DesCartesian Division (via Newton's Method)

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2017-03-22 09:28

Vector Coordinate Geometry

This example illustrates the concept of DesCartesian division, involving the division of rational numbers. Using GeoGebra commands such as Point, Intersect, Segment, Vector, Line, etc., specific geometric shapes are constructed. This example is suitable for high school mathematics education, helping students understand the geometric meaning of rational number division.

GeoGebra Commands & Parameters

Point(xAxis) → A
Intersect(xAxis, yAxis) → O
Segment(O, A) → a
Point(yAxis) → B
Segment(O, B) → b
Segment(A, B) → d
Vector(A, B) → u
Vector(B, A) → v
Point(yAxis) → C
Segment(C, O) → f
Line(C, v) → g
Point(f) → D
Point(xAxis) → E
Ray(D, E) → h
Intersect(g, h) → F
Vector(C, F) → w
Line(C, F) → i
Line(C, v) → j
Point(xAxis) → G
Ray(A, G) → k
Intersect(j, k) → H
Segment(H, C) → l
Vector(C, H) → c
Segment(F, D) → m
Segment(H, D) → n
Segment(C, F) → p
Segment(C, H) → q
Point(v) → I
Point(v) → J
Segment(I, J) → r
Segment(B, A) → s
Point(r) → L
Line(B, L) → t
Line(H, C) → e
Intersect(f, n) → M
Line(C, F) → f_1

AI Drawing Prompt Reference

Draw the x-axis and y-axis, take a point on the x-axis, and connect the origin to this point to form a segment. Take a point on the y-axis, connect the origin to this point to form a segment, and then connect the point on the x-axis to the point on the y-axis to form another segment. Draw a vector from the point on the x-axis to the point on the y-axis, and draw another vector from the point on the y-axis to the point on the x-axis. Take another point on the y-axis, draw a segment from this point to the origin along the y-axis, and draw a line through this point in the direction of the vector on the y-axis. Connect the intersection point to the point on the y-axis with a segment, and draw a ray from this point in the direction of the vector. Connect the intersection point to the point on the x-axis with a segment, and draw a ray from this point along the x-axis direction. Connect the intersection point to the point on the y-axis with a segment, and draw a line from this point in the direction of the vector. Take a point in the direction of the vector, and connect the two points to form a segment. Take another point on the x-axis, and draw a ray from the point on the x-axis along the x-axis direction. Connect the intersection point to the point on the y-axis with a segment, and draw a line from this point in the direction of the vector.

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