SageMath is a powerful open-source tool for mathematical
computations, and its 3D plotting capabilities are truly impressive!
In this guide, you'll learn about basic 3D plots, surfaces of
revolution, implicit plots, contour plots, Platonic solids,
and interactive visualizations — plus visual examples, a quick
reference table, and expanded challenges!
π Reference: SageMath3D Plotting Documentation (PDF)
1. 3D Plotting in SageMath
Example: Basic 3D Graph
Plot the surface:
over the domain 
.
πΈ Visual Example
You can also enrich the plot with a green sphere:
1.1 Surface of Revolution
Create surfaces by rotating curves about an axis!
1.2 Implicit 3D Plots
Plot surfaces defined by equations like:
1.3 Contour Plots
Surface and contour plot of
1.3.1 Platonic Solids
Create stunning 3D solids like tetrahedrons, cubes, and
icosahedrons!
2. Interactive Plotting
Control plots dynamically using widgets!
Adjust parameters and watch the graph change instantly! ✨
3. Practice Exercises
Challenge yourself:
π§ Core Exercises
- Figure
Eight Curve
Hint:
- Use
.
- Set t
as the parameter.
- Prime
Functions
Plot 
Observe patterns!
Hint:
- Use
SageMath’s built-in
function.
- Try
plotting with
.
- Regular
Polygons Inside Circle
Plot a unit circle and inscribe polygons with 
Hint:
- Plot
the circle using
- Generate
polygon vertices with trigonometric functions.
- Surface
and Contour
Hint:
- Use plot3d
for the surface.
- Use contour_plot
for the contour.
- Surface
of Revolution
Revolve region between 
about the z-axis, 
.
Hint:
- First
plot the curves
- Then
use revolution_plot3d on the region (maybe piecewise or separate plots).
- You
might need to create parametric curves first.
π Expanding Challenges
(Bonus Ideas!)
Final Thoughts
SageMath is a playground for mathematical creativity!
Now that you know how to plot 3D graphs, revolve curves, and build interactive
visualizations — imagine what you could build next! π¨π§
Next up: Animations, parametric surfaces, and
aesthetic tricks to make your 3D plots pop even more.
Happy plotting! π
π What's Next?
Ready to dive deeper into the world of SageMath?
In the next post, we’ll explore the Calculus of One Variable —
including how to easily compute limits, derivatives, integrals,
and even visualize changes beautifully with SageMath.
Stay tuned — it’s going to make calculus feel natural and
fun! π―
π Coming soon: "Calculus
of One Variable with SageMath"
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