3D Surface Plotter

This application creates an interactive 3D surface plot of the mathematical function:

$f(x,y) = x^{3.7} + y^{1.5} - 5$

Understanding the Function

This function combines two terms with different powers:

• $x^{3.7}$: A term that grows rapidly as x increases, with a fractional exponent of 3.7
• $y^{1.5}$: A term that grows more slowly with y, with an exponent of 1.5
• -5: A constant that shifts the entire surface down by 5 units

Features of the Plot

The 3D surface plot provides several interactive features:

• Hover Information: Move your cursor over any point on the surface to see its exact (x, y, z) coordinates
• Rotation: Click and drag to rotate the plot and view it from different angles
• Zoom: Use your mouse wheel or pinch gesture to zoom in and out
• Pan: Right-click and drag to pan the view

Customizing the View

You can adjust the x and y ranges to explore different regions of the surface:

• X range: Controls the domain in the x-direction
• Y range: Controls the domain in the y-direction

Note that the y minimum should be non-negative since $y^{1.5}$ is only defined for $y \geq 0$ in the real number system.

Color Mapping

The surface is colored using the Viridis color scale, where:

• Purple/blue colors represent lower z-values
• Green colors represent intermediate z-values
• Yellow colors represent higher z-values

This color mapping helps visualize the height variations across the surface.