Logarithmic Transformation (4)
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Exploring Exponential & Logarithmic Functions
Exploring Exponential & Logarithmic Functions
This example illustrates the power property of logarithms through dynamic exploration. It uses commands like Dilate, Segment, Distance, Midpoint, Circle, Intersect, Vector, Translate, and Rotate in GeoGebra. Suitable for high school math education and learning.
GeoGebra Commands & Parameters
Dilate(A, If[0 < c ≤ 1, 1 - c, 0], B) → A'Segment(A, A') → gDistance(A, B) → distanceABMidpoint(C, D) → ISegment(F, E) → hCircle(F, h / 3) → dIntersect(d, h, 1) → JMidpoint(J, E) → KDilate(C, If[1 < c ≤ 2, 2 - c, 0], I) → C'Segment(C, C') → iDilate(I, If[2 < c ≤ 3, 3 - c, 0], D) → I'Segment(I, I') → jDistance(C, D) → distanceCDDistance(C, D) → eDistance(F, E) → distanceFEMidpoint(H, G) → LDilate(F, If[3 < c ≤ 4, 4 - c, 0], J) → F'Dilate(J, If[4 < c ≤ 5, 5 - c, 0], K) → J'Dilate(K, If[5 < c ≤ 6, 6 - c, 0], E) → K'Segment(F, F') → nSegment(J, J') → pSegment(K, K') → qDilate(H, If[6 < c ≤ 7, 7 - c, 0], L) → H'Dilate(L, If[7 < c ≤ 8, 8 - c, 0], G) → L'Segment(H, H') → rSegment(L, L') → sDistance(H, G) → distanceHGDilate(B, If[8 < c ≤ 9, 9 - c, 0], I) → B'Dilate(B, If[9 < c ≤ 10, 10 - c, 0], D) → B'_1Vector(B, B') → uTranslate(A, u) → A'_1Translate(A', u) → A''Segment(A'_1, A'') → g'Vector(B, B'_1) → vTranslate(A, v) → A'_2Translate(A', v) → A''_1Segment(A'_2, A''_1) → g'_1Dilate(C, If[10 < c ≤ 11, 11 - c, 0], F) → C'_1Vector(C, C'_1) → wTranslate(A'_1, w) → OTranslate(A'', w) → A'''Segment(O, A''') → g''Rotate(O, If[11 < c ≤ 12, ((-(c - 11)) * π), (-π)], J) → O'Rotate(A''', If[11 < c ≤ 12, ((-(c - 11)) * π), (-π)], J) → MSegment(O', M) → g'''Rotate(O', If[12 < c ≤ 13, ((-(c - 12)) * π), (-π)], K) → O''Rotate(M, If[12 < c ≤ 13, ((-(c - 12)) * π), (-π)], K) → M'Segment(O'', M') → tDilate(F, If[13 < c ≤ 14, 14 - c, 0], H) → F'_1Vector(F, F'_1) → u_1Translate(O, u_1) → O'_1Translate(A''', u_1) → NSegment(O'_1, N) → g'''_1Translate(O', u_1) → O''_1Translate(M, u_1) → M'_1Segment(O''_1, M'_1) → f_1Translate(O'', u_1) → O'''Translate(M', u_1) → M''Segment(O''', M'') → t'Rotate(O''', If[14 < c ≤ 15, ((-(c - 14)) * π), (-π)], M'') → PRotate(M'', If[14 < c ≤ 15, ((-(c - 14)) * π), (-π)], M'') → M'''Segment(P, M''') → t''Textfield(b) → InputBox1
AI Drawing Prompt Reference
Draw a logarithmic transformation figure by first performing a dilation with point A as the center and point B as the scaling center to generate point A'. Then, connect A and A' to form segment g. Calculate the distance of AB and find the midpoint I of segment g. Continue constructing a series of segments and circles through scaling and rotation operations, ultimately forming a series of interconnected segments and points to demonstrate the properties of logarithmic transformations.
The prompt above was compiled from the original drawing commands and is for reference only.