Inspiring and Creative Resources & Tutorials for Science-Curious People
Can you alter this figure-eight-shaped pastry in order to thread the stick into the second loop? Obviously, you cannot unthread the stick from the pastry nor cut the pastry in any way!
The trick is explained in my book: “Impossible Folding Puzzles and Other Mathematical Paradoxes” available on Amazon: https://amazon.com/dp/0486493512/?tag=archimelabpuz-20
Doesn’t fit? Reconstruct!
The “Klein Bottle” is what happens when you merge two “Möbius Strips” together: the resulting shape will still have only one side – with its inside and outside merging into one. Obectively, such a paradoxical shape is clearly not possible within our 3-D reality and requires a fourth dimensional jump at some point to make it all come together. Also, because true Klein bottles do not have discernible “inside” or “outside”, they have ZERO VOLUME. As a result, these objects can only be simulated as an “impossible art” in our world, or only modeled with a “fake” 3-D intersection, instead of a true extra-dimensional joint. There are a lot of Klein Bottle model variants, this one is the most intriguing.
Mathematics is sometimes weird… Read more: The hole truth of topology.
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”
An intriguing Möbius maze created by Dave Phillips. Did you notice that the arrows, which should indicate the direction to follow, are wrongly placed?
Showing why a doughnut and a mug are topologically equivalent…
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”
