Quadrature of the Rectangle
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Functions on the Domain of Space - Polygons
This example demonstrates the geometric method to transform the area of a rectangle into a square. It involves core mathematical concepts such as geometric construction, similar triangles, area calculation, and the concept of limits. The construction utilizes GeoGebra commands and objects like Polygon, Circle, Ray, Intersect, Segment, Midpoint, Semicircle, and OrthogonalLine. It is suitable for high school mathematics education, helping students understand geometric transformations and the application of limit ideas in area problems.
GeoGebra Commands & Parameters
Polygon(B, C, A, D) → poly1, b, c, a, dCircle(B, d) → eRay(C, B) → fIntersect(e, f) → E, FSegment(C, F) → gMidpoint(g) → GSemicircle(C, F) → hOrthogonalLine(B, g) → iIntersect(h, i) → H,Polygon(H, B, 4) → poly2, j, k, l, m, I, JSegment(G, H) → nSegment(C, G) → pSegment(B, F) → qSegment(D, B) → r