Some Mathematical GIFs

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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.

par_n_tan

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

heptagon

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

ellipse

ellipsebande

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.

area_circ

pi_unrolled

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

phi

The following 3 GIFs are the illustrations of Pythagorean Theorem.

pythag

pythanimpythagoras3d

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.

trig

trig3

trign

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

sinax

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

rect2pol

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.

cardiod

cardioid_par

The following two GIFs demonstrate the creation of hypotrochoids.

hypotrochoid

hypotrochoid2

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.

cdc

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

gram-schm

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

continuity

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

taylortaylor2

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.

fourier2

fourier

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

cubincube

spiral

batflaps

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