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Showing posts with label geometry. Show all posts
Showing posts with label geometry. Show all posts

Magnets and Geometry

A bunch of us are in the middle of a short fad of fascination with magnets. I recently purchased about a thousand gold-plated spherical 6mm N35 neodymium-iron-boron magnets from Edwin Science. These are strong enough that swallowing two of them would probably require surgery. But I am not dumb enough to eat them, being far more interested in building things out of them, and thus I give you some photos of the nifty things I did when I got them, and some tips on how to assemble them. I regret not having the artistic skills or patience to illustrate all of the information I want to share here, but hopefully those interested can follow along.

The first building block is a loop of magnets, with the poles aligned circumferentially (that is, a string of aligned magnets joined end to end). In the photos below, anywhere you see two parallel rows of magnets arranged in a square configuration, that indicates the adjacent rows are aligned in opposite directions, and almost always part of separate loops. If the rows are arranged in a triangular configuration, that indicates they are aligned in the same direction. The loops can be treated as polygons (squares, pentagons, hexagons, octagons, etc) to create polyhedra. The strength of the magnets causes them to exert force in the direction of perfect alignment, which gives rigidity to what would otherwise be flexible circles.

Truncated OctahedronOctahedronOctahedronGreat RhombicuboctahedronCuboctahedronDodecahedronDodecahedronDodecahedronDodecahedronDodecahedron, truncated

Two or more loops of the appropriate relative size can be stacked to form a shape somewhere between a cone and a pyramid. 5-10-15-20 makes a pentagonal pyramid, 4-8-12-16 makes a square pyramid, 6-9-12-15 (a "loop" of 3 magnets is not stable) makes a triangular pyramid. For reasons related to the bulk of the individual spheres, the triangular pyramid is too tall and too circular to be of much use, which is unfortunate since a triangle is by far the most useful shape for building polyhedra. The square pyramid is better, but far less useful. This leaves the pentagonal pyramid as the building block of choice for a large number of assemblies. Each "pyramid" can be assembled from as few as two to as many as four concentric rings (a fifth ring results in most structures being too heavy to support their own weight... until I get some N52 spheres!). Each layer can be "up" or "down", so you may get a rippled surface instead of a cone shape, and the entire resulting shape can be installed into the final product pointing out or in. Also of note is that the pyramids have a "handedness". Where the rings can be simply flipped over if they are out of alignment, the pyramids have to be inverted if you need to flip them.

15-magnet Pentagon UnitDodecahedron, inverted pyramid faces, assemblyDodecahedron, inverted pyramid facesDodecahedron, offset pyramid facesTwelve Pentagon EggSix Pentagon CylinderDodecahedron, pyramid facesDodecahedron, pyramid facesDodecahedron, pyramid facesDodecahedron, pyramid faces, interior mountingTwelve Pentagon RingTetrahedronDodecahedron, pyramid faces, interior mountingRhombic Prism