Why is the intercept typed in as a 1 in stats packages (R, python) When using statistics software, When defining your linear models, why is the intercept typed in as a 1, rather than "const" or "intercept" or something. What significance does 1 have? 
Is there some historic reason? Or is this logical in some way I am failing to grasp? The intercept could very well be any number.
Example from statsmodels library in python:
model = smf.ols('Height ~ 1', data = height_sample_data)

I know lmer package for R is very similar.
 A: It is logical, once you consider the matrix notation that your formula will be translated into internally. In the matrix, the non-constant predictors will be translated into (one or more) columns, and the intercept will be translated into a column consisting entirely of ones.
For instance, in R you would write a very simple OLS as:
lm(z~1+x+y)

In matrix notation, this would be translated into a model
$$ \begin{pmatrix} z_1 \\ z_2 \\ \vdots \\ z_n \end{pmatrix} =
\begin{pmatrix} 1 & x_1 & y_1 \\ 1 & x_2 & y_2 \\ \vdots & \vdots & \vdots \\ 1 & x_n & y_n \end{pmatrix}
\begin{pmatrix} \beta_0 \\ \beta_x \\ \beta_z \end{pmatrix}
+\begin{pmatrix} \epsilon_1 \\ \epsilon_2 \\ \vdots \\ \epsilon_n \end{pmatrix},
$$
and now you see where the $1$ comes from.

Actually, you could leave the 1+ out, since R will always presume you want to include an intercept, so this is completely equivalent to 
lm(z~x+y).

However, if you want to suppress the intercept, you would write something like
lm(z~x+y-1),

which would be translated into a matrix without a 1 column:
$$ \begin{pmatrix} z_1 \\ z_2 \\ \vdots \\ z_n \end{pmatrix} =
\begin{pmatrix} x_1 & y_1 \\ x_2 & y_2 \\ \vdots & \vdots  \\ x_n & y_n \end{pmatrix}
\begin{pmatrix} \beta_x \\ \beta_z \end{pmatrix}
+\begin{pmatrix} \epsilon_1 \\ \epsilon_2 \\ \vdots \\ \epsilon_n \end{pmatrix},
$$
