3D-Printed Objects

These surfaces were implemented in Mathematica and exported to the STL model format using the Export function. Then they were printed using a LulzBot TAZ 5 3D printer.

"Stewart"

An exercise from Stewart's calculus text:

Describe and sketch a solid such that:

When illuminated by rays parallel to the $z$-axis, its shadow is a circular disk.

If the rays are parallel to the $y$-axis, its shadow is a square.

If the rays are parallel to the $x$-axis, its shadow is an isosceles triangle.

Multivariable Limit

An example of a function for which the limit as $(x,y) \to (0,0)$ does not exist: $$ f(x,y) = \dfrac{x^3 y}{x^6+y^2}. $$


	Along $y=x^3$ the values of the function approach 1/2 as $(x,y) \to (0,0)$, though the values approach zero along any linear path!

Tanglecube

A personal favorite from MathWorld: $$ x^4 - 5x^2 + y^4 - 5y^2 + z^4 - 5z^2 + 11.8 = 0 $$

3D printer in action printing the tanglecube

Cross-Sectional Solid

The base of this solid is the region bounded by the curves $y=0$, $x=6$, $y=\dfrac{x^2}{6}$. Vertical cross-sections perpendicular to the $x$-axis are rectangles whose heights are half the lengths of their bases.

3D-printed cross-sectional solid with highlighted boundary curve