Creating a panda using mathematical functions can be a fun and creative project! Below is a step-by-step guide with the equations you can use to graph a panda on Desmos, along with some explanations of how they contribute to the overall design.
Concept
The concept is to create a panda, which can symbolize playfulness, peace, and nature.
Functions Used
Below are the mathematical functions categorized by their types:
-
Linear Functions:
- Eyes:
- Left Eye: \(y = \frac{1}{5}x - \frac{15}{5}\) with domain [-5, -3].
- Right Eye: \(y = \frac{1}{5}x - \frac{15}{5}\) with domain [3, 5].
- Eyes:
-
Quadratic Functions (to form curves):
- Head shape: \(y = -0.1(x^2) + 8\) with domain [-10, 10].
- Body shape: \(y = -0.2(x^2) + 4\) with domain [-5, 5].
- Ears:
- Left ear: \(y=-\frac{1}{5}(x + 7)^2 + 10\) with domain [-11, -3].
- Right ear: \(y=-\frac{1}{5}(x - 7)^2 + 10\) with domain [3, 11].
-
Exponential Functions:
- Nostrils: \(y = e^{-(x-1)^2}\) with domain [0.7, 1.3].
- Mouth: \(y = -e^{-(x-0.5)^2} + 3\) with domain [-3, 3].
Drawing the Panda
Step-by-step Implementation
-
Head Shape: Use the quadratic function to create a rounded head.
- \(y = -0.1(x^2) + 8\), domain: [-10, 10].
-
Body Shape: Use another quadratic function.
- \(y = -0.2(x^2) + 4\), domain: [-5, 5].
-
Ears: Use quadratic equations for the ears:
- Left Ear: \(y = -\frac{1}{5}(x + 7)^2 + 10\), domain: [-11, -3].
- Right Ear: \(y = -\frac{1}{5}(x - 7)^2 + 10\), domain: [3, 11].
-
Eyes: Use linear functions to outline the eyes.
- Left Eye: \(y = \frac{1}{5}x - 3\), domain: [-5, -3].
- Right Eye: \(y = \frac{1}{5}x - 3\), domain: [3, 5].
-
Nostrils: An exponential function to represent the shape of the nostrils gives a soft curve.
- Nostrils: \(y = e^{-(x-1)^2}\), domain: [0.7, 1.3].
-
Mouth: An exponential function that dips downwards.
- Mouth: \(y = -e^{-(x-0.5)^2} + 3\), domain: [-3, 3].
Visual Representation
You would input these functions into the Desmos graphing calculator, making sure to apply the respective domain and range restrictions as you specified. The head will form a rounded top shape, while the ears will sit on top of it, and the eyes will add detail, along with the nostrils and mouth for facial features.
Sharing on Desmos
After you’ve input all your functions and adjusted your graph for aesthetics, click on the share button in Desmos, copy the link, and submit it as needed.
Reflection
This project will help you explore the interactions of various functions and how they can form recognizable shapes that tell a story—in this case, the delightful image of a panda.
Presentation
When you present your work, explain why you chose a panda, how each function contributed to the design, and any challenges you faced during the process, such as balancing the functions to make them visually appealing.
Final Thoughts
This creative approach not only deepens your understanding of linear, quadratic, and exponential functions, but also illustrates how mathematics can intersect with art, enhancing both your analytical and creative skills. Enjoy your project!