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Christmas card 7: Geometric Construction and Trigonometric Functions

Christmas card 7: Geometric Construction and Trigonometric Functions
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2021-09-13 03:53
TrigonometryInequalityGeometric Construction
In collections STEAM like Leonardo
This example demonstrates geometric construction using GeoGebra, integrating trigonometric functions and inequality concepts. Key mathematical concepts include triangle properties, trigonometric function graphs, and inequality solving. Construction involves commands like Segment, Sequence, and application of tags such as Prism, Nierówności. Suitable for high school students or college freshmen to learn foundational geometry and trigonometry, and understand geometric construction in mathematics.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. Segment(A, C) → g
  3. Sequence(A + (i / n * (B - A)), i, 1, n) → l1, {(-1.924, -4.1882248672916385), (-1.928, -3.6890659481993784), (-1.932, -3.1899070291071183), (-1.936, -2.6907481100148587), (-1.94, -2.191589190922599), (-1.944, -1.6924302718303386), (-1.948, -1.193271352738079), (-1.952, -0.6941124336458193), (-1.956, -0.1949535145535597), (-1.96, 0.30420540453869993), (-1.964, 0.8033643236309596), (-1.968, 1.302523242723221), (-1.972, 1.8016821618154806), (-1.976, 2.30084108090774), (-1.98, 2.8)}
  4. Sequence(A + (i / n * (C - A)), i, 1, n) → l2, {(-1.3853333333333333, -4.6833837863838985), (-0.8506666666666667, -4.679383786383898), (-0.31599999999999984, -4.6753837863838985), (0.21866666666666656, -4.671383786383898), (0.753333333333333, -4.6673837863838985), (1.2880000000000003, -4.663383786383898), (1.8226666666666667, -4.6593837863838985), (2.357333333333333, -4.655383786383898), (2.8919999999999995, -4.6513837863838985), (3.426666666666666, -4.647383786383898), (3.9613333333333323, -4.6433837863838985), (4.496, -4.639383786383898), (5.030666666666667, -4.6353837863838985), (5.565333333333333, -4.631383786383898), (6.1, -4.6273837863838985)}
  5. Sequence(Segment[Element[l1, i], Element[l2, n - i]], i, 1, n) → l3, {7.50243317899925, 7.0227173678458685, 6.589398065824041, 6.212191765317101, 5.901867349086053, 5.669418127223363, 5.52468258041275, 5.474621936288361, 5.5218117583099255, 5.663821753999343, 5.893801883834325, 6.201973593030554, 6.5773554160736944, 7.009157161029136, NaN}
  6. Segment(B, D) → h
  7. Segment(D, C) → i
  8. Sequence(D + (i / n * (B - D)), i, 1, n) → l4, {(5.3933333333333335, 2.8), (4.866666666666666, 2.8), (4.34, 2.8), (3.813333333333333, 2.8), (3.2866666666666666, 2.8), (2.76, 2.8), (2.233333333333333, 2.8), (1.706666666666666, 2.8), (1.1799999999999997, 2.8), (0.6533333333333333, 2.8), (0.12666666666666693, 2.8), (-0.40000000000000036, 2.8), (-0.9266666666666676, 2.8), (-1.453333333333334, 2.8), (-1.9800000000000004, 2.8)}
  9. Sequence(D + (i / n * (C - D)), i, 1, n) → l5, {(5.9319999999999995, 2.3048410809077398), (5.944, 1.8096821618154801), (5.9559999999999995, 1.31452324272322), (5.968, 0.8193643236309602), (5.9799999999999995, 0.3242054045387004), (5.992, -0.17095351455355967), (6.004, -0.6661124336458193), (6.016, -1.1612713527380794), (6.028, -1.656430271830339), (6.04, -2.151589190922599), (6.052, -2.646748110014858), (6.064, -3.141907029107119), (6.076, -3.6370659481993792), (6.088, -4.132224867291638), (6.1, -4.6273837863838985)}
  10. Sequence(Segment[Element[l1, i], Element[l4, n - i]], i, 1, n) → l6, {7.004056960572518, 6.565869731004808, 6.182718675254993, 5.865399269053174, 5.625063593303911, 5.471864924069088, 5.4132064934789845, 5.452140571378311, 5.586627117889353, 5.810034575959505, 6.112620916480434, 6.483309389392439, 6.911150431282421, 7.386219154905109, NaN}
  11. Sequence(Segment[Element[l2, i], Element[l5, n - i]], i, 1, n) → l7, {7.493629779032726, 7.004651139557827, 6.561703358512035, 6.1747005919157, 5.854747380630247, 5.613320714041377, 5.460845634411571, 5.404855567316714, 5.448325928276839, 5.588936409945056, 5.819650163418935, 6.1303025138447405, 6.509458722076431, 6.945909577159736, NaN}
  12. Sequence(Segment[Element[l4, i], Element[l5, n - i]], i, 1, n) → l8, {6.966943618867196, 6.549679773285034, 6.186956856367482, 5.888861810094959, 5.665604995065043, 5.526264087761806, 5.477247286834372, 5.520960892856598, 5.655254970877808, 5.873920041734749, 6.167989363935135, 6.527279463636403, 6.9416705384994275, 7.401913995690645, NaN}

AI Drawing Prompt Reference

Draw a geometric figure consisting of two triangles and multiple line segments. One triangle has vertices on the x-axis, and the other on the y-axis. Connect corresponding vertices of these triangles with line segments to create a complex geometric structure. Pay attention to the lengths and positional relationships of the line segments, as well as the symmetry and layering of the overall figure.
The prompt above was compiled from the original drawing commands and is for reference only.