Plane Curve Panoramas

Expository Pages

An Introduction to Plane Curves: some characteristics to be observed
A Gallery of Conic Sections: 11 graphs of conic sections

Eccentricity of a Conic (GIF animation): see the conic graph change as its eccentricity varies

A Gallery of Cubic Plane Curves: 45 graphs of cubic plane curves

Trisectrix of Maclaurin (GIF animation): see how this graph can be used to trisect an angle
Witch of Agnesi (GIF animation): see how the graph is generated as a locus of points

A Gallery of Exponential, Logarithmic, and Hyperbolic Functions: 30 graphs of various functions
Trigonometric Graphs: the six basic graphs understood as projections

Generating the Sine Function: (GIF animation): see the sine function developed from the unit circle
The Trig Functions and the Unit Circle (GIF animation): see the 6 trig functions vary through the first quadrant of the unit circle

Definitions and Graphs of the Inverse Trig Functions: the six inverse trig functions (some with two forms)

Compositions of Trig and Inverse Trig Functions: 108 compositions with 74 different graphs

Taylor Polynomials (GIF animation): see the Taylor polynomials converge to three different functions

Interactive Pages

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All other links should be operational with any web browser.

Exploring Combinations of Functions (webMathematica): input two functions and see the graphs of their sum, differences, product, quotients, and compositions
Coordinate Systems (webMathematica): input a function and see its graph in several different coordinate systems
Basic Transformations in College Algebra (Excel): see the graph change as you vary the coefficients of a square, a cube, a square root, an absolute value, or a reciprocal function
Exploring the Zeros of a Quadratic Function (Excel): vary the coefficients of a quadratic polynomial and watch the zeros respond
Exploring Polynomial Zeros (Excel): vary the coefficients of a quartic polynomial and watch the zeros respond
Curvilinear Coordinates and the Polynomial Function (Excel): vary the coefficients of a quartic polynomial function and watch the graph in rectangular, polar, parabolic, elliptic, or bipolar coordinates
Curvilinear Coordinates and the Square Root Function (Excel): vary the coefficients of the square root function and watch the graph in rectangular, polar, parabolic, elliptic, or bipolar coordinates
Exploring the General Conic Graph (Excel): see the graph change as you vary the 6 coefficients of the general quadratic equation
Exploring Quartic Plane Curves (Excel): see the graph change as you vary the 15 coefficients of the general quartic equation
Curvilinear Coordinates and the Exponential Function (Excel): vary the coefficients of the exponential function and watch the graph in rectangular, polar, parabolic, elliptic, or bipolar coordinates
Curvilinear Coordinates and the Logarithmic Function (Excel): vary the coefficients of the logarithmic function and watch the graph in rectangular, polar, parabolic, elliptic, or bipolar coordinates
Curvilinear Coordinates and the Sine Function (Excel): vary the coefficients of the sine function and watch the graph in rectangular, polar, parabolic, elliptic, or bipolar coordinates
Curvilinear Coordinates and the Tangent Function (Excel): vary the coefficients of the tangent function and watch the graph in rectangular, polar, parabolic, elliptic, or bipolar coordinates
Curvilinear Coordinates and the Secant Function (Excel): vary the coefficients of the secant function and watch the graph in rectangular, polar, parabolic, elliptic, or bipolar coordinates
Curvilinear Coordinates and the Inverse Sine Function (Excel): vary the coefficients of the inverse sine function and watch the graph in rectangular, polar, parabolic, elliptic, or bipolar coordinates
Curvilinear Coordinates and the Inverse Tangent Function (Excel): vary the coefficients of the inverse tangent function and watch the graph in rectangular, polar, parabolic, elliptic, or bipolar coordinates
Exploring Fourier Series (webMathematica): vary the generic Fourier series term, and see the effect on the graph
Rose Analyzer (webMathematica): vary the parameters in the polar equation of the rose
Limacon Analyzer (webMathematica): vary the parameters in the polar equation of the limacon
Lissajous Curve Analyzer (webMathematica): vary the parameters in the parametric equations of family of curves of Lissajous