U) → z4If(A16 < 10, "0" + A16, "" + A16) → A18If(B16 < 10, "0" + B16, "" + B16) → B18If(C16 < 10, "0" + C16, "" + C16) → C18Textfield(userinputhour) → InputBox1Textfield(userinputminute) → InputBox2If(useranswerhour ≟ A16, true, false) → answerhourcorrectIf(useranswerminute ≟ B16, true, false) → answerminutecorrectPolygon(D', N, M) → tg2_{err}, m_1, d', nPolygon(I, G, B') → tg3_{err}, b', i, gIf(answerhourcorrect, false, If[answerminutecorrect, false, true]) → answerbothwrongMidpoint(A, D') → M_{AD'}Rotate(M_{AD'}, -15°, A) → M_{D}Ellipse(A, D', M_{D}) → dMidpoint(A, B') → M_{AB'}Rotate(M_{AB'}, -45°, A) → M_{B'}Ellipse(A, B', M_{B'}) → eSequence(Rotate[D, (-6° * i), A], i, 1, 60) → Li2Circle(Element[Li2, If[A16 ≟ 0, 60, (A16 * 5)]], 0.7) → f
AI 绘图提示语参考
画一个五分钟计时器,包含一个中心圆和多个旋转角度标记,通过圆、旋转、切线和相交等操作构建,展示时间与角度的关系,最终形成计时器的几何形态。
以上提示语为根据原始绘图命令整理而来,仅供参考。