Graph Defined in Polar Coordinates

The format of definition has one of the following forms:

R(fi)

R(fi);fi_min

R(fi);fi_min,fi_max

R(fi);_,fi_max

where

R(fi) - is an expression which (after evaluations) can contain only variable, corresponding to polar angle φ. By default, variable name is fi.

fi_{min –}  minimal value of polar angle

fi_{max –}  maximal value of polar angle

If neither fi_min,  nor fi_max  are specified, the graph is plotted for φ varying over [0, 2π].

If fi_max  is not specified, the graph is plotted for φ > fi_{min .}     If fi_min  is not specified, the graph is plotted for φ < fi_{min .}  

ArtSGraph does not plot graph for negative values of radial vector, i.e. where R(fi) is negative. This is typical for Russian mathematical tradition. For instance the graph of R=cos(3*fi) has three petals, not six.

Examples:

1                                  ; ρ = 1 - circumference with radius equal to 1
cos(3*fi)                      ; trefoil,  ρ = cos(3*φ)

fi;0,4*pi                       ; 2 turns of Archimedes’ spiral:  ρ = φ

exp(fi);-pi/2,pi/2          ; arc of logarithmic spiral ρ = exp(φ) right to axis of ordinates