There is a weird transformation known as \( WT999999P2 \), also known as The W9 transformation. Little is known about it. However, it is known that it is certainly used to transform a square into a smaller square, following few steps and other wierd transformations. Some weird manual indicates the following about the transformation:
Step 1: Inscribe a regular octagon in the square, using method I8-v2.
Step 2: Find isosceles triangle by rule T8 in octagon from step 1
Step 3: Inscribe a circle in the triangle from step 2
Step 4: Inscribe a square in the circle from step 3.
The initial square is transformed into the square from step 4
And now, the questions will be asked. If we have a square whose side length is \( 10^5 \), after applying transformation three times, what will be the new side length. If that new length is \( L \), answer shall be entered as \( \left\lfloor L \right\rfloor \).
If you just grasped: "Oh dear"
Because within you, lies a fear,
That something is left unclear,
It can be asked right over here.