Math Toys

Dudeney's Dissection 3D Print

Get this set here!

From Etsy: BUY NOW: Dudeney'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.

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. Interestingly the four parts are all different in shape (the green and yellow pieces are similar but not the same). 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.

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 


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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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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. 

120 Sided Fair Dice

Get one here! Many colors to choose from. 
From Amazon: BUY NOW 120 sided dice 

120 Sided Fair Dice: mathematically this die has the maximum possible number of sides with equal area. Two mathematicians, Robert Fathauer and Henry Segerman, realized that the oddly named regular polyhedron (disdyakis triacontahedron) had the needed geometry to make a 120 sided fair die. Like the familiar 6 sided die, the d120 has the following properties: every side must have equal area and the numbers on parallel sides (top and bottom) must sum to the same number. The inventors admit that they do not have any suggested use for these dice- they made them purely because mathematically it was possible to do so!


Square Kaleidocycle

This book has many versions of kaliedocycles: cut out and glue to make many interesting mathematical objects.

From Amazon: BUY NOW: MC Escher Kaleidocyles

Square Kaleidocycle: a ring of eight linked tetrahedra. The hinged connections allow the ring to be rotated through its center. The faces of the pyramids are decorated with the famous tessellation work of MC Escher, a pattern of interlocking lizards. Note that as the kaleidocycle is rotated the lizards at the center change through each of four colors. Made from card stock, this kaleidocycle was cut and assembled from a book by mathematicians Doris Schattschneider and Wallace Walker. 

Mirror Illusion Motion Bank

A few of these are available on eBay as of this posting. 

From eBay: BUY NOW: Mirror Illusion Bank

Mirror Illusion Spacecraft Bank: Symmetry + Reflection = Illusion. Deposit a coin (which seems to vanish) and a spacecraft of some sort states to revolve within a silver ring seemingly suspended in space. The symmetry of the ring and craft allows a half of these objects to appear as a whole, and a AA battery powers a motor which drives gears to slowly spin the portion of the mirror inside the ring (with the spacecraft attached). The best version of the mirror illusion box I’ve seen.

 


Pythagorean Puzzle

Available here: 
From Creative Crafthouse: BUY NOW Pythagorean Puzzle

Pythagorean Puzzle: a proof, in physical form, of one of the most famous equations concerning the sides of any right triangle. The area of a square with side c of the hypotenuse is indeed equal to the sum of the areas of the squares of side a and b. This kit also allows at least two other ways to prove this theorem named after the famous Greek mathematician from 500 BC. One of the most used formulas when calculating vectors in physics classes ?

Pocket Scintillator Kinetic Art

Logan sometimes has items for sale here:

From Etsy: BUY NOW: PocketScintillators

Pocket Scintillator Card: three sheets of seemingly random arrays of translucent colored pixels produce words and images when stacked- shift the stack of sheets and a second images appears! Innovative kinetic optical art by inventor, artist, software developer Logan Kerby @thanksplease who kindly sent me these cards encoded with @physicsfun themes.

Steinmetz Bicylinder

Three choices of metal- order one today! 

From KickStarter: ORDER NOW: Steinmetz Bicylinder

Steinmetz Bicylinder: intersect two cylinders at right angles and the remaining confined space is the bicylinder- shown here machined from stainless steel. The bicylinder casts a circular shadow along two orientations, and a square shadow perpendicular to those. In addition the curve created along where the two cylinders meet is an ellipse- as seen with the object spinning along the intersection axis. Fun fact: the area and volume of this object are known to be A=16r^2 and V=16r^3/3. Thanks to Zac Eichelberger of Math Meets Machine for sending me one of his creations. 

 

 


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.

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. 

In and Out Illusion

A similar arrow illusion available here:

From Etsy: Buy Now: Stubborn Arrow Illusion 

In or Out Illusion: this 3D printed sculpture incorporates the now famous Stubborn Arrow Illusion and features both a left and right handed version. These ambiguous object illusions are a fairly recent invention by mathematician Kokichi Sugihara of Meiji University in Japan which take advantage of a clever combination of perspective, and viewing angle.