动态斜率插画：用构造几何可视化差值与斜率

GeoGebra 命令及参数

1. GCD(deltaY, deltaX) → GCDm
2. GCD(numerYint, deltaX) → GCDy
3. If(sgn(deltaY / deltaX) ≥ 0, "", "-") → textSignN
4. If(sgn(numerYint / deltaX) > 0, "+", "-") → textSign
5. If(deltaXR ≟ 1, textSignN + deltaYR, textSignN + "\, \frac{" + deltaYR + "}{" + deltaXR + "}") → textslopeN
6. If(denomYintR ≟ 1, textSign + numerYintR, textSign + "\frac{" + numerYintR + "}{" + denomYintR + "}") → textYint
7. If(denomYintR ≟ 1, If[numerYintR ≟ 1, textSign, textSign + numerYintR], textSign + "\frac{" + numerYintR + "}{" + denomYintR + "}") → textMID
8. OrthogonalLine(B, xAxis) → a_2
9. OrthogonalLine(A, yAxis) → c
10. Intersect(a_2, c) → C
11. Line(A, B) → d
12. Polygon(A, B, C) → poly1, c_1, a_1, b_1
13. Distance(B, C) → distanceBC
14. Distance(A, C) → distanceAC
15. Intersect(a_2, c) → D
16. Segment(A, D) → e
17. Segment(C, B) → f
18. GCD(deltaY_1, deltaX_1) → GCDm_1
19. If(sgn(deltaY_1 / deltaX_1) ≥ 0, "", "-") → textSignN_1
20. If(deltaXR_1 ≟ 1, textSignN_1 + deltaYR_1, textSignN_1 + "\, \frac{" + deltaYR_1 + "}{" + deltaXR_1 + "}") → textslopeN_1
21. Line(A_1, B_1) → d_1
22. Angle(B, D, A) → α
23. Segment(A, B) → g
24. GCD(deltaY_2, deltaX_2) → GCDm_2
25. If(sgn(deltaY_2 / deltaX_2) ≥ 0, "", "-") → textSignN_2
26. If(deltaXR_2 ≟ 1, textSignN_2 + deltaYR_2, textSignN_2 + "\, \frac{" + deltaYR_2 + "}{" + deltaXR_2 + "}") → textslopeN_2
27. Line(A_2, B_2) → d_2
28. Segment(A_2, B_2) → g_1
29. GCD(deltaY_3, deltaX_3) → GCDm_3
30. If(sgn(deltaY_3 / deltaX_3) ≥ 0, "", "-") → textSignN_3
31. If(deltaXR_3 ≟ 1, textSignN_3 + deltaYR_3, textSignN_3 + "\, \frac{" + deltaYR_3 + "}{" + deltaXR_3 + "}") → textslopeN_3
32. Line(A_3, B_3) → d_3
33. Segment(A_3, B_3) → g_2
34. Slope(g) → h
35. Dilate(A, If[0 < i ≤ 1, 1 - i, 0], D) → A'
36. Vector(A, A') → u
37. Dilate(D, If[1 < i ≤ 2, 2 - i, 0], B) → D'
38. Vector(D, D') → v
39. Line(A, B) → j
40. Midpoint(A, C) → E
41. Mirror(B, k) → B'
42. Distance(A, B') → distanceAB'
43. Distance(B', B) → distanceB'B
44. Polygon(A, B', B) → t1, b_5, a_6, b'
45. Dilate(A, If[0 < i ≤ 1, 1 - i, 0], B') → A'_1
46. Vector(A, A'_1) → w
47. Dilate(B', If[1 < i ≤ 2, 2 - i, 0], B) → B''
48. Vector(B', B'') → l
49. Intersect(m, n) → F
50. Dilate(A, If[0 < i ≤ 1, 1 - i, 0], F) → A'_2
51. Vector(A, A'_2) → p
52. Dilate(F, If[1 < i ≤ 2, 2 - i, 0], B) → F'
53. Vector(F, F') → q
54. Distance(A, F) → distanceAF
55. Distance(F, B) → distanceFB
56. Polygon(A, F, B) → t3, b_6, a_7, f_1
57. FractionText(i_1) → text8