surface example

3D Mexican Hat Surface Graph

A central peak surrounded by a circular valley.

z = (1 - x^2 - y^2) * exp(-(x^2 + y^2) / 2)

Quick facts

  • Formula: z = (1 - x^2 - y^2) * exp(-(x^2 + y^2) / 2)
  • Category: surface
  • Tags: surface, calculus, z=f(x,y)

What this graph represents

The polynomial term changes sign while the exponential term damps the edge.

Where it appears in calculus

Useful for radial symmetry and wavelet intuition.

How to use this graph

  1. Rotate the surface by dragging with your mouse or finger
  2. Use the Embed button to copy an <iframe> for your LMS or lesson page
  3. Click PNG to export a classroom-ready image
  4. Click Formula or LaTeX to copy the equation for your notes

Embed this graph

Use the Embed button in the calculator to copy a ready iframe for blogs, LMS pages, and lesson notes.

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Teacher prompt

Question: Why is there a ring-shaped valley?

Answer: The factor 1 minus radius squared becomes negative outside the center.

Related graphs

Explore more surface examples and compare shapes, slices, and contour behavior.

Ridge Surface

z = exp(-x^2)

A ridge that is constant in the y direction.

Valley Surface

z = y^2 - 2*x

A parabolic valley tilted along the x-axis.

Spiral Height Surface

z = atan(y / (x + 0.001))

A wrapped height field based on angle.

Checkerboard Surface

z = floor(abs(sin(x) * sin(y)) * 4) / 4

A stepped checkerboard made from quantized waves.

Fourier Demo Surface

z = sin(x) + sin(2*y)/2 + sin(3*x)/3

A layered wave made from several sine terms.

Distance Field

z = min(sqrt((x - 2)^2 + y^2), sqrt((x + 2)^2 + y^2))

A surface showing distance to the nearer of two points.

Explore more tools

Use these free browser tools to extend your graphing workflow.

3D Surface Plotter

Plot z=f(x,y), rotate, and export

Embed Builder

Create ready-to-use iframe embeds

Worksheet Export

Export graph images for classroom worksheets

How to Graph z=f(x,y)

Step-by-step guide for beginners