Equilateral Triangular Kaleidoscope
This inexpansive kaleidoscope is available here:
From increadiblescience: BUY NOW: Moire Tube Kaleidoscope
Click here for affordable, precision made scopes with angled mirrors: Kaleidoscope Symmetries Explored
See more kaleidoscopes in my collection: Kaleidoscopes
Equilateral Triangular Kaleidoscope: three mirrors arranged in a 60-60-60 degree triangle creates the appearance of a plane filled with triangles (or equivalently a honeycomb lattice)- perhaps the most common mirror configuration design, this inexpensive kaleidoscope produces an excellent example of the reflection pattern. As a bonus the exterior tube on this scope incorporates a kinetic Moirè pattern. The kaleidoscope was invented by the famous Scottish physicist Sir David Brewster (1781-1868), and has become an entire field of artistic endeavor.
Hexacon and Sphericon Rollers
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From Etsy: BUY NOW: Hexacon and Sphericon Rollers
Hexacon Roller: beautiful 3D printed versions of a recent mathematical discovery of new developable rollers (objects that roll where every point on the roller’s surface comes into contact with the plane upon which it rolls). Similar to the sphericon (based on a square) the hexacon rolls in a straight line with a peculiar wobble motion but has a hexagonal cross section (swipe to see video loop of each in motion). The hexacon (2019) and sphericon (1980) are two of a family of such rollers called polycons discovered by David Hirsch, and described in a paper by Hirsch and Seaton published in 2020.
Mathematica Eames Souvenir
Wikipedia has great info about Mathematica and where to see it.
The Poincare Disk is a representation of non-Euclidean gemometry and tesselations can look amazing- M.C. Escher used this math for his famous Circle Limit woodcut.
Mathematica features a large Galton Board (click to get one).
Mathematica Eames Souvenir: from the 1961 opening of “Mathematica: A World of Numbers and Beyond” by the famous design team of Charles and Ray Eames this souvenir of card stock features a tessellation of the hyperbolic plane (a Poincaré Disk) with triangles on the front and on the reverse is the title of the exhibit but hidden within an anamorphic font. Amazing math art before the age of computer graphics! There are three versions of the exhibit and all can still be seen at museums in Boston, Atlanta, and Dearborn.
Motion of Rolling Sphericons
Get these and other amazing developable rollers here:
From Etsy: BUY NOW: Hexacon and Sphericon Rollers
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Sphericons are unique solids that roll in such a way that every point on their surface comes in contact with the plane. Solids from the sphericon family all have one side and two edges. Each sphericon is based on an even sided regular polygon, with the basic sphericon derived from a square, and the next two possible shapes are the hexa-sphericon and octo-sphericon, each rolling with a more complicated path.
Hyperboloid Spinner
Kit available here:
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Hyperboloid Spinner: HypnoGizmo
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Hyperboloid Spinner: the HypnoGizmo toy consists of a set of slanted straight nylon lines arranged to form the outline of a hyperboliod- the quadratic surface related to the revolution of hyperbola around its axis of symmetry. As the device rotates the beads slide along in succession on one of the straight paths leading to the complex visual display. So much fun math in this toy!
Kostick Stars
Two versions available here:
From Art of Play: BUY NOW: Kostick's Stars
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Here is the detail of the connections of the 6 star from the patent document:
Learn more about John Kostick here: John and Jane Kostick handcrafted mathematical constructions
Kostick Stars: The geometric forms of these kinetic sculptures snap into place due only to the balanced tension forces between thear slightly bent bronze wires. The large star is comprised of six struts, each made of 5 wires, which are made to intersect and weave though each other with beautiful geometric regularity. Similarly the small star has 4 struts each made of 3 wires. The ends of the 6 struts of the large star become the 12 vertices of an icosahedron, and the ends of the 4 struts of the small star point to the 8 corners of a cube. Both stars can be collapsed along many of the symmetry axes. Invented and patented in 1970, these stars are still produced and sold by artist and designer John Kostick.
Chiral Aperiodic Monotile Puzzle
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From Etsy: BUY NOW: Specter Tile Set by Nervous Syestem
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Read the published paper: A chiral aperiodic monotile
Chiral Aperiodic Monotile: these puzzle pieces are all identical in shape, based on special family of forms called “specters”, and are key to a major mathematical discovery in May of 2023. Specters will tessellate a plane to infinity, similar to how squares or hexagons can tile out with no gaps. However specters are identically shaped tiles which fill the plane aperiodically- if one tries to shift a part of a specter tiling, the shifted part will not align or match up with any other part of the same tiling- all the way out to infinity! The fact that aperiodic tessellations exist at all is pretty amazing, and Sir Roger Penrose (Nobel prize in physics 2020) is also famous for discovering a pair of regularly shaped polygons in the 1970s that tile in this aperiodic way. Specters were discovered by the same team of mathematicians (Smith, Myers, Kaplan, and Goodman-Strauss) who discovered “the hat” aperiodic monotile in March 2023, but the hat needs its mirror image to complete the tiling whereas the specter does not. An amazing development found only two months after the initial major breakthrough. Credit to the @nervous.system design team for modifying the specter into an interlocking puzzle piece form- and assembling these without gaps is a fair challenge!
Shashibo Puzzle Dissected
Get this cube puzzle (in a variety of colors and patterns) here:
From Amazon: BUY NOW: Shashibo Cube
From Art of Play: BUY NOW : Shashibo Geometric Art
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Shashibo Puzzle Dissected: I cut apart one of these puzzles to better understand the geometry: it is indeed a cube dissected into 12 equal irregular tetrahedra as seen here. The embedded magnets still allow construction of the cube. Of course the symmetrically placed hinges (along with strategically placed magnets) creates the real magic of the Shashibo puzzle- a device with more that 70 geometrically interesting and aesthetic configurations including a rhombic dodecahedron as well as the cube.
Zulu Telephone Wire Bowl
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From Etsy: BUY NOW: Zulu Wire Bowls
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Geometric Weaving: this Zulu telephone wire bowl, made in the traditions of South Africa, features a brilliant spiral pattern. The bright colors come from weaving strands of colored wires- the kind used to connect phones throughout buildings. This particular pattern inspired using a rotating base to display this bowl as kinetic sculpture.
Jacob's Ladder Image Flip
This item came to me in my Fall 2023 Curiosity Box subsciption:
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See my other versions of the Jacob's Ladder
Jacob’s Ladder Image Flip: this Curiosity Box Inq the Octopus themed toy flips between two famous aperiodic tilings- Penrose rhombs on one side and the recently discovered einstein hat on the other. The earliest description of the ribbon hinged “Jacob’s Ladder” mechanism that creates this kinetic illusion of cascading blocks dates back to a magazine article from Scientific American magazine in 1889.
Color Spirit Kaleidoscope
Avalible in a number of colors from these sources:
From Nellie Bly's: BUY NOW: Color Spirit Kaleidoscopes
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Color Spirit Kaleidoscope: a side lit kaleidoscopic with sparkling and kinetic mandala. The intricate patterns seen come from shiny trinkets that flow in oil, and two mirrors that are precisely aligned at a 60 degree angle to produce the sixfold symmetry. This affordable yet top quality kaleidoscope is from the Color Spirit line of artist Karl Schilling.
Symmetric Sticks Puzzle
Geometry as art and play-- get this affordable puzzle here:
From Etsy: BUY NOW: Symmetric Sticks Puzzle
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Symmetric Sticks Puzzle: 30 identical pieces, each with two notches as shown, can create 12 interlocking pentagons in a perfect symmetry- look carefully and you can see that each rod is in an identical configuration with the 4 others that connect with it. Precision notches on the rods allow them to interlock with elastic tension such that vector sum of the 4 forces sum to zero in this tensegrity type equilibrium. The dodecahedron, with its 30 edges and 12 sides, is the basis of this puzzle sculpture.
Cubendi Dissected Cube Puzzle
Thie new dissection puzzle is available here:
From Amazon: BUY NOW: Cubendi Cube
Get the sister cube puzzle here:
From Amazon: BUY NOW: Shashibo Cube
From Art of Play: BUY NOW : Shashibo Geometric Art
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Cubendi Puzzle: Dissect a cube into 4 equal irregular tetrahedra + 8 equal irregular triangular pyramids, connect these 12 pieces symmetrically with hinges and add 48 magnets to create the Cubendi cube. This assembly can make a number of surprising symmetrical forms including this rectangular prism with a square hole. More math fun with this second hinged dissection cube puzzle from the makers of the Shashibo Cube.
Mirror Anamorphic Lenticular Cup & Saucer
Now available here:
From Amazon: BUY NOW: Anamorphic Wavy Cups & Saucers
See all the amazing illusions and art avaialble from Luycho: Luycho | A New world on Mirrors
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Mirror Anamorphic Lenticular Cup & Saucer: a flamingo sits in a nest of flowers, revealed when the cylindrical mirrored cup is put in place. This beautiful design by Luycho uses both mirror anamorphic reflection and an accordion type lenticular dual image (turning the plate 180 degrees trades images). Art meets math and physics once again!
