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Fractions in the Circle

Fractions in the Circle
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2020-05-28 16:30
Circle
This example demonstrates the concept of fractions in a circle. It involves key math concepts such as fractions, equilateral triangles, and inequalities. Using GeoGebra commands like Circle, Rotate, Segment, Angle, and CircleSector, the construction of fractions in a circle is illustrated. Suitable for middle school and above students to learn geometric construction.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Rotate(B, (360°) / Denumerator, A) → B'
  3. Rotate(B', (360°) / Denumerator, A) → B''
  4. Rotate(B'', (360°) / Denumerator, A) → B'''
  5. Rotate(B''', (360°) / Denumerator, A) → C
  6. Rotate(C, (360°) / Denumerator, A) → C'
  7. Rotate(C', (360°) / Denumerator, A) → C''
  8. Rotate(C'', (360°) / Denumerator, A) → C'''
  9. Rotate(C''', (360°) / Denumerator, A) → D
  10. Rotate(D, (360°) / Denumerator, A) → D'
  11. Rotate(Rotate[Rotate[Rotate[Rotate[Rotate[Rotate[Rotate[Rotate[Rotate[B, (360°) / Denumerator, (10, 4)], (360°) / Denumerator, (10, 4)], (360°) / Denumerator, (10, 4)], (360°) / Denumerator, (10, 4)], (360°) / Denumerator, (10, 4)], (360°) / Denumerator, (10, 4)], (360°) / Denumerator, (10, 4)], (360°) / Denumerator, (10, 4)], (360°) / Denumerator, (10, 4)], (360°) / Denumerator, (10, 4)) → E
  12. Rotate(E, (360°) / Denumerator, A) → E'
  13. Rotate(E', (360°) / Denumerator, A) → E''
  14. Segment(B, A) → f
  15. Segment(B', A) → g
  16. Segment(B'', A) → h
  17. Segment(B''', A) → i
  18. Segment(C, A) → j
  19. Segment(C', A) → k
  20. Segment(C'', A) → l
  21. Segment(C''', A) → m
  22. Segment(D, A) → n
  23. Segment(D', A) → p
  24. Segment(E, A) → q
  25. Segment(E', A) → r
  26. Rotate(B, (360° * Numerator / Denumerator), A) → B'_1
  27. Angle(B, A, B'_1) → α
  28. CircleSector(A, B, B'_1) → d