Sculptures of basic mathematical functions

thingiverse

The calculation of percentage can be performed with the formula p = W / G, where W stands for the relative number and G for the whole number. The result p times 100 gives the result in percentage. It is possible to interpret the formula as as functional equations: p(W,G) = W / G, W(p,G) = p G, G(W,p) = W / p. The first and and third equation have the form f(x,y) = x / y and the second one f(x,y) = x y. Two of the three designs are 3D 'plots' of these functions. They can be used in the 7th class to provide an additional view on percentage calculation, or later as an inverse problem: Find a function with which this shape has been created! The third design is a 3D 'plot' of the equation for the kinetic energy: E(m,v) = 1/2 m v^2, with m for mass and v for velocity. A further application of the objects is to demonstrate iso-lines by dipping the objects e.g. into colored water. The objects are no "remixes", but have been inspired by http://www.thingiverse.com/thing:24897 . Instructions The stl files "...256.stl" can be printed directly, but the scaling should be adjusted. The files "...maple18.stl have not been printed yet (they should generate a smoother surface). Function height maps with an inplane resolution of 256 x 256 have been created using Maple 18 (see enclosed .mws file and bmp images). A limitation of the function values helps prevent cusps which could not be printed cleanly. The .stl files have been created using the jar file heightmap2stl on thingiverse (http://www.thingiverse.com/thing:15276). This approach also works with previous versions of Maple, but Maple 18 has the advantage that it can directly output stl files. Here are the commands for plotting x/y: p := plot3d({0, Heaviside(x)Heaviside(-x+1)Heaviside(y)Heaviside(-y+1)(min(.1*x/y, .8)+0.5e-1)}, x = -0.1e-1 .. 1.01, y = -0.1e-1 .. 1.01, grid = [160, 160]); # at least in the academic version the size of the plot structure is limited to 1 MB stl:="....stl"; exportplot(stl, p); If it is intended to illustrate isolines with liquids consider the buoyancy of the printed object - it depends on the material used and the filling density.