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Sum of First n Natural Numbers by Ng Yew Hong

Sum of First n Natural Numbers by Ng Yew Hong
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2017-07-10 07:23
VectorSequenceCoordinate GeometryGeometric ConstructionSlider Animation
This example demonstrates the sum of the first n natural numbers through graphical computation and verification. Core math concepts include sequence summation, coordinate geometry, and vector operations. Construction highlights involve commands like Sequence, Vector, Mirror, Translate, Element, and Segment in GeoGebra to visualize and validate the formula. Suitable for high school mathematics education to intuitively understand the geometric meaning of sequence summation formulas.

GeoGebra Commands & Parameters

  1. Sequence(Sequence[(i, k), k, 0, (d_1 * i) - 1, d_1], i, 1, n) → list2
  2. Sequence(Sequence[(i, k), k, 0, i], i, 1, n) → list3
  3. Sequence(Sequence[Polygon[Element[Element[list2, m], r], Element[Element[list3, m], r], 4], r, 1, m], m, 1, n) → list4
  4. Vector(C, D) → v
  5. Sequence((i, (-a1)), i, 0, n) → first
  6. Sequence(Sequence[Polygon[Element[Element[list2, i], r], Element[Element[list2, i + 1], r], (x(Element[Element[list2, i + 1], r]), y(Element[Element[list2, i + 1], r]) + d_1), (x(Element[Element[list2, i], r]), y(Element[Element[list2, i], r]) + d_1)], r, 1, i], i, 1, n + 2) → list6
  7. Sequence(Polygon[Element[first, i], Element[first, i + 1], (x(Element[first, i + 1]), y(Element[first, i + 1]) + a1), (x(Element[first, i]), y(Element[first, i]) + a1)], i, 1, n + 1 - 1) → list1
  8. Vector((0, 0), (0, 1)) → u
  9. Mirror(list6, O) → list6'
  10. Translate(list6', Vector[((-a1) * u)]) → list6''
  11. Mirror(list1, O) → list1'
  12. Translate(list1', Vector[((-a1) * u)]) → list1''
  13. Vector((-0.5, 0), (-0.5, ((n - 1) * d_1) + a1)) → w
  14. Vector((-0.5, ((n - 1) * d_1) + a1), (-0.5, 0)) → z
  15. Element(first, n + 1) → EE
  16. Mirror(EE, O) → EE'
  17. Segment(EE, EE') → c