Demonstrating Unstable Balance
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This example dynamically demonstrates an unstable balance phenomenon through graphical transformations, visually presenting the relationship between equilibrium and tilting. Core mathematical concepts include vector operations, reflection transformations, sequence generation, and analytical geometry calculations of line segment intersections. Construction highlights the use of GeoGebra commands: Sequence, Vector, Mirror, Translate, Element, Line, Intersect, and Segment. Suitable for high school students learning vectors, transformations, and dynamic geometry, it can be used for mathematical modeling of physical mechanics principles.
GeoGebra Commands & Parameters
Sequence(1 / n, n, 1, k) → l1Sequence(Sum[l1, j], j, 0, k) → l2Sequence((1 / 2 * Element[l2, i]), i, 1, k) → l3Vector(((-Element[l3, k]) - 1, 0, (-0.1 * k)), (0, 0, 0)) → uSequence((Element[l3, i] + 1, -0.5, (0.1 * (i + 1))), i, 1, k - 1) → l5Sequence((Element[l3, i] + 1, 0.5, (0.1 * (i + 1))), i, 1, k - 1) → l6Sequence((Element[l3, i] + 2, -0.5, (0.1 * (i + 1))), i, 1, k - 1) → l5bSequence((Element[l3, i] + 2, 0.5, (0.1 * (i + 1))), i, 1, k - 1) → l6bSequence((Element[l3, i] + 2, -0.5, (0.1 * i)), i, 1, k - 1) → l7Sequence(Polygon[Element[l5, i], Element[l6, i], Element[l6b, i], Element[l5b, i]], i, 1, k - 1) → l8Sequence(Prism[Element[l8, i], 0.1], i, 1, Length[l8]) → l9Mirror(l9, (0, 0, 0)) → l9'Translate(l9', u) → l9''Element(l9'', A1) → B1Element(l9'', A2) → B2Element(l9'', A3) → B3Element(l9'', A4) → B4Element(l9'', A5) → B5Element(l9'', A6) → B6Element(l9'', A7) → B7Element(l9'', A8) → B8Element(l9'', A9) → B9Element(l9'', A10) → B10Element(l9'', A11) → B11Element(l9'', A12) → B12Element(l9'', A13) → B13Element(l9'', A14) → B14Element(l9'', A15) → B15Element(l9'', A16) → B16Element(l9'', A17) → B17Element(l9'', A18) → B18Element(l9'', A19) → B19Element(l9'', A20) → B20Element(l9'', A21) → B21Element(l9'', A22) → B22Element(l9'', A23) → B23Element(l9'', A24) → B24Element(l9'', A25) → B25Element(l9'', A26) → B26Element(l9'', A27) → B27Element(l9'', A28) → B28Element(l9'', A29) → B29Element(l9'', A30) → B30Element(l9'', A31) → B31Element(l9'', A32) → B32Element(l9'', A33) → B33Element(l9'', A34) → B34Element(l9'', A35) → B35Element(l9'', A36) → B36Element(l9'', A37) → B37Element(l9'', A38) → B38Element(l9'', A39) → B39Element(l9'', A40) → B40Element(l9'', A41) → B41Element(l9'', A42) → B42Element(l9'', A43) → B43Element(l9'', A44) → B44Element(l9'', A45) → B45Element(l9'', A46) → B46Element(l9'', A47) → B47Line(A, zAxis) → fIntersect(f, xOyPlane) → BSegment(A, B) → gMirror(l9'', g) → l9'''Mirror(B2, g) → C2Mirror(B3, g) → C3Mirror(B4, g) → C4Mirror(B5, g) → C5Mirror(B6, g) → C6Mirror(B7, g) → C7Mirror(B8, g) → C8Mirror(B9, g) → C9Mirror(B10, g) → C10Mirror(B11, g) → C11Mirror(B12, g) → C12Mirror(B13, g) → C13Mirror(B14, g) → C14Mirror(B15, g) → C15Mirror(B16, g) → C16Mirror(B17, g) → C17Mirror(B18, g) → C18Mirror(B19, g) → C19Mirror(B20, g) → C20Mirror(B21, g) → C21Mirror(B22, g) → C22Mirror(B23, g) → C23Mirror(B24, g) → C24Mirror(B25, g) → C25Mirror(B26, g) → C26Mirror(B27, g) → C27Mirror(B28, g) → C28Mirror(B29, g) → C29Mirror(B30, g) → C30Mirror(B31, g) → C31Mirror(B32, g) → C32Mirror(B33, g) → C33Mirror(B34, g) → C34Mirror(B35, g) → C35Mirror(B36, g) → C36Mirror(B37, g) → C37Mirror(B38, g) → C38Mirror(B39, g) → C39Mirror(B40, g) → C40Mirror(B41, g) → C41Mirror(B42, g) → C42Mirror(B43, g) → C43Mirror(B44, g) → C44Mirror(B45, g) → C45Mirror(B46, g) → C46Mirror(B47, g) → C47Element(l9'', A48) → B48Mirror(B48, g) → C48Element(l9'', A49) → B49Mirror(B49, g) → C49Element(l9'', A50) → B50Mirror(B50, g) → C50Element(l9'', A51) → B51Mirror(B51, g) → C51Element(l9'', A52) → B52Mirror(B52, g) → C52Element(l9'', A53) → B53Mirror(B53, g) → C53Element(l9'', A54) → B54Mirror(B54, g) → C54Element(l9'', A55) → B55Mirror(B55, g) → C55Element(l9'', A56) → B56Mirror(B56, g) → C56Element(l9'', A57) → B57Mirror(B57, g) → C57Element(l9'', A58) → B58Mirror(B58, g) → C58Element(l9'', A59) → B59Mirror(B59, g) → C59Element(l9'', A60) → B60Mirror(B60, g) → C60Mirror(B1, g) → C1