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负数乘法演示

负数乘法演示
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2020-06-08 03:41
函数几何作图
①本范例通过动态图形演示负数乘法的几何意义；②涉及核心数学概念包括负数乘法规则、数轴对称、几何变换；③作图要点运用了椭圆(Ellipse)、圆弧(Arc)、平移(Translate)、镜像(Mirror)等GeoGebra命令与对象；④适合初中及以上学生理解乘法运算规律，也可用于微积分初步教学。

GeoGebra 命令及参数

  1. Ellipse((a / 2, sqrt(abs(4 - a^(2) / 4))), (a / 2, (-sqrt(abs(4 - a^(2) / 4)))), 2) → c1
  2. Arc(c1, (0, 0), (a, 0)) → left1
  3. Arc(c1, (a, 0), (0, 0)) → right1
  4. Translate(c1, Vector[(a, 0)]) → c2
  5. Translate(c2, Vector[(a, 0)]) → c3
  6. Translate(c3, Vector[(a, 0)]) → c4
  7. Translate(c4, Vector[(a, 0)]) → c5
  8. Arc(c2, ((a * 2), 0), (a, 0)) → right2
  9. Arc(c3, ((a * 3), 0), ((a * 2), 0)) → right3
  10. Arc(c4, ((a * 4), 0), ((a * 3), 0)) → right4
  11. Arc(c5, ((a * 5), 0), ((a * 4), 0)) → right5
  12. Arc(c2, (a, 0), ((2 * a), 0)) → left2
  13. Arc(c3, ((2 * a), 0), ((3 * a), 0)) → left3
  14. Arc(c4, ((3 * a), 0), ((4 * a), 0)) → left4
  15. Arc(c5, ((4 * a), 0), ((5 * a), 0)) → left5
  16. Mirror(c1, x = 0) → c6
  17. Mirror(c2, x = 0) → c7
  18. Mirror(c3, x = 0) → c8
  19. Translate(c8, Vector[((-a), 0)]) → c9
  20. Translate(c9, Vector[((-a), 0)]) → c10
  21. Arc(c10, ((-4 * a), 0), ((-5 * a), 0)) → left10
  22. Arc(c10, ((-5 * a), 0), ((-4 * a), 0)) → right10
  23. Ellipse((a / 2, sqrt(abs(4 - a^(2) / 4))), (a / 2, (-sqrt(abs(4 - a^(2) / 4)))), 4) → c
  24. Arc(c6, ((-a), 0), (0, 0)) → left6
  25. Arc(c7, ((-2 * a), 0), ((-a), 0)) → left7
  26. Arc(c8, ((-3 * a), 0), ((-2 * a), 0)) → left8
  27. Arc(c9, ((-4 * a), 0), ((-3 * a), 0)) → left9
  28. Arc(c6, (0, 0), ((-a), 0)) → right6
  29. Arc(c7, ((-a), 0), ((-2 * a), 0)) → right7
  30. Arc(c8, ((-2 * a), 0), ((-3 * a), 0)) → right8
  31. Arc(c9, ((-3 * a), 0), ((-4 * a), 0)) → right9