Draft:Squared Constant

The Squared Constant is a mathematical constant created by concatenating the decimal representations of perfect squares in sequential order. This results in an infinite, non-repeating decimal number.

The Squared Constant is formed by writing each perfect square consecutively after a decimal point:

0.149162536496481100121144169...

Here:

$1^{2}=1$

$2^{2}=4$

$3^{2}=9$

$4^{2}=16$

$5^{2}=25$

$6^{2}=36$

$7^{2}=49$

And so on...

This pattern continues indefinitely, as there are infinitely many perfect squares. The Squared Constant does not terminate or repeat, reflecting the infinite nature of perfect squares. Similar to Champernowne's constant, which is formed by concatenating all positive integers, the Squared Constant is constructed by concatenating perfect squares.

While primarily of theoretical interest, the Squared Constant exemplifies how structured patterns can emerge from fundamental mathematical sequences. It may serve as a basis for exploring properties of numbers and sequences in mathematical research.