Golden Section Division of a Line Segment

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2021-10-13 01:22

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This example demonstrates how to divide a line segment into the golden ratio. Key math concepts include geometric construction, similarity transformation, coordinate geometry, and the golden ratio. Construction highlights involve commands like Segment, OrthogonalLine, Point, Midpoint, Circle, and Intersect. Suitable for high school and above students to understand the construction and application of the golden ratio.

GeoGebra Commands & Parameters

Segment(A, B) → f
OrthogonalLine(B, f) → g
Point(g) → p
Midpoint(f) → S
Circle(B, S) → c
Intersect(c, g, 2) → C
Segment(B, C) → h
Segment(A, C) → i
Circle(C, B) → d
Intersect(d, i) → D,
Segment(D, C) → j
Circle(A, D) → e
Intersect(e, f) → E,
Segment(A, E) → k
Segment(E, B) → l

AI Drawing Prompt Reference

Draw a line segment and divide it into two parts according to the golden ratio. Key objects include the segment, a perpendicular line, a point, a midpoint, a circle, and intersection points. The construction order starts with the segment, then the perpendicular line, the midpoint, and uses the circle and intersection points to determine the division point. Finally, show line segments from the start to the division point and from the division point to the end.

The prompt above was compiled from the original drawing commands and is for reference only.