### 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!

### 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.

### Skew Dice

Available here!

From STEMcell Science: **BUY NOW Skew Dice**

Skew Dice: 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 are a special type of polyhedra called asymmetric trigonal trapezohedra which come in right and left handed versions- this set has one of each (mirror images of each other). What allows this shape to be fair like a cube has to do with the 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.

### 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!

### 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.

### 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.

### Rhombic Blocks Mathematical Puzzle

This beautifully made puzzle available here::

From Etsy: **BUY NOW **

Rhombic Blocks

Rhombic Blocks Mathematical Puzzle: There are 9 possible ways three rhombuses can be joined together along a common edge, and similar to pentominoes, these 9 tri-rhombs can tile a polyhedron, in this case a hexagon. There are 14 solutions to this puzzle, and one where no same-colored pieces touch. A beautiful math discovery by puzzle master Stuart Coffin.

### 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!

### 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.

### Ambiguous Object

Available here:

From Amazon (Japan):** BUY NOW set of four ambiguous objects with booklet **

This kit contains four white plastic illusion objects (including the object in the video) and a booklet. I used the translate feature in the Chrome browser to place my order and it shipped to California in three days.

Some 3D prints are available from many makers here:

From eBay:** BUY NOW Ambiguous Objects **

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 **

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.

### Logarithmic Spiral Gears

Amazing creations made here:

From Etsy:** BUY NOW **

Spiral Gear Set

Original 3D print available here:

From Shapeways:** BUY NOW **

Spiral Gear Set

Logarithmic Spiral Gears: an extreme example of non-circular gear sets. This set is based on the famous Fibonacci spiral and evokes the cross section of nautilus shell with internal chambers. If one gear of this set is turned at constant speed, the other will turn with an varying speed. A kind gift laser cut at @hsvsteamworks (thanks Karl!) and based on 3D prints of Misha Tikh and the research of Balint et al.