A 3D regular hexahedron solid (cube) passing through a 2D plane:

## Isogonic Center

In geometry, the **isogonic center** (aka Fermat–Torricelli point) of a triangle, is a point such that the total distance from the three vertices of the triangle to the point is the minimum possible.

## Magic Topology!

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

## Solving An Impossible Packing Problem

Doesn’t fit? Reconstruct!

## Topology & Ethology

## 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.

## Elementary 4-manifold topology

**Impossible Folding Puzzles and Other Mathematical Paradoxes**” .

## Math Humor

Mathematics is sometimes weird… Read more: The hole truth of topology.

## 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”

## Möbius Curiosities

An intriguing Möbius maze created by Dave Phillips. Did you notice that the arrows, which should indicate the direction to follow, are wrongly placed?