Math Toys

Shashibo Geometric Art

ORDER HERE : Shashibo Geometric Art

Shashibo Geometric Art: dissect a cube into 12 equal irregular tetrahedra, connect these pieces symmetrically with hinges, and add 36 magnets to create a device with more that 70 geometrically interesting and aesthetic configurations- a few are shown here. With practice the various transitions can flow very smoothly- this video are some of my initial explorations with this unique puzzle. 

Spherical Dice

A must for any die/dice collectors: 
From Amazon: BUY NOW Spherical Dice 

Click this link for other amazing dice featured on @physicsfun 

Spherical Dice: these fair six "sided" dice are hollow inside with a ball that weights each sphere such that one of the six values is always on top. When these dice are rolled (literally!) the internal weight lands in one of six cavities inside creating a low center of mass which aligns one of the numbers to the top. Another low center of mass toy! 

Hyperboloid Spinner

Available here: 
From Amazon: BUY NOW 
Hyperboliod Spinner: The HypnoGizmo 

From eBay: BUY NOW 
Hyperboloid Spinner: HypnoGizmo 

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!


Ambiguous Object Illusion Mug

From Etsy: BUY NOW Squirkle Mug Ambiguous Object Illusion 

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

From Amazon (Japan): BUY NOW set of four ambiguous objects with booklet 
This kit contains four white plastic illusion objects (including the arrow) and a booklet. I used the translate feature in the Chrome browser to place my order and it shipped to California in a few days. 

The math and physics are described here in this technical journal article by Prof. Sugihara

Ambiguous Object Illusion Mug: circle or a square? It’s all a matter of perspective and viewing angle. The complex shape allows for both to be perceived and is based on the work of mathematician Kokichi Sugihara of Meiji University in Japan, the inventor of this illusion and art form. 

Dandelin Spheres

I found this beautiful model on eBay and I'm not sure of its age or origin. 

Grant Sanderson describes the elegant geometry behind this curious arrangement. 
On YouTube: 3Blue1Brown descibes the Dandelin Spheres  

Wikipedia also has a good description: the Dandelin Spheres

See how sliced cones create conic sections with these colorful foam versions:

From Ammazon: BUY NOW: Conic Sections

Dandelin Spheres: Slicing a cone with a plane can produce an ellipse, and two spheres encapsulated by the same cone will always have the small sphere touching one focus and the large sphere contacting the plane at the other focus. This beautiful acrylic model shows this geometry for one choice of cone width and dissecting plane angle- but it always true. This geometric construction is named for its inventor, French mathematician Germinal Pierre Dandelin back in 1822, and with it he proved theorems concerning properties of ellipses and other conic sections- mathematical entities that play a roll in much physics- including the orbits of planets. Fun math that I wish someone would have showed me back in high school!

Reuleaux Rotor

This toy is availble from Amazon Japan and will ship to the US:

From Amazon.jp: BUY NOW: Reuleaux Rotor Wodden Toy

Reuleaux Rotor: this famous curve of constant width, the Reuleaux triangle, can rotate such that at all times it remains in contact with all four sides of a square. As demonstrated by this wooden toy from Japan, the rotor covers approximately 98.77% of the area of the square, missing only the sharp corners. The curves in the corners are in the shape of an elliptical arc. Fun fact: a Reuleaux triangle has a perimeter equal to pi times its width- just like a circle! 


Tension Integrity Icosohedron: Tensegrity

A nice version of this tensegrity icosohedron is sold as a toy for tiny tots: 
From Amazon: BUY NOW Tensegrity Toy 

 
I constructed this version by referring to the images and descriptions of tensegity on Wikipedia 

Tension Integrity Icosohedron: Six brass struts float isolated from each other but held in a stable configuration by a net of 24 connecting cables. I made this sculpture using hollow brass tubes and weaving through them a single strand of fishing line, which is connected after passing through each tube exactly four times. This configuration of three sets of parallel struts forms a Jessen’s icosahedron under tension, and was invented by the famous architect Buckminster Fuller in 1949.

Nova Plexus Tensegrity Puzzle

Precisions machined and available in brass or stainless steel:

From Art of Play: BUY NOW: Nova Plexus Puzzle

Nova Plexus Puzzle: 12 identical brass rods can create 4 interlocking triangles in a perfect symmetry- look carefully and you can see that each rod is in an identical configuration with the 5 others that connect with it. Precision machined notches on the ends of the rods allow them to interlock with elastic tension such that vector sum of the 5 forces on each rod is zero- creating this astonishing geometry as the equilibrium state. Unlock the ends of any two rods and the system instantly disassembles (swipe to view process in slow motion). Invented/designed by artist and computer scientist Geoff Wyvill in 1978, this puzzle has just recently been made available for sale with a limited production run.

Trammel of Archimedes

Get similar devices here: 

From Etsy: BUY NOW 
Trammel of Archimedes

From eBay: BUY NOW 
Trammel of Archimedes

Trammel of Archimedes: as the shuttles take turns completing their straight line journeys, the end of the crank arm traces an ellipse. 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. This version was crafted from fine maple, cherry, and oak by artisan Neal Olsen. 


Oloids: Solid and Anit-oloid

Order your Anti-Oliod today: available in three types of metal:

From The Matter Collection: ORDER NOW: Anti-Oloids in Brass, Copper, and Steel 

Oloids: “solid hull” and “ruled surface” types made from brass and copper- oloids are unique solids that roll in such a way that every point on their surface comes in contact with the plane. The basis of the oliod’s geometry is that of two connected circles, one perpendicular to the other such that the rim of each circle goes through the center of the other. The shapes you see here are the results of connecting the rims of these circles together with a family of straight lines, one method leads to the solid convex hull form, and another way leads to the ruled oloid (anti-oloid). 

Ultimate Solid of Constant Width

Available in three metals and two finishes.
From The Matter Collection: 
Order NOW: Ultimate Solid of Constant Width- Brass
Order NOW: Ultimate Solid of Constant Width- Steel
Order NOW: Ultimate Solid of Constant Width- Copper

Ultimate Solid of Constant Width: Reuleaux tetrahedrons with specially calculated curved edges become volumes of constant width- possibly the minimum volume that can possess this property. The shape featured here is a new discovery of a solid of constant width that has perfect tetrahedral symmetry. Made from solid steel, brass, and copper- these shapes have constant diameter no matter their orientation and will roll like spheres between two planes- note how the acrylic plate remains parallel to the desktop as the orbiforms roll in between. Currently available on Kickstarter from my friends at the Matter Collection : Reuleaux tetrahedrons with specially calculated curved edges become volumes of constant width- possibly the minimum volume that can possess this property. The shape featured here is a new discovery of a solid of constant width that has perfect tetrahedral symmetry. Made from solid steel, brass, and copper- these shapes have constant diameter no matter their orientation and will roll like spheres between two planes- note how the acrylic plate remains parallel to the desktop as the orbiforms roll in between. Currently available from my friends at the Matter Collection 

Coins of Constant Width

These triangle coins are often available on eBay.

Fron eBay: Search NOW: Bermuda Triangle Coin

The silver proof versions can be expansive, but sometimes the circulated coins (like those in the video) are available at a lower price.

Click to see more: shapes of constant width

Coins of Constant Width: the only coins produced in the shape of the Reuleaux triangle, issued in 1997 and 1998 by Bermuda. The special convex shape of the Reuleaux triangle will roll, because like a circle they have the same diameter from one side to the other, no matter their orientation. To demonstrate this property note here how two straightedge rulers remain parallel as the coins rotate between them, just as one would expect circles to behave! Bermuda triangle (ha!) coins were only produced for two years and featured Elizabeth II on the front and shipwrecks on the back- this one depicts the wreck of the Sea Venture.


Lissajous Roller 

Available from Pyrigan & Co.

From Etsy: BUY NOW: Lissajous Roller Illusion

From ShapeWays: 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.