GeoGebra Geometry and Calculus Example

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2022-07-03 17:49

This example demonstrates the integration of geometric and calculus concepts using GeoGebra. Key mathematical concepts include trigonometry, continuity, sequences and series, and geometric transformations. Construction involves commands like Textfield, Line, Intersect, Polygon, Function, and objects such as A1, A2, A3, A4. Suitable for high school students or college freshmen to learn foundational knowledge in geometry and calculus, and to master GeoGebra drawing techniques.

GeoGebra Commands & Parameters

Textfield(ax) → InputBox1
Textfield(bx) → InputBox2
Textfield(ay) → InputBox3
Textfield(by) → InputBox4
Textfield(b) → InputBox5
Line(A4, xAxis) → i
Line(A3, xAxis) → j
Line(A2, yAxis) → k
Line(A1, yAxis) → l
Intersect(i, l) → A
Intersect(i, k) → B
Intersect(k, j) → C
Intersect(l, j) → D
Polygon(A, B, C, D) → poly1, s, t, d, e
Segment(D', D) → m
Segment(C', C) → n1
Segment(B, B') → q
Segment(A', A) → r
Function(b, ax, bx, ay, by) → o
Surface(ax, s, (t * o(ax, s)), s, ay, by, t, 0, 1) → u1
Surface(bx, s, (t * o(bx, s)), s, ay, by, t, 0, 1) → u2
Surface(s, ay, (t * o(s, ay)), s, ax, bx, t, 0, 1) → u3
Surface(s, by, (t * o(s, by)), s, ax, bx, t, 0, 1) → u4
Integral(b, y) → u
Sequence(ay + (i * (by - ay) / n), i, 0, n) → list1, {0, 0.004, 0.008, 0.012, 0.016, 0.02, 0.024, 0.028, 0.032, 0.036000000000000004, 0.04, 0.044, 0.048, 0.052000000000000005, 0.056, 0.06, 0.064, 0.068, 0.07200000000000001, 0.076, 0.08, 0.084, 0.088, 0.092, 0.096, 0.1, 0.10400000000000001, 0.108, 0.112, 0.116, 0.12, 0.124, 0.128, 0.132, 0.136, 0.14, 0.14400000000000002, 0.148, 0.152, 0.156, 0.16, 0.164, 0.168, 0.17200000000000001, 0.176, 0.18, 0.184, 0.188, 0.192, 0.196, 0.2, 0.20400000000000001, 0.20800000000000002, 0.212, 0.216, 0.22, 0.224, 0.228, 0.232, 0.23600000000000002, 0.24, 0.244, 0.248, 0.252, 0.256, 0.26, 0.264, 0.268, 0.272, 0.276, 0.28, 0.28400000000000003, 0.28800000000000003, 0.292, 0.296, 0.3, 0.304, 0.308, 0.312, 0.316, 0.32, 0.324, 0.328, 0.332, 0.336, 0.34, 0.34400000000000003, 0.34800000000000003, 0.352, 0.356, 0.36, 0.364, 0.368, 0.372, 0.376, 0.38, 0.384, 0.388, 0.392, 0.396, 0.4, 0.404, 0.40800000000000003, 0.41200000000000003, 0.41600000000000004, 0.42, 0.424, 0.428, 0.432, 0.436, 0.44, 0.444, 0.448, 0.452, 0.456, 0.46, 0.464, 0.468, 0.47200000000000003, 0.47600000000000003, 0.48, 0.484, 0.488, 0.492, 0.496, 0.5, 0.504, 0.508, 0.512, 0.516, 0.52, 0.524, 0.528, 0.532, 0.536, 0.54, 0.544, 0.548, 0.552, 0.556, 0.56, 0.5640000000000001, 0.5680000000000001, 0.5720000000000001, 0.5760000000000001, 0.58, 0.584, 0.588, 0.592, 0.596, 0.6, 0.604, 0.608, 0.612, 0.616, 0.62, 0.624, 0.628, 0.632, 0.636, 0.64, 0.644, 0.648, 0.652, 0.656, 0.66, 0.664, 0.668, 0.672, 0.676, 0.68, 0.684, 0.6880000000000001, 0.6920000000000001, 0.6960000000000001, 0.7000000000000001, 0.704, 0.708, 0.712, 0.716, 0.72, 0.724, 0.728, 0.732, 0.736, 0.74, 0.744, 0.748, 0.752, 0.756, 0.76, 0.764, 0.768, 0.772, 0.776, 0.78, 0.784, 0.788, 0.792, 0.796, 0.8, 0.804, 0.808, 0.812, 0.8160000000000001, 0.8200000000000001, 0.8240000000000001, 0.8280000000000001, 0.8320000000000001, 0.836, 0.84, 0.844, 0.848, 0.852, 0.856, 0.86, 0.864, 0.868, 0.872, 0.876, 0.88, 0.884, 0.888, 0.892, 0.896, 0.9, 0.904, 0.908, 0.912, 0.916, 0.92, 0.924, 0.928, 0.932, 0.936, 0.9400000000000001, 0.9440000000000001, 0.9480000000000001, 0.9520000000000001, 0.9560000000000001, 0.96, 0.964, 0.968, 0.972, 0.976, 0.98, 0.984, 0.988, 0.992, 0.996, 1, 1.004, 1.008, 1.012, 1.016, 1.02, 1.024, 1.028, 1.032, 1.036, 1.04, 1.044, 1.048, 1.052, 1.056, 1.06, 1.064, 1.068, 1.072, 1.076, 1.08, 1.084, 1.088, 1.092, 1.096, 1.1, 1.104, 1.108, 1.112, 1.116, 1.12, 1.124, 1.1280000000000001, 1.1320000000000001, 1.1360000000000001, 1.1400000000000001, 1.1440000000000001, 1.1480000000000001, 1.1520000000000001, 1.156, 1.16, 1.164, 1.168, 1.172, 1.176, 1.18, 1.184, 1.188, 1.192, 1.196, 1.2, 1.204, 1.208, 1.212, 1.216, 1.22, 1.224, 1.228, 1.232, 1.236, 1.24, 1.244, 1.248, 1.252, 1.256, 1.26, 1.264, 1.268, 1.272, 1.276, 1.28, 1.284, 1.288, 1.292, 1.296, 1.3, 1.304, 1.308, 1.312, 1.316, 1.32, 1.324, 1.328, 1.332, 1.336, 1.34, 1.344, 1.348, 1.352, 1.356, 1.36, 1.364, 1.368, 1.372, 1.3760000000000001, 1.3800000000000001, 1.3840000000000001, 1.3880000000000001, 1.3920000000000001, 1.3960000000000001, 1.4000000000000001, 1.4040000000000001, 1.408, 1.412, 1.416, 1.42, 1.424, 1.428, 1.432, 1.436, 1.44, 1.444, 1.448, 1.452, 1.456, 1.46, 1.464, 1.468, 1.472, 1.476, 1.48, 1.484, 1.488, 1.492, 1.496, 1.5, 1.504, 1.508, 1.512, 1.516, 1.52, 1.524, 1.528, 1.532, 1.536, 1.54, 1.544, 1.548, 1.552, 1.556, 1.56, 1.564, 1.568, 1.572, 1.576, 1.58, 1.584, 1.588, 1.592, 1.596, 1.6, 1.604, 1.608, 1.612, 1.616, 1.62, 1.624, 1.6280000000000001, 1.6320000000000001, 1.6360000000000001, 1.6400000000000001, 1.6440000000000001, 1.6480000000000001, 1.6520000000000001, 1.6560000000000001, 1.6600000000000001, 1.6640000000000001, 1.668, 1.672, 1.676, 1.68, 1.684, 1.688, 1.692, 1.696, 1.7, 1.704, 1.708, 1.712, 1.716, 1.72, 1.724, 1.728, 1.732, 1.736, 1.74, 1.744, 1.748, 1.752, 1.756, 1.76, 1.764, 1.768, 1.772, 1.776, 1.78, 1.784, 1.788, 1.792, 1.796, 1.8, 1.804, 1.808, 1.812, 1.816, 1.82, 1.824, 1.828, 1.832, 1.836, 1.84, 1.844, 1.848, 1.852, 1.856, 1.86, 1.864, 1.868, 1.872, 1.8760000000000001, 1.8800000000000001, 1.8840000000000001, 1.8880000000000001, 1.8920000000000001, 1.8960000000000001, 1.9000000000000001, 1.9040000000000001, 1.9080000000000001, 1.9120000000000001, 1.9160000000000001, 1.92, 1.924, 1.928, 1.932, 1.936, 1.94, 1.944, 1.948, 1.952, 1.956, 1.96, 1.964, 1.968, 1.972, 1.976, 1.98, 1.984, 1.988, 1.992, 1.996, 2}
Element(list3, faces) → Selectedvector

AI Drawing Prompt Reference

Draw a quadrilateral formed by points A, B, C, D and project it onto the coordinate system. Construct four surfaces u1, u2, u3, u4 using function o and parameters b, a, x, y to form a 3D surface structure. Calculate the integral u for volume and generate an arithmetic sequence from 0 to 1. The figure should illustrate the integration of geometry and calculus, showing the relationship between the surface and the sequence.

The prompt above was compiled from the original drawing commands and is for reference only.