Project MathemGL

Aim:

To implement Standard Math’s Interactive Animations using OpenGL, to make understanding of the important concepts of mathematics using Animations.

Potential Users:

Mathematics Enthusiasts.

Potential Work:

Animations include as follows:

• Formation of the locus of the Conic Sections namely, Circle, Ellipse and Parabola.
• Cross-section of Cone to show different Conic Sections, including Hyperbola.
• Animations to show some Standard Limits of Sin, Cos and Tan.

Description:

Graphical proofs of standard limits:

• lim┬(x→0)⁡〖(sin x)/x 〗= 1
• lim┬(x→0)〖(⁡cos⁡ x) 〗= 1
• lim┬(x→0)⁡〖(tan⁡ x)/x 〗= 1

Locus of Conic Sections:

Circle: Circle is the locus of all the points at equidistant from a given fixed point, Center.

Ellipse: Ellipse is the locus of all the points such that sum of distances of the point from two given fixed points, Focii is constant.

Parabola: Parabola is the locus of all the points at equidistant from a given fixed point, Focus and a line, Directrix.

Formation of Conic Sections from Cone:

Circle: Circle is a conic section obtained by cutting the cone by a plane parallel to the base.

Ellipse: Ellipse is a conic section obtained by cutting the cone by a plane at angle < 90 with respect to base.

Parabola: Parabola is a conic section obtained by cutting the cone by a plane at angle > 0 (not equal to 0) with respect to its axis.

Hyperbola: Hyperbola is a conic section obtained by cutting the cone by a plane parallel to its axis.

Limitations:

• After selecting one animation, program needs to be run again for selecting other animation to be displayed.

• For showing the cross-section of cone to generate different conic sections, clipping viewport has been used. But, the idea was to use a plane with some colour so that it is clearly visible that the cone is being cut by a plane to get the required conic section.

Conclusion:

We have shown graphical proofs of standard limits using plot of trigonometric functions. We have also shown how different conic sections can be drawn using pencil, thread and fixed pins (with fixed lines in case of parabola). We have visualized how conic sections are formed from cross-section of a cone.