Math Toys

Dudney's Dissection 3D Print

Get this set here!

From Etsy: BUY NOW: Dudney's Dissection 3D Print

Dudeney's Dissection: an equilateral triangle canbe cut (dissected) into four pieces that will then assemble into a square. This 3D printed version comes as a puzzle- fit the pieces in each of two containers- a square and a triangle, which also makes it clear the two supplied shapes are of equal area. Fun fact: It is not known if a similar three piece dissection is possible. Also called Haberdasher's problem and described in 1907 by Henry Dudeney it is the only 4 piece solution known.

Pencil Hyperboloid

Choose your color and get one here: 
From Etsy: BUY NOW 
Hyperboloid Pencil Holder 


don't forget a set of pencils: 
From Amazon: BUY NOW 
Colored Pencil Sets 


Better yet- get some thermochromic color changing pencils! 
From Educational Innovations: BUY NOW 
Heat-Sensitive Pencils 

Pencil Hyperboloid: a perfect gift for any math teacher- the precisely oriented holes in this base direct 16 pencils to reveal a hyperboloid, the 3D surface traced by revolving a diagonal(skew) line, the outline of which is the conic section of the hyperbola. A doubly ruled surface for any desktop!

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!


In-Feed Google

Pentominoes

Get this set here: 
From Etsy: BUY NOW Hardwood Pentominoes 

Many versions available here: 
From Amazon: BUY NOW Pentominoes 

Pentominoes: the 12 possible arrangements of five identical squares joined edge to edge. Since 5x12=60, the pentominoes can tile a 6 x 10 rectangle with no gaps (2339 ways to do this- yet even finding one solution is a challenge). I love this beautiful set from artist/woodworker Ron Moore where each pentomino is made from a different kind of hard wood. 

Mirror Anamorphosis

This image by István Orosz is available as a poster and as a puzzle: 
From Amazon: BUY NOW Mysterious Island Puzzle 
From MathArtFun.com: BUY NOW Mysterious Island Poster 

For those who want to see the math behind this art, here is an initial paper on the topic published in 2000 in the American Journal of Physics: Anamorphic Images by Hunt et al. 
Many books are available (with mirror cylinders) from Amazon: Anamorphic Art in Books 

Mirror Anamorphosis: this famous print by artist István Orosz has a hidden anamorphic image revealed by placing a mirrored cylinder over the depiction of the moon in the image. The work visualizes a scene from the book “The Mysterious Island” by the science-fiction author Jules Verne- whose portrait emerges in the reflection on the cylinder. The math describing this mapping is quite complex and was given in detail in a physics journal in 2000, but before that Martin Gardner described the math in 1975. Repost for this week’s theme as I head to G4G! 


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Shadow Stereographic Projection

These mathematical art objects are created by Henry Segerman and available here: 
From Shapeways: BUY NOW Mathematical Art 

Wikipedia has a nice introduction to the math and applications of stereographic projection

Shadow Stereographic Projection: 3D printed sculptures that cast geometric shadows. When illuminated by a point source of light (placed at the top pole of the sphere) the shadow cast by the rays of light represent a one to one mapping of the points on the sphere to points on the plane- creating a square grid, and a honeycomb of regular hexagons. Stereographic projection is often used in representing the geography of the globe of our planet on to a flat map. Mathematical art by Henry Segerman. 

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). 


Hexa Sphericon

Sphericon and Hexa-sphericon: order your set today! 
From the Matter Collection: BUY NOW The Sphericon (Hex and Regular) 

Hexa-Sphericon: Sphericons are unique solids that roll in such a way that every point on their surface comes in contact with the plane. 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. 

Kinetic Traced Hyperboloid

This hard to find sculpture curretnly available here:

From Amazon: Hyperbolic Kinetic Sculpture

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 

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! 


Orbiforms

Latest orbiforms available here: 
From Kickstarter: Order NOW 
Orbiforms in Steel, Brass, or Copper

Orbiforms: volumes of constant width 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 stays parallel to the table as the orbiforms roll underneath. The first set shown are based on the Reuleaux triangle and the second set are based on a Reuleaux pentagon. Currently available on Kickstarter from my friends at @altdynamic 

Oloids: Solid and Anit-oloid

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

From KickStarter: ORDER NOW: Anti-Oloids in Brass, Copper, and Steel 

Beautiful solid oloids available right now here:

From the Matter Collection: BUY NOW: 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). 

Dudeney's Dissection

Get this version here: 
From Grand Illusions Ltd: Dudeney's Dissection 

A nice wood version is available here: 
From Etsy: BUY NOW Dudeney's Dissection 

See both Wikipedia and Wolfram MathWorld for more details on the history and math of this geometrical oddity. 

Dudeney's Dissection: an equilateral triangle can be cut (dissected) into four pieces that will then assemble into a square. This hinged model is comprised of precision machined and anodized aluminum, and can be folded back and forth between the two simplest regular polygons. It is not known if a similar three piece dissection is possible. Also called the haberdasher's problem and described in 1907 by Henry Dudeney it is the only 4 piece solution known. 


Hyperbolic Holes

This inexpensive kit available here: From eBay: 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- just the right size to clear the curved openings.

Tessellating Geckos

These laser cut hardwood geckos are available here: 
From Etsy: BUY NOW Tessellating Geckos 

Tessellating Geckos: MC Escher inspired lizard cutouts interlock precisely to tile a surface with no overlaps or gaps. Laser cut from maple, walnut, and cherry wood by maker/artist Craig Caesar and inspired by MC Escher’s “Study of Regular Division of a Plane with Reptiles” 1939. G4G week: Martin Gardner wrote about the art and math of Escher in 1961- which helped create the popularity that his work has experienced ever since.

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!