# Some Mathematical GIFs

Here are some GIFs I have collected over internet that explain mathematical ideas. The following GIF explain what is meant by tangent/parallel lines and asymptotes.

The following GIF explains how to construct a regular heptagon using straight edge and compass.

The following 2 GIFs explain what an ellipse is and how to draw it.

The area of the circle with unit radius is $\pi$ and so is the circumference of the circle with unit diameter. The following 2 GIFs illustrate that.

The following GIF explain a method to find the Golden Ratio ($\phi$).

The following 3 GIFs are the illustrations of Pythagorean Theorem.

If you move along a unit circle with center at origin, then its coordinates are $(\cos \theta, \sin \theta )$. The following 3 GIFs exploit this fact.

The following GIF explains that how a sine wave is compressed or expanded if its period is changed.

The following GIF explain how to plot a graph by moving from rectangular to polar coordinates.

The following 2 GIFs demonstrate the creation of cardoid. In first a cardoid is obtained by rotating a circle around one of half its radius. The second one shows a parametric equation for the curve.

The following two GIFs demonstrate the creation of hypotrochoids.

In the following GIF, circles of radius 1 and 3 roll together along a straight line, tracing out a fixed cycloid along with rotating cardioids and deltoids.

The animation illustrates the Gram-Schmidt process for obtaining an orthonormal basis of vectors for 3-dimensional euclidean space.

All differential functions are continuous but not vice versa. The following animation shows a continuous function that is not differential at zero.

Taylor series is used for approximation of functions. The following 2 animations show a sinusoid and its Taylor polynomials of different orders.

The following 2 animations demonstrates the Fourier Series and Transform.It demonstrates how a series of waves with increasing frequencies, and carefully chosen decreasing amplitudes, adds up to give a square wave with flat peaks and troughs. Fourier analysis provides a method for choosing the amplitudes of the waves.

The last 3 GIFs are misc curves. The last one is the batman curve.