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Size of Square Roots

Size of Square Roots
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2019-08-27 11:27
PolygonFunctionSequenceGeometric ConstructionGraphing
This example demonstrates the relationship between square roots and the side lengths of squares, visually represented through a scatter plot. It involves core mathematical concepts such as square roots, functions, ellipses, rhombuses, and polygon constructions. Key GeoGebra commands and objects used include Polygon, DivisorsList, Factors, Sequence, RemoveUndefined, Last, and Element. Suitable for high school mathematics education, helping students understand the connection between function graphs and geometric shapes, and enhancing spatial reasoning skills.

GeoGebra Commands & Parameters

  1. Polygon((0, 0), (a, 0), 4) → poly1
  2. DivisorsList(n) → list1
  3. Factors(n) →
  4. Sequence(sqrt(Element[list1, i]), i, 1, Length[list1]) → list2
  5. Sequence(Div[Element[list2, i], 1], i, 1, Length[list2]) → list3
  6. Sequence(If[Element[list2, i] ≟ Element[list3, i], Element[list3, i]], i, 1, Length[list3]) → list4
  7. RemoveUndefined(list4) → list5
  8. Last(list5) → list7
  9. Element(list7, 1) → A
  10. Sequence(Segment[((sqrt(n) * i / A), 0), ((sqrt(n) * i / A), sqrt(n))], i, 0, A) → list6
  11. Sequence(Segment[(0, (sqrt(n) * i / A)), (sqrt(n), (sqrt(n) * i / A))], i, 0, A) → list8
  12. Polygon((0, 0), (sqrt(n) / A, 0), (sqrt(n) / A, sqrt(n) / A), (0, sqrt(n) / A)) → poly2, c, d, e, f