Teaching guide
Surface Graph and Contour Map Relationship
Contours are horizontal slices of the 3D graph projected into 2D.
Use the interactive graph first, then connect the visual shape to the written rule.
Classroom check
Q: What does a tight contour spacing mean?
A: It usually means the surface height changes quickly.
Try it yourself
Use the interactive calculator below to experiment with this concept.
Related guides
Graph z=f(x,y)
Type a formula, choose x and y ranges, then rotate the result to inspect slices.
Saddle vs Minimum
A saddle curves up in one direction and down in another, unlike a true minimum.
Teacher Setup
Use locked views, hidden formulas, and reveal prompts for classroom embeds.
Export PNG
Use the export button after rotating the graph to the desired angle.