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 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 ().

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 . 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.

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