In this video, a practical application of topology is presented through a simple knot technique for styling plant pots. This method transforms standard planters into trendy hanging displays.
Topology: A Hole Through a Hole in a Hole…
Have you ever pondered the nature of holes? These peculiar void-like spaces that seem to exist in the fabric of reality, yet defy simple categorization… Are they real objects that we can interact with, like a donut or a Swiss cheese? Are they abstract mathematical entities, part of the strange world of topology? Or do they exist only in our minds, as metaphysical concepts that arise from the limitations of our perception?
Explore these intriguing questions through our specially crafted posters and merchandise, which delve into the fascinating nature of holes. Discover them in our online gallery.
Hang the poster to spark endless curiosity, or wear the t-shirt to carry a conversation starter wherever you go.
Amazing Disentanglement Puzzle
How to transform ordinary rulers into captivating feats of magic? Equip yourself with two standard 30 cm rulers, made of wood or other materials. Attach a 20 cm string to each ruler by threading it through the hole at one end (see Fig. 1). Form a cord loop around one ruler, knotting the loose end of the cord, as depicted in figures 2 and 3. Ensure the string ring is not too tight, allowing it to glide smoothly along the ruler.
Repeat with the second ruler, threading the cord through the loop of the first ruler, as shown in figure 4.
The challenge is to separate the rulers without cutting or unraveling the cords. Despite the apparent difficulties, the solution unfolds seamlessly.
This string puzzle can also be build using two plastic pipes and two curtain rings (see figure 5).
The Geometry of the Bees
When constructing a honeycomb, bees aim to minimize wax usage and honey consumption, using the least wax necessary for a comb with maximum honey storage. The wax cells are designed with interlocking opposing layers, sharing facets at closed ends while having open ends facing outwards (see fig. 1). Each cell is a ten-sided structure with a rhombic decahedron form – a hexagonal prism with three rhombi at its closed end (fig. 2). Mathematicians have extensively studied the highly efficient isoperimetric properties of these cells. The question remains: What angle alpha maximizes volume while minimizing surface area on each cell face when the hexagonal prism’s faces have a width of 1 unit?
Continue reading “The Geometry of the Bees”Unfolding Knot
Complex knot equivalent to the unknot.
Possible Impossible Cube
Is it possible to 3D print an impossible cube ? Here is a way to do it… After all, it’s all about perspective!
Source: Wolfram Community
Impossible Structure
Perpetual Escher’s waterfall
Autokinetic Wireframe Cubes
Curiously enough, the cubes don’t move, only the background color changes…
Here is our tutorial to create an amazing autokinetic animation.
Trefoil Klein Bottle
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.
When a plane intersects a dodecahedron
A cross-section of the dodecahedron can be an equilateral triangle, a square, a regular pentagon, a regular hexagon (two ways), or a regular decagon.
