Comparing Slopes (3D)
In three dimensions a surface does not have one slope — it has a different one in every direction. This simulation lets you pick a point and a direction, then compare the steepness you get along each choice.
How to use this simulation
- Choose a point on the surface
- Rotate the direction of travel through 360°
- Compare two slope readings side by side
What to look for
- Slope varies continuously as you swing the direction around
- There is always a direction of zero slope, running along the contour line
- The steepest ascent and steepest descent directions are exactly opposite
The physics behind it
The slope of a surface at a point depends on the direction you walk. Partial derivatives give the slopes along the x and y axes, and the directional derivative combines them for any other heading. The gradient vector points along the direction of steepest ascent, and its magnitude is that maximum slope.