Creating a visually appealing panda design using mathematical functions is a creative and fun project! Below is a structured outline along with sample functions that you can use to design a panda on Desmos.
Concept: Panda Drawing
1. Planning Your Design:
- The subject of your design is a panda. The panda has a round body, a round head, eyes, ears, and arms. Each of these parts can be represented using a combination of linear, quadratic, and exponential functions.
2. Functions to Use:
- Linear Functions: These can create arms, legs, and the outline of the body.
- Quadratic Functions: These can be used for creating the rounded shapes of the head and body.
- Exponential Functions: Can be creatively used to give a playful effect, maybe for the ears or unique parts of the eyes.
Equations:
Here are some sample functions designed as a panda:
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Head (Quadratic): \[ y = -0.2(x^2 - 9) + 6, \quad \text{domain: } [-3, 3] \]
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Body (Quadratic): \[ y = -0.1(x^2) + 2, \quad \text{domain: } [-4, 4] \]
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Left Ear (Circle): \[ (x + 2)^2 + (y - 7)^2 = 1, \quad \text{(centered at (-2, 7), radius 1)} \]
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Right Ear (Circle): \[ (x - 2)^2 + (y - 7)^2 = 1 \]
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Left Eye (Circle): \[ (x + 1)^2 + (y - 5)^2 = 0.5, \quad \text{(Iris of the eye)} \]
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Right Eye (Circle): \[ (x - 1)^2 + (y - 5)^2 = 0.5 \]
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Pupil of Left Eye (Circle): \[ (x + 1)^2 + (y - 5)^2 = 0.1 \]
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Pupil of Right Eye (Circle): \[ (x - 1)^2 + (y - 5)^2 = 0.1 \]
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Nose (Circle): \[ (x)^2 + (y - 4)^2 = 0.3 \]
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Mouth (Linear): \[ y = -0.5|x| + 3.8, \quad \text{domain: } [-1, 1] \]
Applying Domain and Range Restrictions
Make sure to apply any domain and range restrictions to ensure certain elements of the panda do not overlap unwantedly. For example, limit the domain of the mouth function to create a smile limited on the x-axis.
Graphing in Desmos
- Log in to your Desmos account and enter the equations.
- Adjust the colors of each part for aesthetic success.
- Share the link to your Desmos graph once finished.
Feedback & Reflection:
- After sharing with peers, consider their input on clarity and appeal. Modify your design based on their suggestions.
Presentation:
Prepare to explain the mathematical functions used, their contributions to the design, and your learning process throughout the project.
Final Reflection:
After the project, take time to reflect on the process, detailing what you learned about function types, challenges encountered, and how mathematics can create art.
By following this outline, you should be well on your way to creating a panda with mathematical equations! Good luck!