# 52: Mathematics

One is the square of one
and is zero plus the first odd number.
Each successive square
is the previous square
plus each successive odd number.
The first odd is one plus zero,
and each successive odd
is each corresponding natural number
plus the previous. In general,
x plus x minus one,
or two x minus one.
Putting these observations together,
we can generate the series of squares
with a series of simple additions—
The square of x,
where x is the series of natural numbers,
is the square of one less than x
plus the corresponding odd,
two x minus one:
x^{2} = (x - 1)^{2} + (2x - 1).
This equation tells us the relations
between the natural numbers,
the odd numbers,
and the squares.
Further, when transposed
to a Cartesian grid and the
real numbers (positive
and negative), it traces out
a conic section, the parabola
whose apex is at the center,
and whose left and right arms
reach upward to infinity.