勾股定理演示 by txywishes
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①本范例通过动态演示直角三角形三边关系验证勾股定理;②涉及核心数学概念包括勾股定理、直角三角形、几何作图;③构造过程中运用了点、线段、圆、正方形、向量、平移、旋转等GeoGebra命令与对象;④适合初中及以上学生及数学爱好者用于理解勾股定理及其应用。
GeoGebra 命令及参数
PointIn(a) → BCircle(A, B) → cSegment(A, B) → sABOrthogonalLine(A, sAB) → perpLineAIntersect(c, perpLineA, 1) → C_1Polygon(A, B, 4) → sqSmall, f, g, h, i, D, EPolygon({A, B, D, E}) → sqSmall2Centroid(sqSmall) → centreSqSmallVector(A, C_1) → uAC1Ray(C_1, uAC1) → horizRayPoint(horizRay) → CPolygon(B, C, 4) → sqBig, n, p, q, r, H, ICentroid(sqBig) → centreSqBigVector(centreSqSmall, centreSqBig) → vCentreSqSmallToBigPolygon(C, A, 4) → sqMed, j, k, l, m, F, GCentroid(sqMed) → centreSqMedOrthogonalLine(centreSqMed, n) → perpBCOrthogonalLine(centreSqMed, perpBC) → sIntersect(perpBC, j) → ptSqMedACIntersect(s, m) → ptSqMedCGIntersect(perpBC, l) → ptSqMedFGIntersect(s, k) → ptSqMedAFVector(centreSqMed, B) → vCentreSqMedToBVector(centreSqMed, C) → vCentreSqMedToCVector(centreSqMed, I) → vCentreSqMedToIVector(centreSqMed, H) → vCentreSqMedToHPolygon({C, ptSqMedCG, centreSqMed, ptSqMedAC}) → quadCPolygon({G, ptSqMedFG, centreSqMed, ptSqMedCG}) → quadGPolygon({F, ptSqMedAF, centreSqMed, ptSqMedFG}) → quadFPolygon({A, ptSqMedAC, centreSqMed, ptSqMedAF}) → quadATranslate(quadA, Vector[(paramMoveToC / 100 * vCentreSqMedToC)]) → quadAMoveTranslate(quadC, Vector[(paramMoveToB / 100 * vCentreSqMedToB)]) → quadCMoveTranslate(quadF, Vector[(paramMoveToH / 100 * vCentreSqMedToH)]) → quadFMoveTranslate(sqSmall2, Vector[(paramMoveSmall / 100 * vCentreSqSmallToBig)]) → sqSmall2MoveTranslate(quadG, Vector[(paramMoveToI / 100 * vCentreSqMedToI)]) → quadGMoveAngle(C, A, B) → αPolygon({A, B, C}) → triPolygon({B, C, H, I}) → sqBigBgTextfield(ans) → InputBox1
AI 绘图提示语参考
画一个直角三角形,并在其两条直角边和斜边上分别作正方形。通过动态演示,展示三个正方形的面积关系验证勾股定理,包含点、线、圆、向量、旋转和平移等几何构造,适合理解勾股定理及其应用。
以上提示语为根据原始绘图命令整理而来,仅供参考。