The Holoscope: Cube with Spheres
Order a holoscope from the artist's gallery here:
The artwork of Gary Allison: BUY NOW Holoscopeworld.com
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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.
Oloids: Solid and Anit-oloid
Order your Anti-Oliod today: available in three types of metal:
From The Matter Collection: ORDER NOW: Anti-Oloids in Brass, Copper, and Steel
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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).
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
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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.
Steinmetz Bicylinder
3D printed versions available here along with many other amazing geometrical objects:
From Etsy: BUY NOW: Steinmetz Bicylinder
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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.
Dudeney's Dissection 3D Print
Get this set here!
From Etsy: BUY NOW: Dudeney's Dissection 3D Print
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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.
In and Out Illusion
Similar objects available here- from Etsy: BUY NOW: Ambiguous Objects
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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.
Beaded Kaleidocycle
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From Etsy: BUY NOW: Beadwork Kaleidocycle
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Beaded Kaleidocycle: based on a geometry of six linked tetrahedra with hinged connections that allow the ring to be rotated through its center. Intricate beadwork meets math in this kinetic artwork by Erin Peña.
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
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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.
Superellipsoid
Vintage Super Eggs of Piet Hein can be found here:
From Etsy: BUY NOW: Superellipsoid by Piet Hein
Get one in brass from this shop:
From Etsy: BUY NOW: Brass Super Egg
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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.
Ultimate Solid of Constant Width
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
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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
Trammel of Archimedes
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From Etsy: BUY NOW Trammel of Archimedes
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Trammel of Archimedes: as the shuttles take turns completing their straight line journeys, the end of the crank arm traces an ellipse. Sometimes sold as a “do nothing machine” or “nothing grinder”, far from doing nothing this simple and crucially important mechanism demonstrates how rotational motion can be converted into translational oscillatory motion- such as how a piston can drive an engine’s crankshaft. This version was crafted from fine maple, cherry, and oak by artisan Neal Olsen.
Ambiguous Object Illusion Mug
From Etsy: BUY NOW Squirkle Mug Ambiguous Object Illusion
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
The math and physics are described here in this technical journal article by Prof. Sugihara.
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Ambiguous Object Illusion Mug: circle or a square? It’s all a matter of perspective and viewing angle. The complex shape allows for both to be perceived and is based on the work of mathematician Kokichi Sugihara of Meiji University in Japan, the inventor of this illusion and art form.
Spherical Dice
A must for any die/dice collectors:
From Amazon: BUY NOW Spherical Dice
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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!
Curves of Constant Width
Get a set here:
From Maths Gear: BUY NOW Curves of Constant Width (set of 4)
Click here for 3D Solids of Constant Width
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Curves of Constant Width: regardless of the precise shape, any curve of constant width has a perimeter equal to pi times its width! These convex shapes will roll because like a circle they have the same diameter from one side to the other no matter their orientation. Here are two famous examples: the Reuleaux triangle (found in rotary engines) and a Reuleaux pentagon- note how the two straightedge rulers remain parallel as the shapes rotate between them, just as one would expect circles to behave! These physical representations of the special curves seen here are produced by Maths Gear (Matt Parker and Steve Mould).
Catenary Curve
Get scale models here:
From Amazon: 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!
Tessellating Geckos
Laser cut geckos are available here:
From Etsy: BUY NOW Tessellating Geckos
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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.
Ambiguous Object
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
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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.
120 Sided Fair Dice
Get one here! Many colors to choose from.
From Amazon: BUY NOW 120 sided dice
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he d120: mathematically this die has the maximum possible number of sides with equal area (discovered so far). Two mathematicians, Robert Fathauer and Henry Segerman, realized that the oddly named uniform convex 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!