Math Toys

High Voltage Wood Burn Fractal

Beautiful wood fractal art available here:

From Etsy: BUY NOW: High Voltage Fractal Art

High Voltage Wood Burn Fractal: a classic Lichtenberg fractal created by electrical discharge- in this piece artist/maker Nic Ferretti applied cobalt blue epoxy resin to fill the cavities of the burn pattern and create the look of frozen lightning. Swipe to see my attempt at this process with an old neon sign high voltage transformer using 7500 V at 20 mA. I turned the power off right before the two sides connected to get the fern-like look. The wood is slightly wetted with baking soda dissolved in tap water. WARNING high voltage can kill- do not use a transformer like this unless you are fully trained in electrical high voltage safety. 

Dodecagon to Square Puzzle

Get these and other well made disection puzzles here:

From Etsy: BUY NOW: Square Dissection Puzzles

These puzzles are expertly laser cut and sold by GamesEfce. I spray-painted the pieces of mine to better show the shapes and relationships for the video. 

Square to Dodecagon Dissection Puzzle: a square can be cut (dissected) into polygons and then reassembled into other regular polygons. Amazingly the 12-sided regular polygon can be cut into these six specific pieces that can then fit a square. Swipe to see the minimum cuts dissections for a hexagon, pentagon, and triangle.


Ambiguous Object 

These type of objects were invented by mathematician Kokichi Sugihara, and you can buy his other books here: 
From Amazon: BUY NOW Ambiguous Objects by Kokichi Sugihara 

Also available from Amazon (Japan): BUY NOW set of four ambiguous objects with booklet 

Similar objects available here- from Etsy: BUY NOW Ambiguous Objects

Another illusion design by Kokichi Sugihara of Meiji University in Japan, the inventor of this illusion and art form. A mathematically calculated combination of perspective and the physics of reflection produce this striking illusion that works in many configurations.

The Random Walker

Galton Board version available here: 
From Amazon: BUY NOW 
Galton Board 

The Random Walker: second model of two Galton Boards designed and produced by this version is made to demonstrate probability in investment returns of a global stock market portfolio relating to risk capacity. Slow motion reveals the erratic path of each steel ball (second half of video). The red graph shows the distribution of 592 monthly returns (mean =1%, SD=5%) representing data from 50 years of an IFA Index fund- here the random “walk” of 3000 steel balls falling through 12 levels of branching paths always produce a close match, and both distributions tend toward the famous bell curve distribution. A wonderfully designed modern version of the Galton Box invented by Sir Francis Galton(1894) to demonstrate the Central Limit Theorem - showing how random processes gather around the mean.

Hyperbolic Holes

This inexpensive kit available here:

From Amazon: BUY NOW: Hyperbolic Holes Kit

Hyperbolic Holes: a straight rod, in this case a pencil, glides through a symmetrical pair of curved holes. The design is based on the hyperboloid, the 3D ruled surface traced by an offset rotating diagonal line. This device is sold as an inexpensive kit to assemble yourself, and includes a motor with geared drive and pre-cut pieces. The pencil is my addition- sharpened to just the right size to clear the curved openings.

Lissajous Roller 

Available from Pyrigan & Co.

From Etsy: BUY NOW: Lissajous Roller Illusion

Lissajous Roller: when viewing this 3D printed object from the side one sees a projection of a 3:2 Lissajous curve, but the object is actually cylindrical in frame and can roll towards or away from the viewer. When in motion a “dual axis illusion” is produced where the object appears to be rotating about a vertical axis. Invented by Bill Gosper and produced by Pyrigan & Co. 

10 Hex Puzzle

This and other beautiful and well made puzzles are available on Etsy: 
From Etsy: BUY NOW 10 Hex Puzzle 

Two great resources about these polyhexs: polyform puzzler page and puzzleworld page 

10 Hex Puzzle: this puzzle is comprised of pieces which are the set of all ways three and four hexagons can be joined with a common edge. There are 3 trihexs and 7 possible tetrahexs, and similar to pentominoes, these 10 polyhexs can assemble into a large hexagon. Amazingly there are exactly 12,290 solutions to this puzzle- but it’s still a challenge to find just one! 

Uphill Roller

This set available here:

From Amazon: BUY NOW: Uphill Roller Double Cone

Uphill Roller: a double cone (like two funnels connect by their tops) will roll up a set of inclined rails. Although the bi-cone rolls toward the higher end, its center of mass descends due to the geometry of the rails. This curious construction was first published in 1694 by the noted surveyor William Leybourn to promote “recreation of diverse kinds” towards the “sublime sciences”. Physics fun from three centuries ago!

The Klein Bottle

The best Klein Bottles are made by Cliff Stoll, astronomer, mathematician and artist. Every one-sided, zero volume bottle is packaged and shipped by Cliff himself. Get one today! 
From ACME Klein Bottles: Buy NOW Klein Bottles by Cliff Stoll 

Wikipedia has great details on the Klien Bottle, and the amazing Cliff Stoll

The Klein Bottle: 3D representation of a four dimensional mathematical object with one side, no edges, and zero volume. Kind of like a Möbius strip with no edges.* Math meets glass art! Many thanks to Cliff Stoll for this kind gift and a great visit including a wonderful tour of his collection of mathematical oddities. *only achievable in 4D. 

Hexa Sphericon

Sphericon and Hexa-sphericon: beautiful works of art in metal- available here!
From the Matter Collection: BUY NOW The Sphericon (Hex and Regular) 

3D printed as well as handmade sphericons and similar shapes avaiable here:

From Etsy: BUY NOW: Sphericons 

Hexa-Sphericon: Sphericons are unique solids that roll in such a way that every point on their surface comes in contact with the plane- following the path shown here with white paper. Solids from the sphericon family all have one side and two edges. Each sphericon is based on a regular polygon, with the basic sphericon derived from a square, and here- a more interesting case with more complex rolling motion- from a hexagon. 

Infinity Cube Sculpture

Get an infinity cube here (many colors and sizes to choose from):

From Ricardo Churchill (Etsy): BUY NOW: Infinity Cube

Infinity Cube Sculpture: crafted from solid stainless steel and powder coated orange, the geometry of this mathematical sculpture is the perimeter of the faces of a cube traced by a nonintersecting connection of equal line segments. When viewed from a corner, a cube has a hexagonal cross section, and some may recall the famous logo of Silicon Graphics computers based on such an infinity cube (a design by Scott Kim). Rotating this “tubed cube” along a diagonal axis reveals the interesting symmetries of this geometric construction.

Polarized Light Cell Kaleidoscope

Click here for affordable, precision made scopes with angled mirrors: Kaleidoscope Symmetries Explored

Similar Kaleidoscopes available here:

From Amazon: BUY NOW Fluid Flow Kaleidoscope 
From eBay: Fluid Flow Kaleidoscope

See more kaleidoscopes in my collection: Kaleidoscopes

Polarized Light Cell Kaleidoscope: the amazing colors you see from the object cell of this 3 mirror kaleidoscope are generated by manipulating the polarization of light- the object in the clear wand is a strip of clear cellophane in oil which has the property of optical rotation. These property allows for an incredible range of color formation when placed between two linear polarization filters (swipe for demonstration). A creation of kaleidoscope artist Ron Kuhns.

Soma and Rhoma Puzzles

The Rhoma Cube is a vintage item and can sometimes be found on eBay:

From eBay: Search NOW: Rhoma and Soma Puzzles

Soma Cubes are available in a wide viariety: 

From Amazon: BUY NOW: Soma Cube

From Etsy: BUY NOW: Soma Cube

SOMA and RHOMA Puzzles: Replace every cube in the Soma puzzle with a rhombohedron to create the Rhoma puzzle- where the seven slanted pieces now make a larger rhombohedron. Here I’ve painted the corresponding Soma and Rhoma pieces to match on these sister puzzles that share identical edge lengths. While there are 240 ways to make the larger cube from the 7 Soma pieces, there is only one solution for the 7 Rhoma pieces. The original Soma Cube is a math toy has an interesting connection to physics- invented by Danish scientist and artist Piet Hein who claimed that this puzzle idea came to him as he was listening to a lecture on Quantum Mechanics by Werner Heisenberg in 1933. The seven pieces are all the ways 3 or 4 cubes can be joined, such that each piece has at least one inside corner.

Electromagnetic Levitation Module

Get this kit here (comes complete as shown in my video):
From engineDIY: BUY NOW: Magnetic Levitation Module

The featured sculture is by Bathsheba Grossman, affordable and beautiful math art available here:
From Etsy: BUY NOW: Soliton Sculpture

Electromagnetic Levitation Module: this engineered control system uses adjustable electromagnets (four copper coils) and and two Hall effect magnetic field sensors (held firm embedded in white silicone) to levitate an 5cm diameter neodymium magnet platform about 3 cm in mid-air. A feedback loop informed by the Hall effect sensors allows fine tuning of the magnetic field to exactly balance the pull of gravity, and is powered by a standard USB connection. The platform also rotates, perfect for showcasing one of my metal 3D printed mathematical sculptures by Bathsheba Grossman.

Arrow on Mobius Strip

Get this 3D printed object of math topology here:

From Etsy: BUY NOW: Mobius Strip with Arrow

Arrow on Möbius Strip: on the geometry of a Möbius strip a right pointing arrow points left after one trip around, a second trip restores the original orientation. This mathematical property is called non-orientability, and is also true of Klein bottles which I’ve posted about. I love how this 3D printed model, designed and produced by Wes Pegden, allows one to physically manipulate and intuit this somewhat obscure mathematical property. 

Dymaxion Map

Get one there:

From Art of Play: BUY NOW: Dymaxion Folding Globe

Dymaxion Map: today some math fun with this unique mapping of the Earth where the globe is projected onto an icosahedron and then unfolded onto two dimensions. Invented by the famous architect R. Buckminster Fuller, the Dymaxion projection map is designed such that it does not have a “right way up” and showing the continents as “one island Earth”. This mapping also produces less distortion of relative areas and shapes- note here that Greenland looks, correctly, much smaller than Africa- unlike what is seen on many world maps where they look the same size. This version, designed by Brendan Ravenhill, uses flat magnets to allow a very satisfying transformation between the flat 2D net and the 3D icosahedron “globe”.

3-Shuttle Trammel of Archimedes

Get this device here:

BUY NOW: 3 shuttle device

This device came in my Curiosity Box subscrition. A great way to start collecting your own physics toys (and other brain food):

From the Vsauce team: BUY NOW: The Curiosity Box (New box will ship soon- get a great deal now)

Get similar (two shuttle) devices here: 

From Etsy: BUY NOW 
Trammel of Archimedes

3-Shuttle Trammel of Archimedes: as the shuttles take turns completing their straight line journeys, the end of the crank arm traces an ellipse. This precision 3-shuttle version by the VSauce team came in my @thecuriositybox - made with high quality molded plastic parts that produce very smooth movement- a wonderful addition to my collection! Sometimes sold as a “do nothing machine” or “nothing grinder”, far from doing nothing this simple and crucially important mechanism demonstrates how rotational motion can be converted into translational oscillatory motion- such as how a piston can drive an engine’s crankshaft.