How to Make a Gubby in Desmos Graphing Calculator
Generate custom equations to create your own "Gubby" character in Desmos. Adjust the size and position to get the perfect mathematical art.
Main Body Equation
Gubby Preview
Visual representation of your generated Gubby.
| Component | Desmos Equation Format | Mathematical Type |
|---|---|---|
| Body | (x-h)² + (y-k)² = r² | Circle (Implicit) |
| Eyes | (x-h)² + (y-k)² = r² | Circle (Implicit) |
| Mouth | y = a(x-h)² + k | Parabola (Quadratic) |
What is how to make a gubby in desmos graphing calculator?
The term "Gubby" refers to a popular, minimalist character often used in the math community to demonstrate the power of coordinate geometry. Learning how to make a gubby in desmos graphing calculator is a fantastic way for students and hobbyists to practice circle equations, transformations, and domain restrictions.
Who should use this? Anyone from middle school students learning about the coordinate geometry formulas to advanced users looking to create complex Desmos art tutorials. A common misconception is that you need complex calculus to draw characters; in reality, most "Gubbies" are built using simple algebraic functions.
how to make a gubby in desmos graphing calculator Formula and Mathematical Explanation
To create a Gubby, we use a combination of implicit circle equations and quadratic functions. The process involves shifting the origin $(h, k)$ and scaling the radius $r$.
| Variable | Meaning | Unit | Typical Range |
|---|---|---|---|
| h | Horizontal Offset | Units | -10 to 10 |
| k | Vertical Offset | Units | -10 to 10 |
| r | Radius of Body | Units | 1 to 20 |
| a | Mouth Curvature | Constant | 0.1 to 0.5 |
The body is defined by $(x – h)^2 + (y – k)^2 = r^2$. The eyes are smaller circles placed at $(h \pm 0.4r, k + 0.3r)$, and the mouth is a parabola $y = a(x-h)^2 + (k – 0.2r)$ with a restricted domain to keep it within the body.
Practical Examples (Real-World Use Cases)
Example 1: The Standard Gubby
If you set the radius to 5 and the center to (0,0), your equations for how to make a gubby in desmos graphing calculator would be:
- Body: $x^2 + y^2 = 25$
- Eyes: $(x \pm 2)^2 + (y – 1.5)^2 = 0.56$
- Mouth: $y = -0.1x^2 – 1$
Example 2: The Giant Gubby
For a larger version at position (10, 10) with a radius of 10:
- Body: $(x – 10)^2 + (y – 10)^2 = 100$
- Eyes: $(x – 6)^2 + (y – 13)^2 = 2.25$ and $(x – 14)^2 + (y – 13)^2 = 2.25$
How to Use This how to make a gubby in desmos graphing calculator Calculator
- Enter the Scale (Radius) to determine how large your character will be.
- Adjust the Center X and Y positions to move the Gubby around the graph.
- The calculator automatically generates the four primary equations needed.
- Click "Copy Equations" to save them to your clipboard.
- Open Desmos and paste each equation into a new expression line.
Interpreting results is easy: the primary equation is your main circle, while the intermediate values provide the facial features. For better aesthetics, you can use advanced Desmos shading by changing the "=" to "<" in the body equation.
Key Factors That Affect how to make a gubby in desmos graphing calculator Results
- Coordinate Scaling: If your Desmos axes are not square, the Gubby might look like an ellipse.
- Domain Restrictions: To make the mouth look perfect, you often need to add $\{|x-h| < 0.5r\}$ to the end of the parabola.
- Eye Proportions: We use a factor of 0.15 times the radius for eye size to maintain a "cute" look.
- Vertical Placement: Placing eyes too high or too low changes the character's expression significantly.
- Line Thickness: In Desmos, you can adjust the "width" of the lines to make the Gubby look bolder.
- Color Filling: Using inequalities like $(x-h)^2 + (y-k)^2 \le r^2$ allows you to fill the Gubby with color.
Frequently Asked Questions (FAQ)
Can I make the Gubby blink?
Yes, by using a slider for the y-radius of the eyes, you can turn the eye circles into flat lines, simulating a blink.
How do I change the Gubby's color?
In Desmos, click and hold the colored icon next to the equation to select a different color or enable shading.
Why does my Gubby look squashed?
Ensure your graph settings are set to "Square" so the X and Y units are equal in length.
Is there a way to animate the Gubby?
Replace the X or Y position values with a variable (like 'a') and add a slider in Desmos to watch it move!
Can I add a hat?
Absolutely! You can use a triangle (polygon) or another semi-circle equation on top of the head.
What are the best graphing calculator basics for art?
Mastering transformations $f(x-h)+k$ is the most important skill for creating any Desmos art.
How do I make the mouth smile more?
Increase the 'a' value in the parabola equation $y = a(x-h)^2 + k$. A more negative 'a' creates a deeper smile.
Can I use parametric equations guide for Gubbies?
Yes, parametric equations like $(r \cos t, r \sin t)$ are often more efficient for complex rotations.
Related Tools and Internal Resources
- Desmos Art Tutorial – A deep dive into creating complex characters.
- Graphing Calculator Basics – Essential skills for every math student.
- Parametric Equations Guide – Moving beyond simple functions.
- Math Meme Culture – Why characters like Gubby become popular.
- Advanced Desmos Shading – How to color your mathematical creations.
- Coordinate Geometry Formulas – The math behind the art.