What does θ (theta) in a parametric equation stand for?

Question

In this curve given by WolframAlpha, there are some terms that have θ(theta) towards the end of each parametric equation. What does theta stand for?

Answer 1

It is the Heaviside theta function. Its output is 1 when the input is positive, and zero when the input is negative. The value of $\theta(0)$ is not agreed upon by everyone. Its purpose in the function you gave is to "turn on" and "turn off" different parts of the function to splice together different curves into one curve.

Answer 2

It is the Heaviside Step Function, which is basically the Unit Step Function.

It is defined as:

$$u_c(t) = \theta_c(t) = H_c(t)=\begin{cases} 0, & t < c \\ 1, & t \ge c \end{cases}$$

Here is a plot for $c = 0$, which is written $u(t)$ or $u_0(t)$ or $\theta(x)$:

This function is very useful for solving many types of problems and has an interesting history from it controversial founder Heaviside.

Here is a nice tutorial and these are useful notes or notes.