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Freehand Pottery Bowl Surface of Revolution

Freehand Pottery Bowl Surface of Revolution
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2019-11-24 09:16
FunctionSolid GeometryTransformation
In collections GeoGebra 3D & AR: Geometry Resources & Challenges
This example demonstrates creating a 3D surface of revolution by rotating a freehand 2D cross section. Key mathematical concepts include functions, rotation, and solid geometry. GeoGebra commands used include Function, Rotate, and Surface. Suitable for high school and above students learning about surface of revolution construction.

GeoGebra Commands & Parameters

  1. Function({1.10836, 6.7518, 0.20816, 0.20816, 0.2170333333333383, 0.22590666666667167, 0.23478, 0.23478, 0.23478, 0.23478, 0.23478, 0.23478, 0.23478, 0.23478, 0.23478, 0.2436533333333383, 0.2525266666666717, 0.2614, 0.2614, 0.2614, 0.2614, 0.2614, 0.26805500000000504, 0.27471, 0.281365000000005, 0.28802, 0.2968933333333384, 0.30576666666667174, 0.31464, 0.3235133333333384, 0.3323866666666717, 0.34126, 0.35013333333333846, 0.35900666666667175, 0.36788, 0.3856266666666717, 0.40337333333333847, 0.42112, 0.43886666666667185, 0.4566133333333385, 0.47436, 0.49210666666667197, 0.5098533333333386, 0.5276, 0.55422, 0.58084, 0.60746, 0.625206666666672, 0.6429533333333387, 0.6607, 0.70063, 0.74056, 0.7494333333333388, 0.7583066666666722, 0.76718, 0.80711, 0.84704, 0.8559133333333389, 0.8647866666666723, 0.87366, 0.8914066666666723, 0.9091533333333389, 0.9269, 0.9446466666666723, 0.9623933333333389, 0.98014, 0.9978866666666724, 1.0156333333333392, 1.03338, 1.07331, 1.11324, 1.1309866666666724, 1.1487333333333394, 1.16648, 1.1931, 1.21972, 1.24634, 1.2640866666666726, 1.2818333333333394, 1.29958, 1.3262, 1.35282, 1.37944, 1.3971866666666728, 1.4149333333333394, 1.43268, 1.47261, 1.51254, 1.530286666666673, 1.5480333333333396, 1.56578, 1.64564, 1.663386666666673, 1.6811333333333398, 1.69888, 1.7255, 1.75212, 1.77874, 1.796486666666673, 1.81423333333334, 1.83198, 1.8586, 1.88522, 1.91184, 1.95177, 1.9917, 2.009446666666673, 2.02719333333334, 2.04494, 2.08487, 2.1248, 2.15142, 2.17804, 2.20466, 2.24459, 2.28452, 2.32445, 2.36438, 2.391, 2.41762, 2.44424, 2.48417, 2.5241, 2.55072, 2.57734, 2.60396, 2.64389, 2.68382, 2.76368, 2.80361, 2.84354, 2.87016, 2.89678, 2.9234, 2.96333, 3.00326, 3.04319, 3.08312, 3.12305, 3.16298, 3.20291, 3.24284, 3.2783333333333413, 3.3138266666666745, 3.34932, 3.42918, 3.46911, 3.50904, 3.5889, 3.62883, 3.66876, 3.70869, 3.74862, 3.78855, 3.82848, 3.8551, 3.88172, 3.90834, 3.94827, 3.9882, 4.06806, 4.10799, 4.14792, 4.22778, 4.30764, 4.3875, 4.42743, 4.46736, 4.54722, 4.58715, 4.62708, 4.70694, 4.74687, 4.7868, 4.82673, 4.86666, 4.94652, 5.02638, 5.10624, 5.14617, 5.1861, 5.22603, 5.26596, 5.34582, 5.38575, 5.42568, 5.50554, 5.54547, 5.5854, 5.66526, 5.74512, 5.78505, 5.82498, 5.90484, 5.94477, 5.9847, 6.02463, 6.06456, 6.14442, 6.22428, 6.26421, 6.30414, 6.384, 6.46386, 6.54372, 6.6502, 6.73006, 6.80992, 7.10274, 7.28908, 7.39556, 7.5819, 7.66176, 7.8481, 8.35388}) → f
  2. Rotate(f, π / 2, xAxis) → f_1
  3. Rotate(f_1, n, zAxis) → a
  4. Surface(f_1, n, zAxis) → b

AI Drawing Prompt Reference

Create a pottery bowl surface by first drawing a freehand 2D cross section, then rotating this cross section around the y-axis to generate a 3D surface. The cross section starts wide at the bottom, narrows in the middle, and tapers to a point at the top.
The prompt above was compiled from the original drawing commands and is for reference only.