Ambiguous Object Illusion Set
This wonderful and afffordabe set includes four illusion objects and a mirror:
From curiositybox.com: BUY NOW: Inq's Ambiguous Illusion Kit (sold out)
Similar objects available here- from Etsy: BUY NOW: Ambiguous Objects
Ambiguous Object Illusion Set: This kit comes with four objects (three shown here) invented by mathematician Kokichi Sugihara of Meiji University in Japan. Polygons appear as circles in a mirror and vice versa, and the famous “stubborn arrow” that will only point to the right (or, in a mirror, to the left). I like how the base is also an ambiguous pentagon/circle, which like all these objects, is a result of a clever combination of reflection, perspective, and viewing angle. Thanks to the Vsauce team for producing this kit!
The Holoscope: Cube with Spheres
Order a holoscope from the artist's gallery here:
The artwork of Gary Allison: BUY NOW Holoscopeworld.com
The Holoscope: a cube of mirrors with the interior viewed from one corner and illuminated by light entering from glass spheres at the other seven vertices. A type of kaleidoscope based on truncated Platonic solids by artist Gary Allison. Each holoscope has stained glass on the exterior and front surface mirrors on the inside which create the amazing and seemingly impossible spaces within.
Beaded Kaleidocycle
Get similar beadwork geometric art here:
From Etsy: BUY NOW: Beadwork Kaleidocycle
Beaded Kaleidocycle: based on a geometry of six linked tetrahedra with hinged connections that allow the ring to be rotated through its center. Intricate beadwork meets math in this kinetic artwork by Erin Peña.
The Holoscope : Icosahedron
Order a holoscope from the artist's gallery here:
The artwork of Gary Allison: BUY NOW Holoscopeworld.com
Look through other holoscopes in my collection here: Holoscope Kaleidoscopes
The Holoscope Icosahedron: the intricate beauty of multiple internal reflections from 20 triangular mirrors in the shape of this famous platonic solid. The interior is viewed from one corner and illuminated by light entering from glass spheres placed at all of the other 11 vertices. A type of kaleidoscope based on mirrored polyhedra by artist Gary Allison, (swipe to see the dodecahedron and cube) and future posts will include tetrahedron and octahedron holoscope forms as I complete my Platonic solids set. Each holoscope has stained glass on the exterior and front surface mirrors on the inside which create the amazing and seemingly impossible spaces within.
Sphere Sticks Geometric Puzzle
Get this affordable and amazing puzzle here:
From Etsy: BUY NOW: Sphere Sticks
Sphere Sticks Puzzle: 30 identical wood 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 cut 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.
High Voltage Fractal in Wood
Amazing creations made here:
From Etsy store EngravedGrain: BUY NOW High Voltage Fractal
High Voltage Fractal in Wood: a Lichtenberg fractal created by a high voltage electrical current flow across a piece of wood. Since wood is an insulator a light coating of conducting water (for instance a solution of baking soda or salt) is first applied to the surface. Metal electrodes are then attached at each end of the wood piece and a dangerous source of high voltage is applied (such as a microwave oven transformer or neon light transformer).
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.
Holoscopes: Dodecahedron and Cube
Order a holoscope from the artist's gallery here:
The artwork of Gary Allison: BUY NOW Holoscopeworld.com
Look through other holoscopes in my collection here: Holoscope Kaleidoscopes
Holoscopes: polyhedra of mirrors (dodecahedron and cube) with the interior viewed from one corner and illuminated by light entering from glass spheres placed at all of the other vertices. A type of kaleidoscope based on mirrored polyhedra by artist Gary Allison @holoscope2000, and future posts will include tetrahedron, octahedron, and icosahedron holoscope forms as I complete my Platonic solids set. Each holoscope has stained glass on the exterior and front surface mirrors on the inside which create the amazing and seemingly impossible spaces within.
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.
Platonic Solids Dice Set
Get this nice set of regular polyhedra dice here:
From Etsy: BUY NOW: Polyhedra Dice Set
Less expensive sets of standard plastic dice here:
From Amazon: BUY NOW: Polyhedra Dice Set
Platonic Solids Dice Set: The five famous convex regular polyhedra in the form of fair dice. This set is cast in metal with clean edges and makes for a great way to own these symmetrical objects that have fascinated thinkers ever since the ancient Greeks wrote about them circa 360 BC. Only these five forms meet these criteria (in 3D space) for each face: must be equal in size, be equal in number of sides, each side of equal length, identical in angle were any two sides meet, and have the same number of sides meet at each vertex point of the solid. 2000 years later the famous mathematician Euler determined that for these 5 shapes V-E+F=2, the number of corners (vertices), minus the number of edges, plus the number of faces, will always equal 2.
Spherical Dice
A must for any die/dice collectors:
From Amazon: BUY NOW Spherical Dice
From eBay: 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!
Superellipsoid
Vintage Super Eggs of Piet Hein can be found on eBay:
From eBay: BUY NOW
Superellipsoid by Piet Hein
Get one in brass from this shop:
From Etsy: BUY NOW
Brass Super Egg
Superellipsoid: the "super egg" is a mathematical creation of Danish scientist and artist Piet Hein (also the inventor of the Soma cube puzzle). The equation of the superellipse is that of a regular ellipse, but raising both sides to the power of 2.5 instead of 2- the resulting curve had a flattened end that allows the superellipsoid to stand upright. The superelljpse has found use in architecture and design. This super egg is made of stainless steel.
Anamorphic Harry Potter Puzzle
No longer in production but available on eBay:
From eBay: BUY NOW: Harry Potter On Reflection Puzzle
Mirror Anamorphic Harry Potter: the conical mirror of the silver container reflects and reveals the distorted scenes in this 200 piece jigsaw puzzle of the famous wizard and school. The shape of the mirror allows for a mathematical operation, a type of affine transformation, to map the distorted image of the puzzle to the restored image reflected by the mirror. Real magic!
Skew Dice (d6 and d12)
Get these skew dice here:
From Amazon: BUY NOW: Skew d6 set
From Amazon: BUY NOW: Skew d12 set
Click here for other amazing dice.
Skew Dice (d6 and d12): these dice are skewed- but their odds aren’t! These unusually shaped dice are completely fair- roll them and the probability of outcomes are identical to a standard set of dice. The odd shapes of the skew d6s are a special type of polyhedra called asymmetric trigonal trapezohedra, and these d12s are tetrahedic pentagon dodecahedrons (swipe). These skew forms come in right and left handed versions(swipe twice) and these sets come with one of each mirror image. What allows these shapes to be fair like a cube has to do with their property of being isohedral, where each face of an object will map onto all other faces via a symmetry of the object. Manufactured by The Dice Lab team of Robert Fathauer and Henry Segerman.
Holoscopes
Order a holoscope from the artist's gallery here:
The artwork of Gary Allison: BUY NOW Holoscopeworld.com
6 and 12 Faced Holoscopes: a cube and dodecahedron of mirrors. A type of kaleidoscope based on truncated Platonic solids by artist Gary Allison @holoscope2000. These holoscopes are in the form of two famous Platonic solids- each with all the corners cut off to allow light to enter through triangular holes. Through the symmetry of the reflections, these triangles appear as an infinite array of tetrahedron shapes in the dodecahedron, and as beautiful repeating stellated octahedrons in the cube. Each holoscope has stained glass on the exterior and front surface mirrors on the inside which create the amazing and seemingly impossible spaces within.
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 recent 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
Inverting Valentines Illusion
This 3D printed illusion available here:
From Shapeways: BUY NOW Red Hearts Illusion Object
Similar item here:
From Etsy: BUY NOW: Red Hearts Illusion
Inverting Valentines Illusion: Love is a matter of perspective in this illusion that depends on viewing angle. A sweet take on the ambiguous object illusion invented by Kokichi Sugihara of Meiji University.
Catenary Curve
Get this scale model here:
From eBay: BUY NOW Scale Gateway Arch
Learn about the sunshield of the James Webb Space Telescope here:
SmarterEveryDay: Episode 270: JWST Sunshield
Click this link for more catenary curve fun!
Catenary Curve: What do the James Webb Space Telescope and the Gateway Arch have in common? The 5 sunshield panels of the JWST are engineered to be pulled into shape by the geometry of the catenary curve (see the latest video from SmarterEveryDay for amazing details on this). The Gateway arch is perhaps the most iconic use of this engineering principle and it matches the shape of a chain hanging from two ends, a curve known as the catenary or hyperbolic cosine- demonstrated here with a scale model souvenir (1”=100’). When an arch is built in the shape of this special mathematical curve the compression forces between each segment are always parallel to the curve- the arch is stable with no tendency to buckle. Famously used in design from the buttresses of Notre Dame to the Gateway Arch, and now in orbit about the Earth-Sun L2 point!