Changing Theta Range now redraws the affected polar graphs. Data plotting and curve-fitting features.
GRAPHMATICA EQUATION FOR HYPOTROCHOIDS PLUS
Here are some examples- An interesting special case of the hypercycloid is the ASTROID which occurs for a4b4c after a /8 radian rotation. is a powerful, easy-to-use, equation plotter with numerical and calculus features: Graph Cartesian functions, relations, and inequalities, plus polar, parametric, and ordinary differential equations. Fixed formatting of equations produced by Find Derivative so derivatives of tan(x) and cot(x) graph correctly on reload.Ĩ. ( )cos( ) sin( / 1) ( )sin( ) cos( / 1) + y a b c ab and x a b c a b P P These equations yield a HYPOCYCLOID when bc and a HYPOTROCHOID when c differs from b. Fixed issues which could cause a fatal error graphing an equation to also corrupt memory or crash the program.ħ.
You can of course add explicit parentheses around function parameters to clarify your intent.Ħ. For instance, y = sinx cosx now parses as y=(sin x)*(cos x) rather than y=sin(x*cos x). Adjusted associativity of implied function parameters to assume that a factor which contains another function call was meant to multiply the first function call, not the function parameter. The single shared point is now evaluated to see if it is an intersection or not.ĥ. In this model, the curves each have five nodes. The ratio of the radius of the rolling disc to the radius of the outer ring will determine the number of nodes the hypotochoid will have. Fixed bug which caused Find Intersection on two curves with only a single point of their domains in common to display a spurious "Cannot solve this equation using Newton's method" error. An infinite number of hypotrochoids can be formed, depending on the distance of the tracing point from the center of the rolling circle.
Fixed bug which could cause the "Guess for off-screen intersection" entered in the Find Intersection dialog box to be ignored.Ĥ. Fixed a rare memory corruption issue in curve fitting code.ģ. Fixed y=x^(-(2/3)) to be correctly identified as an even power, so it draws both sides of the graph.Ģ.
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