Square Cross Sections Perpendicular to x-Axis
- Steve Phelps
I want to build square cross sections between the parabola and the x-axis. 1. Enter the function. I entered f(x) = -(x-1)(x-6). I did not use a doman restriction. 2. This only works if the EDGES of the solid are formed using parametric equations. This is the CURVE() command in GeoGebra. 3. Enter a = curve(t,f(t),0,t,1,6). This is the functions expressed parametrically. Parametrically, this is x(t) = t, y(t) = f(t), z(t) = 0, as t varies from 1 to 6 4. By habit, I name the edge ABOVE a as aa. Enter aa=curve(t,f(t),f(t),t,1,6) 5. Then, enter b=curve(t,0,0,t,1,6) for the edge along the x-axis 6. Enter bb=curve(t,0,f(t),t,1,6) for the edge above b.
To graph the top surface, enter Surface( u aa(t) + (1-u) bb(t), u,0,1,t,1,6) Think of this as the parameter u being used to stretch one curve to another.
To graph the rear surface, enter Surface( u a(t) + (1-u) aa(t), u,0,1,t,1,6)
To graph the bottom surface, enter Surface( u a(t) + (1-u) b(t), u,0,1,t,1,6)
To graph the front surface, enter Surface( u b(t) + (1-u) bb(t), u,0,1,t,1,6)