Transcendental Meditation (TM)

Spiritual development technique developed and promoted by Maharishi Mahesh Yogi, a former Hindu ascetic. A movement that became popular in the West in the 1960s, it is based on specific meditation techniques and is not strictly connected with any religious tradition, though the perspective behind it has roots in Vedanta. Practice entails the mental repetition of a mantra in order to still the activity of thought and experience a deeper level of consciousness. Through this process, the practitioner finds deep relaxation, which can lead to inner joy, vitality, and creativity.

Learn more about Transcendental Meditation (TM) with a free trial on Britannica.com.

The butterfly curve is a transcendental plane curve discovered by Temple H. Fay. The curve is given by the parametric equations:

$x\; =\; sin(t)\; left(e^\{cos(t)\}\; -\; 2cos(4t)\; -\; sin^5left(\{t\; over\; 12\}right)right)$

$y\; =\; cos(t)\; left(e^\{cos(t)\}\; -\; 2cos(4t)\; -\; sin^5left(\{t\; over\; 12\}right)right)$

or by the following polar equation:

$r=e^\{sin\; theta\}\; -\; 2\; cos\; (4\; theta\; )\; +\; sin^5left(frac\{2\; theta\; -\; pi\}\{24\}right)$

See also

• Butterfly curve (algebraic)

References

• Fay, Temple H. (1989). "The Butterfly Curve". Amer. Math. Monthly 96 (5): 442–443.

External links

• Butterfly Curve from MathWorld
• An animation based on the butterfly curve: video The script to reproduce it with gnuplot: script