surface example

3D Fourier Demo Surface Graph

A layered wave made from several sine terms.

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

Quick facts

  • Formula: z = sin(x) + sin(2*y)/2 + sin(3*x)/3
  • Category: surface
  • Tags: surface, calculus, z=f(x,y)

What this graph represents

The added harmonics create richer surface detail.

Where it appears in calculus

Use it as a first visual for Fourier-style composition.

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 the wave shape more complex?

Answer: Several sine waves with different frequencies are added together.

Related graphs

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

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.

Elliptic Gaussian

z = exp(-(x^2 / 8 + y^2 / 2))

A stretched bell surface with different widths by axis.

Anisotropic Paraboloid

z = x^2 / 4 + y^2

A bowl that curves more sharply along y than x.

Two Peak Surface

z = exp(-((x - 2)^2 + y^2)) + exp(-((x + 2)^2 + y^2))

Two smooth hills separated along the x-axis.

Basin and Ridge

z = x^2 - cos(3*y)

A parabolic basin crossed by repeated ridges.

Exponential Slope

z = exp(0.25*x) * cos(y)

A wave whose amplitude grows along x.

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