Parametric Cat

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2014-11-20 16:27

In collections Curves

This example demonstrates how to draw a cat using parametric equations. It involves core math concepts like parametric curves, curve sketching, exponentials, ratios, and real numbers. The construction uses GeoGebra's Curve and Cartesian commands, making it suitable for high school math learning and exploring parametric equations.

GeoGebra Commands & Parameters

CurveCartesian(((-((721 * sin(t))))) / 4 + (196 / 3 * sin((2 * t))) - (86 / 3 * sin((3 * t))) - (131 / 2 * sin((4 * t))) + (477 / 14 * sin((5 * t))) + (27 * sin((6 * t))) - (29 / 2 * sin((7 * t))) + (68 / 5 * sin((8 * t))) + (1 / 10 * sin((9 * t))) + (23 / 4 * sin((10 * t))) - (19 / 2 * sin((12 * t))) - (85 / 21 * sin((13 * t))) + (2 / 3 * sin((14 * t))) + (27 / 5 * sin((15 * t))) + (7 / 4 * sin((16 * t))) + (17 / 9 * sin((17 * t))) - (4 * sin((18 * t))) - (1 / 2 * sin((19 * t))) + (1 / 6 * sin((20 * t))) + (6 / 7 * sin((21 * t))) - (1 / 8 * sin((22 * t))) + (1 / 3 * sin((23 * t))) + (3 / 2 * sin((24 * t))) + (13 / 5 * sin((25 * t))) + sin((26 * t)) - (2 * sin((27 * t))) + (3 / 5 * sin((28 * t))) - (1 / 5 * sin((29 * t))) + (1 / 5 * sin((30 * t))) + ((2337 * cos(t))) / 8 - (43 / 5 * cos((2 * t))) + (322 / 5 * cos((3 * t))) - (117 / 5 * cos((4 * t))) - (26 / 5 * cos((5 * t))) - (23 / 3 * cos((6 * t))) + (143 / 4 * cos((7 * t))) - (11 / 4 * cos((8 * t))) - (31 / 3 * cos((9 * t))) - (13 / 4 * cos((10 * t))) - (9 / 2 * cos((11 * t))) + (41 / 20 * cos((12 * t))) + (8 * cos((13 * t))) + (2 / 3 * cos((14 * t))) + (6 * cos((15 * t))) + (17 / 4 * cos((16 * t))) - (3 / 2 * cos((17 * t))) - (29 / 10 * cos((18 * t))) + (11 / 6 * cos((19 * t))) + (12 / 5 * cos((20 * t))) + (3 / 2 * cos((21 * t))) + (11 / 12 * cos((22 * t))) - (4 / 5 * cos((23 * t))) + cos((24 * t)) + (17 / 8 * cos((25 * t))) - (7 / 2 * cos((26 * t))) - (5 / 6 * cos((27 * t))) - (11 / 10 * cos((28 * t))) + (1 / 2 * cos((29 * t))) - (1 / 5 * cos((30 * t))), ((-((637 * sin(t))))) / 2 - (188 / 5 * sin((2 * t))) - (11 / 7 * sin((3 * t))) - (12 / 5 * sin((4 * t))) + (11 / 3 * sin((5 * t))) - (37 / 4 * sin((6 * t))) + (8 / 3 * sin((7 * t))) + (65 / 6 * sin((8 * t))) - (32 / 5 * sin((9 * t))) - (41 / 4 * sin((10 * t))) - (38 / 3 * sin((11 * t))) - (47 / 8 * sin((12 * t))) + (5 / 4 * sin((13 * t))) - (41 / 7 * sin((14 * t))) - (7 / 3 * sin((15 * t))) - (13 / 7 * sin((16 * t))) + (17 / 4 * sin((17 * t))) - (9 / 4 * sin((18 * t))) + (8 / 9 * sin((19 * t))) + (3 / 5 * sin((20 * t))) - (2 / 5 * sin((21 * t))) + (4 / 3 * sin((22 * t))) + (1 / 3 * sin((23 * t))) + (3 / 5 * sin((24 * t))) - (3 / 5 * sin((25 * t))) + (6 / 5 * sin((26 * t))) - (1 / 5 * sin((27 * t))) + (10 / 9 * sin((28 * t))) + (1 / 3 * sin((29 * t))) - (3 / 4 * sin((30 * t))) - ((125 * cos(t))) / 2 - (521 / 9 * cos((2 * t))) - (359 / 3 * cos((3 * t))) + (47 / 3 * cos((4 * t))) - (33 / 2 * cos((5 * t))) - (5 / 4 * cos((6 * t))) + (31 / 8 * cos((7 * t))) + (9 / 10 * cos((8 * t))) - (119 / 4 * cos((9 * t))) - (17 / 2 * cos((10 * t))) + (22 / 3 * cos((11 * t))) + (15 / 4 * cos((12 * t))) - (5 / 2 * cos((13 * t))) + (19 / 6 * cos((14 * t))) + (7 / 4 * cos((15 * t))) + (31 / 4 * cos((16 * t))) - cos((17 * t)) + (11 / 10 * cos((18 * t))) - (2 / 3 * cos((19 * t))) + (13 / 3 * cos((20 * t))) - (5 / 4 * cos((21 * t))) + (2 / 3 * cos((22 * t))) + (1 / 4 * cos((23 * t))) + (5 / 6 * cos((24 * t))) + (3 / 4 * cos((26 * t))) - (1 / 2 * cos((27 * t))) - (1 / 10 * cos((28 * t))) - (1 / 3 * cos((29 * t))) - (1 / 19 * cos((30 * t))), t, 0, 6.283185307179586) → a

AI Drawing Prompt Reference

Draw a cat's outline using parametric equations to define its shape. Start by drawing the cat's body with complex sine and cosine functions, then add details like ears, tail, and eyes, and finally adjust the parameters to achieve a realistic cat appearance.

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