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Dürer 2 Math Example

Dürer 2 Math Example
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2022-07-20 16:59
TrigonometryCoordinate GeometrySolid GeometryComplex NumberGeometric Construction
In collections circles, ovals, ellipses and architecture
This example demonstrates complex geometric constructions and transformations based on Dürer's geometry; involves core math concepts like cosine, sphere, complex numbers, coordinate geometry, quadrilaterals; constructed using GeoGebra commands such as Point, Semicircle, Polygon, Sequence, Intersect, Midpoint, Conic, Focus, Translate; suitable for high school students and geometry enthusiasts exploring advanced geometric constructions and higher math applications.

GeoGebra Commands & Parameters

  1. Point(xAxis) → D
  2. Point(xAxis) → C
  3. Semicircle(C, D) → c
  4. Point(yAxis) → B
  5. Polygon(A, B, D, C) → vierhoek1, a, b, d, c_1
  6. Sequence(Segment[(-12 + nn, 0), (-12 + nn, 6)], nn, 1, 11) → l1
  7. Point(xAxis) → E
  8. Point(Ray[(14, 0), (15, 0)]) → H
  9. Polygon(E, F, G, H) → vierhoek2, e, g, h, f
  10. Sequence(Segment[(2 + (nn * f / 12), 0), (2 + (nn * f / 12), 6)], nn, 1, 11) → l2
  11. Sequence(Intersect[c, l1(nn)], nn, 1, 5) → l3
  12. Sequence(Segment[l3(nn), (x(H), y(l3(nn)))], nn, 1, 5) → l4
  13. Intersect(l4(1), l2(1)) → I
  14. Intersect(l4(1), l2(11)) → J
  15. Intersect(l4(2), l2(2)) → K
  16. Intersect(l4(2), l2(10)) → L
  17. Intersect(l4(3), l2(3)) → M
  18. Intersect(l4(3), l2(9)) → N
  19. Intersect(l4(4), l2(4)) → O
  20. Intersect(l4(4), l2(8)) → P
  21. Intersect(l4(5), l2(5)) → Q
  22. Intersect(l4(5), l2(7)) → R
  23. Midpoint(F, G) → S
  24. Conic(E, I, K, M, O) → k
  25. Focus(k) → T, U
  26. Midpoint(E, H) → V
  27. Translate(p, Vector[D, V]) → p_{1}

AI Drawing Prompt Reference

Draw a complex geometric figure based on Dürer's geometry, including a semicircle and two quadrilaterals with intersecting line segments. Start by creating points D and C on the x-axis and drawing a semicircle c with C and D as endpoints. Then create point B on the y-axis and draw quadrilateral vierhoek1 with vertices A, B, D, and C. Next, create point E on the x-axis and point H on a ray, and draw quadrilateral vierhoek2 with vertices E, F, G, and H. Construct a series of line segments and find intersection points I, J, K, L, M, N, O, P, Q, and R. Draw an ellipse k with vertices E, I, K, M, and O, and find foci T and U. Finally, find the midpoint V of E and H, and translate point D to V.
The prompt above was compiled from the original drawing commands and is for reference only.