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I'm try to plot (one nappe of) a cone using the paramtric formula (from https://en.wikipedia.org/wiki/Cone#Equation_form) :

where s , t , u range over [ 0 , θ ), [ 0 , 2 π ) , and [ 0 , h ], respectively.

I tried:

      parametric_plot3d((u*tan(s)*cos(t),u*tan(s)*sin(t),u),(u,0,20),(s,0,60*(pi/180)),(t,0,2*pi) )

but it took the third range as plot_points.

Then I tried:

    parametric_plot3d((u*tan(t/6)*cos(t),u*tan(t/6)*sin(t),u),(u,0,20),(t,0,2*pi) )

attempying to let t do double duty as s as well. It plots, but produces:

Which is pretty, but no cigar.

How can I achieve my goal?

I'm try to plot (one nappe of) a cone using the paramtric formula (from https://en.wikipedia.org/wiki/Cone#Equation_form) :

where s , t , u range over [ 0 , θ ), [ 0 , 2 π ) , and [ 0 , h ], respectively.

I tried:

      parametric_plot3d((u*tan(s)*cos(t),u*tan(s)*sin(t),u),(u,0,20),(s,0,60*(pi/180)),(t,0,2*pi) )

but it took the third range as plot_points.

Then I tried:

    parametric_plot3d((u*tan(t/6)*cos(t),u*tan(t/6)*sin(t),u),(u,0,20),(t,0,2*pi) )

attempying attempting to let t do double duty as s as well. also. It plots, but produces:

Which is pretty, but no cigar.

How can I achieve my goal?

I'm try to plot (one nappe of) a cone using the paramtric formula (from https://en.wikipedia.org/wiki/Cone#Equation_form) :

where s , t , u range over [ 0 , θ ), [ 0 , 2 π ) , and [ 0 , h ], respectively.

I tried:

      parametric_plot3d((u*tan(s)*cos(t),u*tan(s)*sin(t),u),(u,0,20),(s,0,60*(pi/180)),(t,0,2*pi) )

but it took the third range as plot_points.

Then I tried:

    parametric_plot3d((u*tan(t/6)*cos(t),u*tan(t/6)*sin(t),u),(u,0,20),(t,0,2*pi) )

attempting to let t do double duty as s also. It plots, but produces:

Which is pretty, but no cigar.

How can I achieve my goal?

I'm try to plot (one nappe of) a cone using the paramtric formula (from https://en.wikipedia.org/wiki/Cone#Equation_form) :

where s , t , u range over [ 0 , θ ), [ 0 , 2 π ) , and [ 0 , h ], respectively.

I tried:

parametric_plot3d((u*tan(s)*cos(t),u*tan(s)*sin(t),u),(u,0,20),(s,0,60*(pi/180)),(t,0,2*pi) )

but it took the third range as plot_points.

Then I tried:

parametric_plot3d((u*tan(t/6)*cos(t),u*tan(t/6)*sin(t),u),(u,0,20),(t,0,2*pi) )

attempting to let t do double duty as s also. It plots, but produces:

Which is pretty, but no cigar.

How can I achieve my goal?

I'm try to plot (one nappe of) a cone using the paramtric parametric formula (from https://en.wikipedia.org/wiki/Cone#Equation_form) :

where s , t , u range over [ 0 , θ ), [ 0 , 2 π ) , and [ 0 , h ], respectively.

I tried:

parametric_plot3d((u*tan(s)*cos(t),u*tan(s)*sin(t),u),(u,0,20),(s,0,60*(pi/180)),(t,0,2*pi) )

but it took the third range as plot_points.

Then I tried:

parametric_plot3d((u*tan(t/6)*cos(t),u*tan(t/6)*sin(t),u),(u,0,20),(t,0,2*pi) )

attempting to let t do double duty as s also. It plots, but produces:

Which is pretty, but no cigar.

How can I achieve my goal?

I'm try to plot (one nappe of) a cone using the parametric formula (from https://en.wikipedia.org/wiki/Cone#Equation_form) :

where s , t , u range over [ 0 , θ ), [ 0 , 2 π ) , and [ 0 , h ], respectively.

I tried:

parametric_plot3d((u*tan(s)*cos(t),u*tan(s)*sin(t),u),(u,0,20),(s,0,60*(pi/180)),(t,0,2*pi) )

but it took the third range as plot_points.

Then I tried:

parametric_plot3d((u*tan(t/6)*cos(t),u*tan(t/6)*sin(t),u),(u,0,20),(t,0,2*pi) )

attempting to let t do double duty as s also. It plots, but produces:

Which is pretty, but no cigar.

How can I achieve my goal?

parametric_plot3d( ( sin(x*arctan(y/x))*sin(y*arctan(y/x)), sin(x*arctan(y/x))*cos(y*arctan(y/x)), sin(x*arctan(y/x)) ), (x,-pi,pi), (y,-pi,pi) )

I'm try to plot (one nappe of) a cone using the parametric formula (from https://en.wikipedia.org/wiki/Cone#Equation_form) :

where s , t , u range over [ 0 , θ ), [ 0 , 2 π ) , and [ 0 , h ], respectively.

I tried:

parametric_plot3d((u*tan(s)*cos(t),u*tan(s)*sin(t),u),(u,0,20),(s,0,60*(pi/180)),(t,0,2*pi) )

but it took the third range as plot_points.

Then I tried:

parametric_plot3d((u*tan(t/6)*cos(t),u*tan(t/6)*sin(t),u),(u,0,20),(t,0,2*pi) )

attempting to let t do double duty as s also. It plots, but produces:

Which is pretty, but no cigar.

How can I achieve my goal?

Update: I found another formulation of the equation on the web and tried:

parametric_plot3d( ( sin(x*arctan(y/x))*sin(y*arctan(y/x)), sin(x*arctan(y/x))*cos(y*arctan(y/x)), sin(x*arctan(y/x)) ), (x,-pi,pi), (y,-pi,pi) )

And got:

I'm try to plot (one nappe of) a cone using the parametric formula (from https://en.wikipedia.org/wiki/Cone#Equation_form) :

where s , t , u range over [ 0 , θ ), [ 0 , 2 π ) , and [ 0 , h ], respectively.

I tried:

parametric_plot3d((u*tan(s)*cos(t),u*tan(s)*sin(t),u),(u,0,20),(s,0,60*(pi/180)),(t,0,2*pi) )

but it took the third range as plot_points.

Then I tried:

parametric_plot3d((u*tan(t/6)*cos(t),u*tan(t/6)*sin(t),u),(u,0,20),(t,0,2*pi) )

attempting to let t do double duty as s also. It plots, but produces:

Which is pretty, but no cigar.

How can I achieve my goal?

Update: I found another formulation of the equation on the web and tried:

parametric_plot3d( ( sin(x*arctan(y/x))*sin(y*arctan(y/x)), sin(x*arctan(y/x))*cos(y*arctan(y/x)), sin(x*arctan(y/x)) ), (x,-pi,pi), (y,-pi,pi) )

And got:

Ditto on teh the absence of stoggie.stoggies.

I'm try to plot (one nappe of) a cone using the parametric formula (from https://en.wikipedia.org/wiki/Cone#Equation_form) :

where s , t , u range over [ 0 , θ ), [ 0 , 2 π ) , and [ 0 , h ], respectively.

I tried:

parametric_plot3d((u*tan(s)*cos(t),u*tan(s)*sin(t),u),(u,0,20),(s,0,60*(pi/180)),(t,0,2*pi) )

but it took the third range as plot_points.

Then I tried:

parametric_plot3d((u*tan(t/6)*cos(t),u*tan(t/6)*sin(t),u),(u,0,20),(t,0,2*pi) )

attempting to let t do double duty as s also. It plots, but produces:

Which is pretty, but no cigar.

How can I achieve my goal?

Update: I found another formulation of the equation on the web and tried:

parametric_plot3d( ( sin(x*arctan(y/x))*sin(y*arctan(y/x)), sin(x*arctan(y/x))*cos(y*arctan(y/x)), sin(x*arctan(y/x)) ), (x,-pi,pi), (y,-pi,pi) )

And got:

Ditto on the absence of stoggies.

I'm try to plot (one nappe of) a cone using the parametric formula (from https://en.wikipedia.org/wiki/Cone#Equation_form) :

where s , t , u range over [ 0 , θ ), [ 0 , 2 π ) , and [ 0 , h ], respectively.

I tried:

parametric_plot3d((u*tan(s)*cos(t),u*tan(s)*sin(t),u),(u,0,20),(s,0,60*(pi/180)),(t,0,2*pi) )

but it took the third range as plot_points.

Then I tried:

parametric_plot3d((u*tan(t/6)*cos(t),u*tan(t/6)*sin(t),u),(u,0,20),(t,0,2*pi) )

attempting to let t do double duty as s also. It plots, but produces:

Which is pretty, but no cigar.

How can I achieve my goal?

Update: I found another formulation of the equation on the web and tried:

parametric_plot3d( ( sin(x*arctan(y/x))*sin(y*arctan(y/x)), sin(x*arctan(y/x))*cos(y*arctan(y/x)), sin(x*arctan(y/x)) ), (x,-pi,pi), (y,-pi,pi) )

And got:

Ditto on the absence of stoggies.