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Universal Abacus

Universal Abacus
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2015-10-16 23:51
FunctionSequenceCoordinate GeometryGeometric ConstructionSlider Animation
In collections Arithmetic Operations (preGED)
This example demonstrates a versatile abacus capable of operating in various bases from binary to hexadecimal. It involves core mathematical concepts like base conversion, modular arithmetic, and geometric constructions. The construction utilizes GeoGebra commands and objects such as If, Mod, Segment, Sequence, and Point. It is suitable for high school students and math enthusiasts for teaching base conversion and algorithm visualization.

GeoGebra Commands & Parameters

  1. If(z ≟ 3, num, num1) → nu
  2. Mod(num, base) → d1
  3. Mod(Div[num, base], base) → d2
  4. Mod(Div[Div[num, base], base], base) → d3
  5. Mod(Div[Div[Div[num, base], base], base], base) → d4
  6. Mod(Div[Div[Div[Div[num, base], base], base], base], base) → d5
  7. Mod(Div[Div[Div[Div[Div[num, base], base], base], base], base], base) → d6
  8. Mod(Div[Div[Div[Div[Div[Div[num, base], base], base], base], base], base], base) → d7
  9. Mod(Div[Div[Div[Div[Div[Div[Div[num, base], base], base], base], base], base], base], base) → d8
  10. Mod(Div[Div[Div[Div[Div[Div[Div[Div[num, base], base], base], base], base], base], base], base], base) → d9
  11. Mod(Div[Div[Div[Div[Div[Div[Div[Div[Div[num, base], base], base], base], base], base], base], base], base], base) → d10
  12. Segment((3.5, -3.6), (14.5, -3.6)) → a
  13. Segment((5.4, -3.6), (11.4, -3.6)) → b
  14. Segment((5.4, -3.6), (12, -3.6)) → c
  15. Sequence(Segment[(5 + (1.1 * t), (-3.6)), (5 + (1.1 * t), (-3.5) + 9.5)], t, 1, 2) → L25
  16. Sequence(Segment[(5.8 + (1.1 * t), (-3.6)), (5.8 + (1.1 * t), (-3.5) + 9.5)], t, 3, 5) → L26
  17. Sequence(Sequence[(4.5 + t, s), t, 0, 10], s, -4, 4, 4) → L31
  18. Sequence(Segment[(4.3, s), (14.7, s)], s, -4, 4, 4) → L32
  19. Sequence({(4.5, s), (14.5, s)}, s, -4, 4, 4) → L33
  20. Segment((4.2, -3.7), (14.8, -3.7)) → d
  21. Point(d) → B
  22. Segment((4.2, 0.3), (14.8, 0.3)) → e
  23. Segment((4.2, 4.3), (14.8, 4.3)) → f
  24. Point(e) → C
  25. Point(f) → D
  26. Sequence(Sequence[Translate[cuenta, Vector[(11.7 - (1.1 * t), s - 4.05)]], s, 1, Element[L11, t]], t, 1, 7) → lista1
  27. Sequence(Sequence[Translate[cuenta, Vector[(11.6 - (1.1 * t), s - 4.05)]], s, 1, Element[L11, t]], t, 4, 5) → lista3
  28. Sequence(Sequence[Translate[cuenta, Vector[(12.4 - (1.1 * t), s - 4.05)]], s, 1, Element[L11, t]], t, 1, 3) → lista4
  29. Sequence(Sequence[Translate[cuentap, Vector[(15 - (1.1 * t), (0.6 * s) - 3.85)]], s, 1, Element[L01, t]], t, 1, 10) → lista2
  30. Sequence(Segment[(5.1 + (1.1 * t), (-3.6)), (5.1 + (1.1 * t), (-3.5) + 9.5)], t, 1, 5) → L12
  31. Sequence(Segment[(2.9 + (1.1 * t), (-3.6)), (2.9 + (1.1 * t), (-3.5) + Min[base, 10] - 0.5)], t, 1, 10) → L02

AI Drawing Prompt Reference

This is a geometric illustration of converting a multi-digit decimal number from binary to hexadecimal. The figure includes colored blocks representing digits, which are moved and rotated to show the conversion process. There are line segments and points that represent conversion steps, along with a central point to mark the final result. The construction order starts with basic digit blocks and gradually adds and moves them to visualize each step of the conversion.
The prompt above was compiled from the original drawing commands and is for reference only.