surface example

3D Sine Wave Surface Graph

Two perpendicular sine waves combined into one surface.

z = sin(x) + sin(y)

Teacher prompt

Why does the pattern repeat in both directions?

Both x and y are inside sine functions, so the graph is periodic along each axis.

min z 0.00max z 0.0056 samples

What this graph represents

Peaks happen where both sine terms are high, and valleys happen where both are low.

Where it appears in calculus

It is a clean way to teach periodicity in two variables.

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Related graphs

Open another surface page and compare shape, slices, and contour behavior.

Saddle Surface

z = x^2 - y^2

A saddle surface curves up in one direction and down in the perpendicular direction.

Gaussian Surface

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

A smooth bell-shaped surface centered at the origin.

Elliptic Paraboloid

z = x^2 + y^2

A bowl-shaped surface that opens upward.

Inverted Paraboloid

z = 12 - x^2 - y^2

A dome-shaped surface with a highest point at the center.