Does every simple closed curve in the plane contain the vertices of a square?
No one knows, but the answer to this question is positive if the curve is sufficiently regular.
Toeplitz’ Conjecture
Elementary 4-manifold topology
Cut any of the loops of strings below and the whole chain comes apart.
You will find many of these kinds of puzzles in my book “Impossible Folding Puzzles and Other Mathematical Paradoxes” .
Transform a Ball with 2 Holes into a CD
Topology is a fascinating branch of mathematics that describes the properties of an object that remain unchanged under “smooth” deformations. If we imagine objects to be made of clay, a smooth deformation is any deformation that does not require the discontinuous action of a tear or the punching of a hole, such as bending, squeezing and shaping. These deformations are called “continuous deformations“. Continue reading “Transform a Ball with 2 Holes into a CD”
Mug to Doughnut
Showing why a doughnut and a mug are topologically equivalent…
How to ‘magically’ untie a shoelace double knot
Topology is 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.
Puzzle-Meister G. Sarcone created this amusing everyday-life topological puzzle to help children to easily take their shoes off.
As 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? Continue reading “How to ‘magically’ untie a shoelace double knot”