Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

but it is tilted about theta=artan(x) wit the upper half of the '8' removed about the midpoint and the lower part removed about the of other half. It looks like a tilted 'S' but flipped, and it's monotonically increasing or decreasing.


share|cite|improve this question
You mean $\propto$ or $\sim$? – Hurkyl Jan 19 '13 at 20:22
$\int$ ? The description could use work – Jonathan Jan 19 '13 at 20:23
the second one, but it reaches a maximum-->minimum or minimum->maximum at the endpoints. – Jennifer Aneta Jan 19 '13 at 20:24
Are you asking about a mathematical symbol for writing, or a geometric shape for drawing? – Hurkyl Jan 19 '13 at 20:25
Is it possibly the logistic function? – MJD Jan 19 '13 at 21:24
up vote 2 down vote accepted

Here's $\theta = \arctan{x}$,

enter image description here

Also note that the sigmoid function is a mathematical function having an "S" shape ("aka": a sigmoid curve). Often, the sigmoid function refers to the special case of the logistic function:

$y = \dfrac{1}{1 + e^{-x}}$

enter image description here

If you are looking for the "reflection" or "inverse" of a "tilted $S$-shaped curve:

The inverse of $\;\theta = \arctan(x)\;$ is $\;x = \tan(\theta),\;$ and when plotted you get what you might be looking for if you restrict $\theta$ to $\theta \in (-\pi/2, \pi/2)$:

$x = \tan(\theta),\; \theta\in \left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$

enter image description here

Somewhat similarly, what you seem to be describing (a reflected/flipped tilted "S") looks a bit like the simple cubic function: $y = x^3$, (the graph can be translated, or rotated to tilt it more.)

$y = x^3$

enter image description here

share|cite|improve this answer
How did this not get any thumbs-up? +1 – Amzoti May 4 '13 at 2:19
$\ddot\smile$. I am at the uni. – Babak S. Sep 28 '13 at 3:08

a sigmoid function It has lots of applications in natural science, e.g., biological populations driven by evolution/natural selection.

share|cite|improve this answer

It is also called the logistic curve.

Another curve that looks much like it is the $\int_{-\infty}^x e^{-t^2} dt$.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.