弧度到转速的转换
几何画板及绘图内容加载中,请稍等……
该范例通过动态演示展示了2π弧度等于一个完整的旋转。核心数学概念包括弧度制和旋转角度。通过使用GeoGebra的Rotate, Angle, CircleArc等命令,学生可以直观地理解弧度与旋转之间的关系。适合初中及以上学生学习几何和三角函数。
GeoGebra 命令及参数
Center(c) → BRotate(A, 1, B) → A'Angle(A, B, A') → αRotate(A', 1, B) → A''Angle(A', B, A'') → βRotate(A'', 1, B) → A'''Angle(A'', B, A''') → γRotate(A''', 1, B) → CAngle(A''', B, C) → δRotate(C, 1, B) → C'Angle(C, B, C') → εRotate(C', 1, B) → C''Angle(C', B, C'') → ζCircleArc(B, A, A') → dCircleArc(B, A', A'') → eCircleArc(B, A'', A''') → fCircleArc(B, A''', C) → gCircleArc(B, C, C') → hCircleArc(B, C', C'') → kRotate(A, If[0 ≤ a ≤ 1, (a * α), α], B) → A'_1CircleArc(B, A, A'_1) → pDilate(B, If[0 ≤ a ≤ 1, 1 - a, 0], A) → B'Segment(B', A) → bCircleArc(B, C'', A) → qCircleArc(B, A'_1, A') → sSegment(B, B') → jSegment(B, A') → lPoint(h) → DSegment(B, D) → RadiusRotate(B', If[1.2 ≤ a ≤ 2.2, ((a - 1.2) * β), β], B) → B''Rotate(d, If[1.2 ≤ a ≤ 2.2, ((a - 1.2) * β), β], B) → d'CircleArc(B, A, B'') → tDilate(B, If[1.2 ≤ a ≤ 2.2, 2.2 - a, 0], A) → B'_1Segment(B'_1, A) → mSegment(B, B'_1) → nDilate(B, If[2.4 ≤ a ≤ 3.4, 3.4 - a, 0], A) → B'_2Segment(B, B'_2) → a_1Segment(B'_2, A) → b_1Rotate(d', If[2.4 ≤ a ≤ 3.4, ((a - 2.4) * β), β], B) → d''Rotate(t, If[2.4 ≤ a ≤ 3.4, ((a - 2.4) * β), β], B) → t'Rotate(A, If[2.4 < a < 3.4, ((a - 2.4) * β), β], B) → A'_2CircleArc(B, A, A'_2) → c_1Dilate(B, If[3.6 ≤ a ≤ 4.6, 4.6 - a, 0], A) → B'_3Segment(B'_3, A) → d_1Segment(B, B'_3) → e_1Rotate(A, If[3.6 < a < 4.6, ((a - 3.6) * β), β], B) → A'_3CircleArc(B, A, A'_3) → f_1Rotate(d'', If[3.6 ≤ a ≤ 4.6, ((a - 3.6) * β), β], B) → d'''Rotate(t', If[3.6 ≤ a ≤ 4.6, ((a - 3.6) * β), β], B) → t''Rotate(c_1, If[3.6 ≤ a ≤ 4.6, ((a - 3.6) * β), β], B) → g_1Dilate(B, If[4.8 ≤ a ≤ 5.8, 5.8 - a, 0], A) → B'_4Segment(B, B'_4) → h_1Segment(B'_4, A) → i_1Rotate(d''', If[4.8 ≤ a ≤ 5.8, ((a - 4.8) * β), β], B) → k_1Rotate(t'', If[4.8 ≤ a ≤ 5.8, ((a - 4.8) * β), β], B) → t'''Rotate(g_1, If[4.8 ≤ a ≤ 5.8, ((a - 4.8) * β), β], B) → p_1Rotate(f_1, If[4.8 ≤ a ≤ 5.8, ((a - 4.8) * β), β], B) → q_1Rotate(A, If[4.8 < a < 5.8, ((a - 4.8) * β), β], B) → A'_4CircleArc(B, A, A'_4) → r_1Dilate(B, If[6 ≤ a ≤ 7, 7 - a, 0], A) → B'_5Segment(B'_5, A) → j_1Segment(B, B'_5) → l_1Rotate(A, If[6 < a < 7, ((a - 6) * β), β], B) → A'_5CircleArc(B, A, A'_5) → s_1Rotate(k_1, If[6 ≤ a ≤ 7, ((a - 6) * β), β], B) → t_1Rotate(t''', If[6 ≤ a ≤ 7, ((a - 6) * β), β], B) → c_2Rotate(p_1, If[6 ≤ a ≤ 7, ((a - 6) * β), β], B) → d_2Rotate(q_1, If[6 ≤ a ≤ 7, ((a - 6) * β), β], B) → e_2Rotate(r_1, If[6 ≤ a ≤ 7, ((a - 6) * β), β], B) → f_2CircleArc(B, C'', A) → g_2
AI 绘图提示语参考
画一个圆心在点B的圆,并在B点绘制一个单位圆弧d。然后以B为圆心,A为起点,按照角度α旋转,绘制一个圆弧d'。接着以B为圆心,A'为起点,按照角度β旋转,绘制一个圆弧t。最后以B为圆心,A''为起点,按照角度γ旋转,绘制一个圆弧t'。
以上提示语为根据原始绘图命令整理而来,仅供参考。