With squares as a theme within the main body of the magazine it would be remiss not to revisit an old idea:
And a reminder.
TO SQ :N
REPEAT 4 [ FD :N RT 90]
END
But why not REPEAT 6 and then turn a little?
Or, why not consider a systematic reduction of the basic design?

Why not then put all the four designs together?

Why not add others that are bigger?
BUT what has this got to do with the following numbers:
0.4142; 1.4142 and 2.4142?
As before the challenge is to produce elegant solutions to any problems asked or any replications that you attempt. Where elegance implies simplicity within the program(s) and procedures devised.
Alternatively you may like to explore the following procedure:
TO NESTSQ :SIDE
IF :SIDE < 2 [STOP]
REPEAT 4 [ NESTSQ :SIDE/3 FD :S RT 90]
END
( Perhaps instead of squares you might like to vary the number of repeats and the angle turned through.)
For absolute beginners who would like to pursue some of the other LOGO activities, elsewhere in the magazine there is a section entitled FIRST FORWARDING.
This is currently having a second airing. It can be found elsewhere within these pages.