Math Toys

Tunnelscope: Circular Mirror Kaleidoscope

Tunnelscope kaleidoscopes of many designs available here:

From Etsy: BUY NOW: Tunnelscopes

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Tunnelscope Circular Reflection Kaleidoscope: in this novel design a straight length of transparent acrylic rod provides the reflective surface, and two wheels filled with resin and interesting shapes of colored glass can each be turned separately to produce a flow of psychedelic patterns. The physics of refraction and total internal reflection allows for multiple reflections of the images down this light pipe “tunnel”, in essence providing a near perfect circular mirror design. A creation of kaleidoscope innovator and artist Roy Cohen, and made from polished brass, cast acrylic, and colored glass. 

Jacob's Ladder Image Flip

This item came to me in my Fall 2023 Curiosity Box subsciption:
Get (or give!) a Curiosity Box subscription here: JOIN NOW: The Curiosity Box

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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. 

 


In-Feed Google 4

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. 

 


Shashibo Earth

Available here:

From Amazon: BUY NOW: Shashibo Earth
From Art of Play: BUY NOW : Shashibo Geometric Art

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Shashibo Earth: the globe of the Earth is mapped to a rhombic dodecahedron in this new design of the Shashibo shape shifting puzzle. Dissect a cube into 12 equal irregular tetrahedra, connect these pieces symmetrically with hinges and add 36 magnets to create the Shashibo- a device with more that 70 geometrically interesting and aesthetic configurations (a few are shown here as the dodecahedron is transformed to a cube).

Five Orbiforms: Volumes of Constant Width

Get this set here:

From Etsy: BUY NOW: set of 5 Solids of Constant Width
Use code: FFMPHYSICSFUN to get 25% off from this shop

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Five Orbiforms: precision 3D printed vo5umes of constant width. These shapes have constant diameter no matter their orientation and will roll like spheres between two planes- note how the acrylic plate stays parallel to the table as the sphere and other orbiforms roll underneath. The one that resembles a pyramid is the Meissner tetrahedron, which is conjectured to be the orbiform of least volume. A sphere is the orbiform of maximal volume, and the others are based on revolutions of the Reuleaux triangle, pentagon, and heptagon respectively. Skillfully printed in two colors by Brandon of Fractal Forest Makes. 

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!


Ambiguous Circles and Squares 

Get these and amny other designs here:

From Shapeways: BUY NOW: 3D printed Illusions 

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Ambiguous Circles and Squares: two more examples of the Sugihara ambiguous object illusion, with “impossible” mirror reflection. Thanks to Gerardo Ortega for sending me these 3D prints of his designs.

Sonic Photonic Visualizer

This item came to me in my Summer 2023 Curiosity Box subsciption:
Get (or give!) a Curiosity Box subscription here: JOIN NOW: The Curiosity Box

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Sonic Photonic Visualizer: a laser reflects from a small mirror mounted on a stretched rubber membrane which allows the projection of complex curves produced by the deformation of the membrane from sound waves. Yet another amazing kit from the VSauce team at @thecuriositybox which uses a balloon as the membrane for the top of the “drum”. The membrane is most sensitive to sound waves in the bass and midrange frequencies and I got the best reaction with my Bluetooth speaker playing Moon Flower by Tahüm- a snippet of which is featured here.

Specular Hologram Knot

Learn more about this art form here:
Zintaglio Arts: Holography by Matt Brand
Click here: to see other specular hologoraphy in my collectiuon.
The full details of the math in this process are described in this paper by Brand

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Specular Hologram Knot: this complex 3D image is created by etched grooves that reflect a point source of light as glints, and each eye sees a slightly different pattern such that, via stereopsis, the shiny points appear to float above or below the surface. Complex mathematical equations must be solved to compute the shape of the thousands curves that are scratched into the surface of the metal plate. The artwork featured here is a creation of Matt Brand of Zintaglio Arts. 

 

 


Mirror Anamorphosis Card

This vintage card is from the 1980s.

Click here: to find more Anamorphic Images and Devices

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Mirror Anamorphosis: perspective often depends on the lens (or in this case, mirror) that is looked through. This vintage card from 1984 contains a cylindrical mirror anamorphic image. Lady Liberty is revealed by bending the flexible Mylar mirror in to a half cylinder.

Galton Boards: Small and Large

Available here: 
From Amazon: BUY NOW: Desk Galton Board 
From Amazon: BUY NOW: Display Galton Board (comes with an wonderful fact filled booklet). 

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Galton Boards Large & Small: 6000 steel balls vs. 3000 in the compact version. Each ball has a 50/50 chance of going left or right at each branch such that the balls are distributed at the bottom by the mathematical binomial distribution (12 layers for the desk version, 14 layers for the deluxe). In addition the number of balls in each bin can be predicted by Pascal’s triangle, where the number on each hexagonal branch point represents the number of possible paths to reach that point from the top. Two extraordinary designs by Philip Poissant and the best version of the Galton Board since its invention by Sir Francis Galton(1894). An amazing demonstration of the Central Limit Theorem for the home or classroom! 

Denary Dice Set

This d1-d10 dice set will be part of the very next Curiosity Box:
Get (or give!) a Curiosity Box subscription here: JOIN NOW: The Curiosity Box

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Denary Dice Set: whimsical and wonderful, this set of dice expands on the standard d4, d6, d8, and d10 to include all integers up to 10- including a d1(!) for which the physics of the design ensures it will always land face up, and a d2, to formalize a coin flip into a die. This set is the creation of the folks at @thecuriositybox and will be shipped out in the next subscription box in a few weeks. 


Galton Board with Pascal's Triangle

Get this amazing Galton Board probabutly demonstrator here: 

From Amazon: BUY NOW: Galton Board (comes with an wonderful fact filled booklet). 

Note: this site contains affiliate links for which I may be compensated

Galton Board with Pascal’s Triangle: 6000 steel balls (and one gold bead) fall through 14 levels of branching paths and always end up matching a bell curve distribution. Each ball has a 50/50 chance of going left or right at each branch such that the balls are distributed at the bottom by the mathematical binomial distribution. In addition the number of balls in each bin can be predicted by Pascal’s triangle, where the number on each hexagonal branch point represents the number of possible paths to reach that point from the top. See if your eyes can follow the path of the gold bead (representing a single random path) in the 240fps slow motion segment of the video. This extraordinary design by Philip Poissant is a modern version of the Galton Board, invented by Sir Francis Galton(1894) to demonstrate the Central Limit Theorem and show how random processes gather around the mean. Made and distributed by Four Pines Publishing Inc. and IFA.com 

Aperiodic Monotile

Learn more about this recent math dicovery here: An aperiodic monotile (arXiv)

Althogh the math says they can tile the plane, getting them to do so is more challenging than one might think! 
Get a set of laser cut hat tiles here:
From Etsy: BUY NOW: "the Hat" monotile set

See other aperoidic tilings in my collection.

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Aperiodic Monotile: this newly discovered 13 sided shape, named “the hat”, will tessellate a plane to infinity, similar to how squares or hexagons can tile out with no gaps. However the hat tiles the plane aperiodically- if one tries to shift a part of a hat 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 that tile in this aperiodic way. However it was not clear until a few weeks ago if a single shaped tile could tessellate aperiodically when the hat was described in a paper by Smith, Myers, Kaplan, and Goodman-Strauss uploaded to arXiv March 20.