thank you very much for the animation. I have a question what if we do not know the equations for instance a topological surface such as Klein bottle or torus how can we animate them ?
In my multivariable calculus class, we studied parameterization of functions. For a torus, use the vector-valued function =, a=0...2pi, b=0...2pi, L=C>1. A motivation for understanding how I developed this parameterization is revolving a circle plus a shift vector around the x-axis.
Thank you so much. I tried to copy what you did, but the animate Parameter are not clickable. How to make it clickable please? I really appreciate you very much.
+kalimahakali I have not been able to get that to work. What I do is use a tool that can perform a screen grab, and I usually use QuickTime Player for that.
I have a question using parametric equations. Here are the equations: (90 cos(2π/9))t and 6 + (90 sin(2π/9))t - 16t^2 .... t=0 Will the grapher pot the points on the graph?
Your first "equation" is just an expression - did you mean that to be an equation, equal to zero? Should this be two equations of the form f(t) = 0 and g(t) = 0, with t running between two values? I am trying to understand exactly what you are trying to plot.
I have a question using parametric equations. Here are the equations: x =(90 cos(2π/9))t and y= 6 + (90 sin(2π/9))t - 16t^2 .... t=0 Will the grapher plot the points on the graph?
