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).
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.
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 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.
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.
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!
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.
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!
These dice are available here:
From Amazon: BUY NOW: Rock Paper Scissors Lizard Spock Dice
RPSLK Dice: the famous Lizard Spock extension to the Rock, Paper, Scissors game expressed on 10 sided dice allowing the study of the non-associative nature of the game (Rock wins Scissors, and Scissors wins Paper, but Rock does not win Paper, etc.), and other interesting math. The original RPS game had three “weapons” and only three rules are needed to play the game. Adding Lizard-Spock makes for 5 gestures, but now 10 rules must be used, including “Spock vaporizes Rock”, “Lizard poisons Spock”, and my favorite “Paper disproves Spock” (swipe to see famous graphic). Interestingly, mathematical analysis shows a similar four weapon game with equal odds of winning is not possible. It was also found that the next possible game with 7 gestures would require 21 rules to play. The Lizard-Spock extension was invented by Sam Kass and Karen Bryla in 2005 and made famous on the sitcom Big Bang Theory.
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.
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.
Get this device here:
From Etsy: BUY NOW: Interactive Logic Gate Display
Interactive Logic Gate Display: the most basic four binary/Boolean logic operations that are the fundamental components of modern computers- presented here appropriately on a standard green printed circuit board (PCB) complete with the truth table for each device. These logic gates are the basic building blocks of any logic circuit, from multiplexers, arithmetic logic units, and computer memory to full microprocessors which may contain hundreds of millions of such gates on a microchip. An educational, elegant, and fun design by Tyler Jacobs.
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
This sculpture available as a 3D print:
From ShapeWays: BUY NOW: Square Circle Illusion
See other amazing geometric illusions here: Ambiguous Objects
Squaring a Circle: from one particular point of view this wireframe sculpture looks like a circle, from another it’s a square! From other viewing angles one can see that the underlying curve is comprised of four identical segments of a parabola. A wonderful example of how a single perspective can be misleading! A math sculpture available as a 3D print by Matt Enlow.
These prescision kaleidoscopes are crafted from front surface mirrors and other specialty materials, many with innovative desgin and construction techiques:
From Etsy: BUY NOW: Kaleidoscopes by Marc Tickle
Tapered 4-Mirror Kaleidoscope: not CGI- these images are produced by mirrors and light! Hidden within this colorful tube are 4 mirrors, 2 rolling glass spheres, and 1 dichroic glass reflector. These elements combine to produce the dynamic and magical images seen through the view window as the device is slightly tilted back and forth and brought in and out of a bright light source. Entitled “Dichroic Disco” this piece is but one of many amazing creations by artist Marc Tickle, taking kaleidoscope design to the next level. Invented by the famous Scottish physicist Sir David Brewster (1781-1868), the kaleidoscope is an ultimate physics toy and entire field of artistic endeavor.
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.
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!
Get these and other amazing developable rollers here:
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.