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TR KAY Fractions: Fraction-Triangle-Trigonometry Correlation Demo

TR KAY Fractions: Fraction-Triangle-Trigonometry Correlation Demo
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2016-12-15 13:54
TrianglePolygonFunctionTrigonometrySequence
This GeoGebra example constructs a scalene triangle and uses its side-length ratios to generate fraction sequences, while integrating trigonometric functions, distributions, and indefinite integrals to reveal connections between fractions and geometric figures. Core mathematical concepts include fraction representation, scalene triangle side relationships, trigonometric functions (e.g., sine, cosine) in ratio calculations, and visualization of fractions via sequences and distributions. Construction highlights: using Point, Sequence, Segment, and Polygon commands to create the triangle and its vertices; storing fraction values in lists (liste1, liste2, liste3); employing functions f, g, h and objects j, k, l, m to plot related curves or shapes; and labeling fractions with text (metin1). Suitable for upper secondary or early university students, this example helps explore integrated applications of fractions, geometry, and trigonometry, and can serve as a cross-disciplinary teaching or modeling resource.

GeoGebra Commands & Parameters

  1. Point(yAxis) → A
  2. Sequence((x(A) + (i * x(D) / denominator), y(D)), i, 1, denominator) → liste1
  3. Point(yAxis) → B
  4. Sequence((x(B) + (i * x(C) / denominator), y(B)), i, 1, denominator) → liste2
  5. Segment(A, D) → f
  6. Segment(A, B) → g
  7. Segment(B, C) → h
  8. Polygon(B, A, Element[liste1, paid], Element[liste2, paid]) → çokgen1, j, k, l, m
  9. Segment(C, D) → i
  10. Sequence(Segment[Element[liste1, i], Element[liste2, i]], i, 1, denominator) → liste3