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”

Intriguing Geometric Dissections

Any two polygons with equal area can be dissected into a finite number of pieces to form each other. One of the most interesting dissection or geometric equidecomposition puzzles is that discovered by Harry Lindgren in 1951 (see Fig. 2 further below). As you know, in this kind of puzzles, the geometric invariant is the area, since when a polygon is cut and its pieces are distributed differently, the overall area doesn’t change.

Lindgren was the first to discover how to cut a dodecagon into a minimal number of pieces that could pave a square, when rearranged differently. His solution is very elegant, he first built a regular Euclidean pavement by cutting a dodecagon as shown in fig. 1.a, then arranging the four pieces symmetrically on the plane (fig 1.b). The tessellation achieved with these pieces corresponds, by superposition, to a regular paving of squares. The example in fig. 2 shows how the puzzle appears once finished.

dodecagon fig. 1

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Linear to rotational motion

Intriguing linear motion perceived as circular motion! Watch as the black balls rotate in a circle, then focus on one ball at a time and you will notice that it follows a straight line. Also, watch at the moment when there are only four balls moving, it forms a rotating square between the four balls. This is just neat example of looking deeper into something so simple and discovering a hidden pattern.

Linear to circular motion

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Pattern with Arabesque paths moving in a linear fashion induces rotational motion to a hexagonal device.