Math Toys

Pickagram Puzzle

Get this well made puzzle here:

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.

Electromagnetic Levitation Module

Get this kit here (comes complete as shown in my video):
From engineDIY: BUY NOW: Magnetic Levitation Module

The featured sculture is by Bathsheba Grossman, affordable and beautiful math art available here:
From Etsy: BUY NOW: Soliton Sculpture

Note: this site contains affiliate links for which I may be compensated

Electromagnetic Levitation Module: this engineered control system uses adjustable electromagnets (four copper coils) and and two Hall effect magnetic field sensors (held firm embedded in white silicone) to levitate an 5cm diameter neodymium magnet platform about 3 cm in mid-air. A feedback loop informed by the Hall effect sensors allows fine tuning of the magnetic field to exactly balance the pull of gravity, and is powered by a standard USB connection. The platform also rotates, perfect for showcasing one of my metal 3D printed mathematical sculptures by Bathsheba Grossman.

Magic Octogon Paradox

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. 


Sphericon Frame Roller

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. 

Coins of Constant Width

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.

2-Mirror Kaleidoscope 

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

Note: this site contains affiliate links for which I may be compensated

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.


Anamorphic Locomotion Cup & Saucer II

Animated bird set available here:
From Amazon: BUY NOW: Luycho Locomotion Cup & Saucer 

Note: this site contains affiliate links for which I may be compensated

Locomotion Anamorphic Cup & Saucer: Another expertly crafted product from @luycho using an amazing combination of barrier grid animation and anamorphic projection rendered on elegant porcelain. The warped image on the saucer is reconstructed by reflection off the surface of the cup, however the gold mirroring is comprised of parallel lines that only reflect part of the image pattern. Turing the cup (or the saucer and cup together) reveals a flying bird! 

Arrow on Mobius Strip

Get this fun demostration printed here:
From Etsy: BUY NOW: Mobius Strip with Arrow

Get the 3D print stl files here:
From printables: download now: Mobius Strip with Arrow

Note: this site contains affiliate links for which I may be compensated

Arrow on Möbius Strip: on the geometry of a Möbius strip a right pointing arrow points left after one trip around, a second trip restores the original orientation. This mathematical property is called non-orientability, and is also true of Klein bottles which I’ve posted about. I love how this 3D printed model, designed and produced by Wes Pegden, allows one to physically manipulate and intuit this somewhat obscure mathematical property. 


Liquid Pythgorean Proof

Get this inexpensive demo here:

From Etsy: BUY NOW: Pythagorean Theorem Proof Wheel

Note: this site contains affiliate links for which I may be compensated

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. 

Impossible Braid 

Get nice examples of mystery braids here:

From Etsy: BUY NOW: Impossible Braid Key Fob

Here is a great video on how to make the mystery braid

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See other Impossible Objects in my collection. 

Mystery Braid: challenge- how can three strands be braided if both sets of ends are connected? A favorite in my collection of “impossible objects”, this leather key fob is braided from a single piece of leather, constructed by making two parallel slits but not cutting the ends. The solution (demonstrated here with red felt) is well known to those in the field of leatherwork- due to a twist of topology it’s possible to make this braid if the number of left strand over right crossings equals the times the right strand crosses over the left. Four strands braided this way is not mathematically possible, but 3, 5, or any odd number can be done!