圆锥侧面积计算演示

GeoGebra 命令及参数

1. Min(Rearrange / 2, 1) → k
2. Point(yAxis) → O
3. Sequence(If[k < 1, (((cl * sin((i * α))) * cos((i * α)) / sin(α)), (-(gap + ((cl * sin((i * α))) * sin((i * α)) / sin(α))))), ((cl * i), (-gap))], i, 0, nCones / 2) → cMovingPosInitialize
4. Max(Rearrange / 2 - 1, 0) → k'
5. Segment(H, (x(H), 0)) → RadiusDisplay
6. Circle((0, Radius), Radius) → c_1
7. Rotate(O, cAngle / 2, cMid) → cLeft
8. Rotate(O, ((-cAngle)) / 2, cMid) → cRight
9. CircleSector(cMid, cRight, cLeft) → cSector
10. Sort(Union[Sequence[Mirror[Element[cMovingPosInitialize, i], yAxis], i, 2, nCones / 2 + 1], cMovingPosInitialize]) → cMovingPos
11. Sequence(Vector[Element[cMovingPos, i + 1] - Element[cMovingPos, i]], i, 1, nCones) → cL_V
12. Sequence(Vector[(-UnitOrthogonalVector[Element[cL_V, i]])], i, 1, nCones) → cL_p
13. Sequence(Element[cMovingPos, i] + (0.5 * Element[cL_V, i]) + (ctHeight * Element[cL_p, i]), i, 1, nCones) → cL_c
14. Sequence(Rotate[cRight, (i * cAngle / nCones), cMid], i, 0, nCones) → cLstartPos
15. Sequence(CircleSector[Element[cL_c, i], Element[cMovingPos, i + 1], Element[cMovingPos, i]], i, 1, nCones / 2) → cmSegmentA
16. Sequence(CircleSector[Element[cL_c, i], Element[cMovingPos, i + 1], Element[cMovingPos, i]], i, nCones / 2 + 1, nCones) → cmSegmentB
17. Translate(Element[cMovingPos, nCones / 2 + 1], (Min[(2 * k'), 1] * (Element[cL_c, 2] - Element[cMovingPos, 2]))) → cstage2Location
18. Vector(Rotate[(-1, 0), ((k' * 180))°]) → cstage2Direction
19. If(¬stage1, Zip[Rotate[B, ((k' * 180))°, cstage2Location], B, Zip[Translate[A, cStage2Translate], A, cmSegmentA]]) → cmSegmentA2
20. Line(O + (0, Radius), xAxis) → q1TopSide
21. Line(O - (0, ctHeight + gap - SlantHeight), xAxis) → q2TopSide
22. Line((0, (-gap) - SlantHeight), xAxis) → q2BottomSide
23. Intersect(Line[Q2topleft, cStage2Translate], q2BottomSide) → Q2bottomleft
24. Intersect(Line[Q2topright, cStage2Translate], q2BottomSide) → Q2bottomright
25. Polygon(Q2topleft, Q2bottomleft, Q2bottomright, Q2topright) → Q2, q2topleft, q2bottomleft, q2bottomright, q2topright
26. Segment(O, cMid) → SlantDisplay
27. LaTeX("\text{\textbf{Instructions: }Use the first slider to divide the lateral area into sections. \\Use the second slider to rearrange the sections.") → SpecInstruc
28. If(k < 1, (-2, 0) + (0, (k * 0.5)), Rotate[Translate[(-2, 1), Vector[(cStage2Translate * 1.3)]], ((k' * 45))°, (1, 0)]) → A
29. LaTeX("\text{\textbf{Question: }What happens when the lateral area of a cone is divided into sections and\\rearranged? What are the dimensions of the parallelogram? What is the total area \\of the net?}") → MainInstruc