Get this mathematical glass art here:
From Etsy: BUY NOW: Klein Bottle
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Wikipedia has great details on the Klein Bottle
Klein Bottle: 3D representation of a four dimensional mathematical object with one side, no edges, and zero volume. Kind of like a MoĢbius strip with no edges.* Math meets glass art with this fun “lamp shaped” version! *only achievable in 4D space
1x1x1 cube
Speed cube version available here:
From Amazon; BUY NOW: 1x1x1 cube
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Completing the collection: the 1x1x1 cube, a silly but logical addition to any twisty cube collection!
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From Craighill & Art of Play: Order Now: Jack in the Box
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Jack in the Box Puzzle: eight solid aluminum pieces form a textured cube when carefully stacked- yet the same eight pieces can also be packed around a six pronged “jack” to form a second smooth silver cube that is barely larger that the first. Similar to the 2D Matsuyama’s paradox puzzle, a small square is centered on each face of the cube in the second solution. Some stages of assembly shown here under rotation to emphasize the beautiful symmetries in the design and avoid spoilers to the challenge. Created by Rod Bogart and engineered into existence by the talented folks at @craighillcompany, and I send a hearty thank you to my friends at @artofplay for sending me this unique and special puzzle.
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From Shire Post Mint: BUY NOW: Magic Octagon Coin
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“Magic Octagon” Challenge: introducing a beautiful copper coin version of this puzzle of successive rotations. Which way will the light arrow point after left and right rotations of the dark arrow? No trickery here- just the math of geometry, symmetry, rotations, and reflections and how our intuitions often fail us upon first attempts. Swipe twice for second challenge. In collaboration with my friends at @shirepostmint
Get these and other well made disection puzzles here:
From Etsy: BUY NOW: Square Dissection Puzzles
These puzzles are expertly laser cut and sold by GamesEfce. I spray-painted the pieces of mine to better show the shapes and relationships for the video.
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Square Dissection Puzzles: a square can be cut (dissected) into polygons and then reassembled into other regular polygons. Shown here: an equilateral triangle, a pentagon, and a hexagon. These are the record holders for smallest number of pieces needed: triangle (4 pieces by Henry Dudeney 1902), hexagon (5 pieces Paul Busschop 1870s) and pentagon (6 pieces Robert Brodie 1891). Fun fact- It is not known if any of these records are the smallest possible, no mathematical proofs yet exist on this question.
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From Art of Play: BUY NOW: PIckagram Puzzle
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Pickagram: an innovative update on the classic Tangram puzzle- magnets added! With pieces that cling together with a satisfying snap, the 2D puzzle formations become 3D abstract sculptures that can stand on their own. From the mind of designer and architect Gilryong Song, with inspiration from the golden ratio in its proportions and angles.
Get this new amazing coin here:
From Shire Post Mint: BUY NOW: Magic Octagon Coin
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Magic Octagon Paradox: flip the coin and the arrows on each side point in opposite directions- however, after a small shift, the same coin has these two arrows pointing in the same direction! A brain teaser that can be explained via geometry, symmetry, rotations, reflections, and how our intuitions often fail us upon first attempts. See my post two weeks back for another fun way to present this challenge. These beautiful copper coins are minted in collaboration with my friends at @shirepostmint and are available now.
Get one here:
From Etsy: BUY NOW: Quantum Sphericon
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Sphericon Frame Roller: beautiful 3D printed version of a developable roller (an object that rolls where every point on the roller’s surface comes into contact with the plane upon which it rolls). The sphericon (based on a square) rolls in a straight line with a peculiar wobble motion and was discovered in 1980 by David Hirsch and is but one of a family of such rollers called polycons.
These triangle coins are often available on eBay.
From eBay: Search NOW: Bermuda Triangle Coin
Click to see more: shapes of constant width and here for 3D shapes of constant width (orbiforms)
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Coins of Constant Width: this post celebrates pi day with coins in the form of Reuleaux polygons- shapes for which their perimeter/diameter = π, just like the circle! The special convex shapes of the Reuleaux triangle (Bermuda 1 dollar) and Reuleaux heptagon (UK 50 pence) will roll, because like a circle they have the same diameter from one side to the other, no matter their orientation. To demonstrate this property note how two straightedge rulers remain parallel as the coins rotate between them, just as one would expect circles to behave. Bermuda triangle (ha!) coins are the only coins produced in the shape of the Reuleaux triangle, issued in 1997-98 and featured Elizabeth II on the front and shipwrecks on the back.
Lief Colson's store is now Colorfulscopes on Etsy with many designs to choose from- all with precision aligned high quality front surface mirrors:
From Etsy store Colorfulcopes : BUY NOW Precision Teleidoscopes
Amazing next-level fine art kaleidoscopes avaibable here:
From Etsy: BUY NOW: Fine Art Kaleidoscopes
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2-Mirror Kaleidoscope: two mirrors, precisely aligned at an 18 degree angle, produce a 10 fold symmetry, where bits of colored plastic morph into stars, pentagons, and flowers as this unique kaleidoscope is turned back and forth. An elegant anodized blue metallic cylinder encapsulates a universe of possible images within. Another amazing kaleidoscope in my expanding collection, made by artist Lief Colson.
Get this inexpensive demo here:
From Etsy: BUY NOW: Pythagorean Theorem Proof Wheel
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Liquid Demo of the Pythagorean Theorem: 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. An excellent print and design by Kiegan Brewer of Printed Teacher Crafts.
Get this 3-color laser cut acrylic version here:
From Kadon Enterprises: BUY NOW: Hexiamond Puzzle
Noce woood versions available here:
From Etsy: BUY NOW: Hexiamond Puzzles
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Hexiamonds Snowflake: this symmetric puzzle is comprised of the hexiamonds- the shapes that represent the 12 ways for which six equilateral triangles can be attached side to side- where we find a hexagon and a skinny parallelogram among the dozen interesting shapes. 55 different solutions can fill this snowflake shape, but only one solution separates the colors. This tri-colored puzzle, made from laser cut acrylic, is the creation of Kate Jones of Kadon Enterprise.
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From TheDiceLab: BUY NOW: Orbiform d4 Dice
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Orbiform Dice Set: the shape of a standard d4 is the tetrahedron whereas this new dice set are in the form of Meissner tetrahedra, which are in turn based on the Reuleaux triangle. The shape of these dice 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 top.
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From Amazon: BUY NOW; Luycho & Oyow Cup and Saucer
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Mirror Anamorphic Lenticular Cup & Saucer: wonderful and whimsical art by Seoul based artist Oyow is showcased in this latest design by Luycho which uses both mirror anamorphic reflection and an accordion type lenticular dual image- place the mirrored cup on the saucer for the reveal! Art intersects once again with math and physics.
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From Wolrd Market: BUY NOW: Wood Decor Borromean Knot
Similar affordable wood scupltures here:
From Aamzon: BUY NOW: Wood Decor Borromean Knots
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Borromean Rings in Wood: three closed loops are linked but no two of the three are linked- if one is broken the other two will not be connected in any way. Fun math, sold as home décor, found at my local Cost Plus World Market store. More math than physics for this item - but there is a bizarre quantum state (Efimov state) where three particles are bound and described by the same math knot theory as these rings.
This sculpture available as a 3D print:
From ShapeWays: BUY NOW: Square Circle Illusion
See other amazing geometric illusions here: Ambiguous Objects
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Squaring Circles: from one particular point of view these wireframe sculptures looks like a circles/squares, from another it’s a square/circle! From other viewing angles one can see that the underlying curves are four identical segments of a parabola conjoined. Further examples of how a single perspective can be misleading! Math sculptures available as a 3D print by Matt Enlow.
Get this math toy here: Toysmith Sproing Ball
Learn more about this shape: Icosododecahedron
Sproing Ball Icosododecahedron: this bouncy ball contains some fun mathematical symmetries. Just six interlocking gear shaped rings create 12 pentagonal faces (shown here in sequence) along with 20 triangular faces. Each “gear ring” also forms an equatorial great circle, producing the underlying polyhedral form of this toy, an icosododecahedron.
Click here for affordable, precision made scopes with angled mirrors: Kaleidoscope Symmetries Explored
Similar Kaleidoscopes available here:
From Amazon: BUY NOW Fluid Flow Kaleidoscope
From Etsy: Fluid Flow Kaleidoscope
See more kaleidoscopes in my collection: Kaleidoscopes
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Polarized Light Cell Kaleidoscope: the amazing colors you see from the object cell of this 3 mirror kaleidoscope are generated by manipulating the polarization of light- the object in the clear wand is a strip of clear cellophane in oil which has the property of optical rotation. These property allows for an incredible range of color formation when placed between two linear polarization filters (swipe for demonstration). A creation of kaleidoscope artist Ron Kuhns.