Math Toys

Tapered Mirror Kaleidoscope 

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 Mirror Kaleidoscope: hidden within this colorful tube are 3 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. This unique teleidoscope design “Disco Dandelion” is but one of many creations by artist Marc Tickle. Invented by the famous Scottish physicist Sir David Brewster (1781-1868), the kaleidoscope is an ultimate physics toy and entire field of artistic endeavor. 

Pentakis Geometric Kaleidoscope

This item is hard to find, but I believe it is in stock here: 
From AHA in Zurich: BUY NOW Pentakis 

for More kaleidoscopes click here

Pentakis Geometric Kaleidoscope: three triangle mirrors in a pyramid configuration create a stellated dodecahedron. The tapered mirrors are in the form of a 60°-72°-60° isosceles triangle with the apex of the pyramid cut off just right to form the triangle of light that is then reflected up to 60 times to create the star in the center of view. Pentakis by Caspar Schwabe. 

Dodecahedron Infinity Mirror

This lamp is interesting, but the fabrication is low quality. Still, it is fun to see the internal reflections and it would make for a great party light. Definitely read the reviews before purchasing! ($30-$45 USD) 

From Amazon: Dodecahedron Infinty Lamp

Dodecahedron Infinity Lamp: lit from within by strips of LEDs the 12 plastic mirrored faces create a universe of interesting internal reflections. While the manufacturing quality of this item is pretty low, when the lights are off it looks pretty amazing.

 


The Galton Board

Available here: 
From Amazon: BUY NOW 
Galton Board 

The Galton Board: 3000 steel balls fall through 12 levels of branching paths and always end up matching a bell curve distribution. Each ball has a 50/50 chance of following each branch such that the balls are distributed at the bottom by the mathematical binomial distribution. One of my favorite finds of 2018! An elegantly 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. In addition the number of balls in each bin can be predicted by Pascal's triangle (printed on the face over the pegs).

CUMOS Cube Kaleidoscope

The CUMOS Cube is a creation of artist Minori Yamazaki. Available for purchase- inquire via the contact info below:

Learn more here: Cosmos in a Box

CUMOS Cube: a variation on the Kaleidoscope by artist @minori.yamazaki that produces a Cosmos in a box. So much wonder hidden within this unassuming white cube where etchings on front surface mirrors produce the repeating geometric patterns. A moving light source (led flashlight) is projected on the cube producing the dazzling animation effect on the multiple reflections. 

Kinetic Traced Hyperboloid

This hard to find sculpture currently available here:

From Amazon:BUY NOW: Hyperbolic Kinetic Sculpture

See also this: DIY kit version

Kinetic Traced Hyperboloid: a straight rod glides through a symmetric pair of curved holes in this kinetic sculpture based on the hyperboloid, the 3D ruled surface traced by an offset revolved straight line. This version is made of anodized aluminum and rotates via gearing and a motor powered by two AA batteries in the base. 


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.

Wobbler Roller

Get this very nice laser cut version here:

From Etsy: BUY NOW: Desk Wobbler

Check out my posts on similar geometric objects: developable rollers

Wobbler Roller: a very simple toy today- two half circle perimeters affixed at right angles which surprisingly can then roll in a straight line with a peculiar wobble motion. When rolling, a wobbler always touches the table top at two points which could be connected by a straight line, and forms the frame of the geometric shape called a sphericon (featured in a previous post). 


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.

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! 

Tessellation Origami

See more of Ekaterina's amazing work on her website gallery: Kusudama me!

Contact her to buy her artwork, or you can buy her books and learn how to fold amazing geometries!

From Amazon: BUY NOW: Ekaterina Lukasheva: Papercraft and Origami

Tessellation Origami: nested spirals and triangles created from one flat sheet of paper! This beautiful work by Ekaterina Lukasheva also demonstrates how folded paper can obtain very different physical properties than that of the original flat paper. When stretched out this paper sculpture prefers to snap back into spirals and triangles, and although most materials bulge out when compressed along one direction, here the design compresses evenly along all three axis of the hexagonal symmetry. Title: Electricity-A Variaton of Spaced unit Opus_T-142.


RPSLK Dice

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. 

Tesseract Projection

Get this CNC machined math art here: 

From AltDynamic: BUYNOW: Hypercube/Tesseract

Tesseract Projection: a shadow of the 4-dimensional analogue to the cube, also called a hypercube or 8-cell. A tesseract(4D) is to a cube(3D) as a cube is to a square(2D). This piece of mathematical art is CNC machined from a solid piece of aluminum and anodized black- a representation, including perspective, of one possible shadow a hypercube could cast into 3D space. Multidimensional mathematics are often used in the formulations of physics, and visualizations such as this one help give insights. Another amazing creation from @altdynamic design studio.

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.


Opticum 3 Font

Get your custom message engraved here: 
From Creative Crafthouse on Etsy: BUY NOW 
Custom Opticum Font Message Plaque 


 
This family of fonts is available here: Opticum 3 from Linotype 

Opticum 3 Font: This laser engraved message uses the Opticum 3 font designed by Erken Kagarov, where indirect lighting reveals the symbols hidden in a maze- created by simply typing out your message using this font. Amazing application of geometry and shadow! 

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.