Cubic EquationsMy Mathematics Pages
Welcome to my mathematics pages. I am putting together some good reference pages on various topics of mathematics. Some of the information here are my discoveries, while most of it are just topics that I found interesting. Use the navigation on the left side (or click on “Menu” above) to peruse through the site. As of September 12, 2009, I don’t have many pages created yet. I am slowly converting my Word documents to HTML.
Most pages on this site shows equations in MathML rendered by MathJax scripts. Javascript will be required to display the equations.
Updates
June 25, 2025: find the roots of cubic equations.
Series from Integration by Parts
June 11, 2025: Series that result from interation of integration by parts.
Decomposition of Rational Functions into Partial Fractions
June 1, 2025: How to decompose rational functions into partial fractions for easier integration.
Finding the Vertex and Focus of a Parabola by Construction
May 29, 2025: This page proves that the vertex of a parabola lies on a line that connects the midpoints of parallel chords of a parabola. It shows how to find the vertex of the parabola and the focus for any arbitrary parabola.
Finding the Center and Foci of an Ellipse by Construction
May 25, 2025: This page proves that the center of an ellipse lies on a line that connects the midpoints of parallel chords of an ellipse. It shows how to find the center of the ellipse, the four vertices and the 2 foci by geometric construction for any arbitrary ellipse.
Equation of an Ellipse with Predetermined Foci
May 12, 2025: This page gives an elegant equation of an ellipse with foci located at any points.
How to graph polar equations, calculate areas, arclengths and some interesting polar curves.
Cubic and the Equilateral Triangle
Updates
(1) Some images have been updated with better graphing software. Some of these images are in the SVG image format for better scalability.
(2) Many Geogebra activities have been included for a hands-on approach to some concepts.
(3) Site has been made friendly for mobile devices. Equations have been split up so they wrap to another line. However, some equations cannot be split and will roll off the page of small devices. In some cases, this was unavoidable.