a fascinating branch of mathematics that describes the
properties of an object that remain unchanged under continuous “smooth” deformations.
Actually, many 3D puzzles are based on topological principles
and understanding some very basic principles may help you
analyze whether a puzzle is possible or not.
G. Sarcone created this amusing everyday-life topological
puzzle to help children to easily take their shoes off.
you know, the standard shoelace knot is designed for quick
release and easily comes untied when either of the working
ends is pulled. Thus, most people think that tying a shoelace
into a double knot is an effective method of making the
knot “permanent”. But is it true?
let’s make a standard shoelace knot following the
steps ‘a’ to ‘f’ of the diagram:
take a shoelace in each hand (a) and cross one lace over
the other (b). Poke the end of the lace through the cross
hole and pull both ends tight (c). Form with each lace
a loop (d). Then, wrap a loop around the other loop and
pass it through the cross hole (e) in order to tie both
loops tight in a half hitch (f). To make the double knot,
cross again the loop over and wrap it around the other
loop (g) and pull both loops until tight (h).
try to untie your shoelaces WITHOUT touching the double