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:
$$
f(x,y) = \dfrac{x^3 y}{x^6+y^2}.
$$
Tanglecube
A personal favorite from MathWorld:
$$
x^4 - 5x^2 + y^4 - 5y^2 + z^4 - 5z^2 + 11.8 = 0
$$
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.
