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Year Zoom: Dynamic Demonstration of Geometry and Functions

Year Zoom: Dynamic Demonstration of Geometry and Functions
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2015-03-04 01:57
FunctionSequenceGeometric Construction
In collections Elementary School Applets
The Year Zoom example demonstrates the dynamic interaction between geometric figures and function graphs. Key mathematical concepts include geometric construction, function graphing, and sequences and series. Construction involves GeoGebra commands such as Segment, Sequence, Element, Join, If, Length, and Midpoint using objects like B, C, D, c, E, d, F, e, G, f, H, g, I, h, J, i, K, j, L, k, M, rightmonthpoint, m, l, list1, rightmonth, A, leftmonthpoint, rightday, b, monthlength, daypoints, hourpoints, righthour, minutepoints, rightminute, leftmonth, leftday, lefthour, leftminute. This example is suitable for high school or university mathematics courses to understand the integration of geometry and functions.

GeoGebra Commands & Parameters

  1. Segment(C, D) → c
  2. Segment(D, E) → d
  3. Segment(E, F) → e
  4. Segment(F, G) → f
  5. Segment(G, H) → g
  6. Segment(H, I) → h
  7. Segment(I, J) → i
  8. Segment(J, K) → j
  9. Segment(K, L) → k
  10. Segment(M, B) → m
  11. Segment(L, M) → l
  12. Sequence(375 - ((375 - Element[rightmonthpoint, Element[list1, 6]] - 5) / 10 * i), i, 0, 10) → rightmonth
  13. Sequence((Element[rightmonth, 11] * (1 - i)) + ((Element[leftmonthpoint, Element[list1, 6]] + Element[list1, 5] + 0.2) * i), i, 0, 1, 0.1) → rightday
  14. Segment(A, C) → b
  15. Element({b, c, d, e, f, g, h, i, j, k, l, m}, Element[list1, 6]) → monthlength
  16. Sequence(Point[{Element[leftmonthpoint, Element[list1, 6]] + i, 0}], i, 0, monthlength) → daypoints
  17. Sequence(Point[{x(Element[daypoints, Element[list1, 5]]) + i, 0}], i, 0, 1.0416666666666667, 0.04167) → hourpoints
  18. Sequence((Element[rightday, 11] * (1 - i)) + ((x(Element[hourpoints, Element[list1, 4] + 2]) + 0.01) * i), i, 0, 1, 0.1) → righthour
  19. Sequence((x(Element[hourpoints, Element[list1, 4] + 1]) + (1 / ((24 * 60)) * i), 0), i, 0, 60) → minutepoints
  20. Join({{Element[righthour, 11], Element[righthour, 11], Element[righthour, 11]}, Sequence[(Element[righthour, 11] * (1 - i)) + ((x(Element[minutepoints, Element[list1, 3] + 2]) + 0.0001) * i), i, 0, 1, 0.1]}) → rightminute
  21. Sequence(-10 + ((Element[leftmonthpoint, Element[list1, 6]] + 5) / 10 * i), i, 0, 10) → leftmonth
  22. Sequence((Element[leftmonth, 11] * (1 - i)) + ((Element[leftmonthpoint, Element[list1, 6]] + Element[list1, 5] - 1.2) * i), i, 0, 1, 0.1) → leftday
  23. Sequence((Element[leftday, 11] * (1 - i)) + ((x(Element[hourpoints, Element[list1, 4] + 1]) - 0.01) * i), i, 0, 1, 0.1) → lefthour
  24. Join({{Element[lefthour, 11], Element[lefthour, 11], Element[lefthour, 11]}, Sequence[(Element[lefthour, 11] * (1 - i)) + ((x(Element[minutepoints, Element[list1, 3] + 1]) - 0.0001) * i), i, 0, 1, 0.1]}) → leftminute
  25. Join({{-10}, leftmonth, {Element[leftmonth, 11], Element[leftmonth, 11]}, leftday, {Element[leftday, 11], Element[leftday, 11], Element[leftday, 11], Element[leftday, 11]}, lefthour, leftminute}) → left
  26. Segment(A, B) → a
  27. Element({"January", "February", "March", "April", "May", "June", "July", "August", "September", "October", "November", "December"}, Element[list1, 6]) → monthname
  28. Join({{375}, rightmonth, {Element[rightmonth, 11], Element[rightmonth, 11]}, rightday, {Element[rightday, 11], Element[rightday, 11], Element[rightday, 11], Element[rightday, 11]}, righthour, rightminute}) → right
  29. Sequence(Segment[Element[daypoints, i], Element[daypoints, i + 1]], i, 1, monthlength) → list2
  30. Element(list2, Element[list1, 5]) → daysegment
  31. Element(list1, 5) → daytext
  32. Segment(Element[hourpoints, 1], Element[hourpoints, 13]) → amsegment
  33. Segment(Element[hourpoints, 13], Element[hourpoints, 25]) → pmsegment
  34. Segment(Element[hourpoints, Element[list1, 4] + 1], Element[hourpoints, Element[list1, 4] + 2]) → hoursegment
  35. If(Mod[Element[list1, 4], 12] ≟ 0, 12, Mod[Element[list1, 4], 12]) → hour
  36. If(Element[list1, 4] < 12, "AM", "PM") → amorpm
  37. Sequence(If[i < 11, Text["0" + (i - 1), (x(Element[minutepoints, i]), 4)], Text[i - 1, (x(Element[minutepoints, i]), 4)]], i, 1, 60) → minutenumbers
  38. Element(left, step) → leftbound
  39. Element(right, step) → rightbound
  40. Length(left) → leftlength
  41. Length(right) → rightlength
  42. Segment(Element[minutepoints, Element[list1, 3] + 1], Element[minutepoints, Element[list1, 3] + 2]) → minutesegment
  43. Element(minutenumbers, Element[list1, 3] + 1) → minute
  44. Sequence(Text[If[Mod[12 + i, 12] ≟ 0, 12, Mod[12 + i, 12]], (x(Element[hourpoints, 1 + i]) - 0.0005, 4)], i, 0, 24) → hournumbers
  45. Sequence(Text[i, (x(Element[daypoints, 1]) - 0.5 + i, 5)], i, 1, monthlength) → list3
  46. Midpoint(minutesegment) → X

AI Drawing Prompt Reference

Create a dynamic calendar time visualization showing the geometric relationship between months, days, hours, and minutes. The left side displays past month dates and time scales, while the right side shows the current month's dates and time scales, connected by function graphs in the middle. Use different colors and line thicknesses to distinguish months, days, hours, and minutes, and label numbers. The overall design presents a complete yearly time cycle, emphasizing the dynamic interaction between geometric construction and function graphs.
The prompt above was compiled from the original drawing commands and is for reference only.