Math Toys

Dodecagon to Square Puzzle

Get these and other well made disection puzzles here:

From Etsy: BUY NOW: Square Dissection Puzzles

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

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. 

Square to Dodecagon Dissection Puzzle: a square can be cut (dissected) into polygons and then reassembled into other regular polygons. Amazingly the 12-sided regular polygon can be cut into these six specific pieces that can then fit a square. Swipe to see the minimum cuts dissections for a hexagon, pentagon, and triangle.

 

High Voltage Wood Burn Fractal

Beautiful wood fractal art available here:

From Etsy: BUY NOW: High Voltage Fractal Art

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

High Voltage Wood Burn Fractal: a classic Lichtenberg fractal created by electrical discharge- in this piece artist/maker Nic Ferretti applied cobalt blue epoxy resin to fill the cavities of the burn pattern and create the look of frozen lightning. Swipe to see my attempt at this process with an old neon sign high voltage transformer using 7500 V at 20 mA. I turned the power off right before the two sides connected to get the fern-like look. The wood is slightly wetted with baking soda dissolved in tap water. WARNING high voltage can kill- do not use a transformer like this unless you are fully trained in electrical high voltage safety. 


The DeltaCELT Rattleback 

Get one here: 

From Etsy: BUY NOW: The DeltaCELT

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

The DeltaCELT: a new rattleback design where the indentations create an asymmetry in the distribution of mass that leads to rotation reversals when spun: 1) If spun clockwise, after about two full rotations, a complicated combination of friction, precession, and instability induced vibrations transforms the rotational energy into into end-to-end rattling (energy of oscillations) and then into rotational energy in the opposite direction. 2) If spun counter-clockwise, after about 30 full rotations the rotational energy translates into side-to-side oscillations leading to a clockwise reversal (swipe to see- less dramatic but still amazing). The design is made of solid brass and has the shape of a bisected prolate ellipsoid in the proportion of the mathematical constant δ =4.669.. (Feigenbaum dynamical constant) giving the name to this new design by astrophysicist Kenneth Brecher. The DeltaCELT comes with the polished slate spinning surface for optimal performance. 

The iTOP

Well engineered brass spinning toys by SiriusEnigmas:

From Etsy: BUY NOW: The iTOP 

From Etsy: BUY NOW: The PhiTOP

From Etsy: BUY NOW: The eTOP

From Etsy: BUY NOW: The PiTOP

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

The iTOP: inverting spinning disk- the equilibrium state for a spinning thing is often different from that of the same object when stationary. When spun, the iTOP almost instantly inverts to raise its center of mass (shown in slow motion because it happens so fast). However, when the rotation speed decreases to a certain rate the system becomes unstable (shown again in slow motion) and flips again before going into a rolling/spinning motion like a coin. This top completes the set of four spin tops by astrophysicist Kenneth Brecher, all made of polished brass and themed on a mathematical constant: iTOP (square-root of -1), PhiTOP (golden ratio, φ), eTOP (base of the natural log), and the PiTOP (C/D of a circle, π). 

 

3D Wordflip Sculpture

Create your own here:

From sparenbergdesign.com: BUY NOW: 3D Wordflip

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3D WordFlip Sculpture: from one point of view my logo appears, rotate 90 degrees and the sculpture reveals my tagline phrase “real magic”. Alternatively the messages can be cast as shadows (swipe to view). Amazingly you can create and print any two phrases of your choosing from the webpage of artist and designer Joris Sparenberg.


Half Seirpinski Octahedron Fractal

Get this amazing 3D print here:
From Etsy: BUY NOW: Seirpinski Pyramid

or print it yourself:
From Thingverse: Seirpinski Pyramid

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

Half Sierpinski Octahedron Fractal: this 3D printed math sculpture is one half of the sixth iteration of what is called “the octahedron flake” a 3D fractal based on the Sierpinski triangle. To make this fractal, on each iteration an inverted triangle is removed from the center of the previous triangle, and if this process is repeated indefinitely one gets the famous fractal. This 3D print used rainbow silk PLA to create the beautiful color gradient base on the .stl files by Rick Tu. Another example of math brought to life via 3D printing! 

 

Squaring Circles

This sculpture available as a 3D print:

From ShapeWays: BUY NOW: Square Circle Illusion

See other amazing geometric illusions here: Ambiguous Objects

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

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. 

The eTOP

Get this and other beautifully crafted math themed tops here: 

Fropm Etsy: BUY NOW: The eTOP

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

The eTOP: an ellipsoid based on the famous Euler’s constant e, diameter 2” and thickness 2/e”- spinning magnets from the magnetic stirrer induce electric currents to flow in the copper eTOP- these currents then create their own magnetic field which opposes the magnets underneath and pushes the eTOP to spin, producing interesting motion and sound. Credit to astrophysicist Kenneth Brecher, the creator of the eTOP, PhiTOP, and this unique means of using Lenz’s Law to spin it up. This top stands up vertically (when spun with sufficient rotational velocity) due to physics similar to that of the tippe-top. The concave mirror keeps the top from wandering off of magnetic stirrer. 


The PiTOP

Well engineered brass spinning toys by SiriusEnigmas

From Etsy: BUY NOW: The PiTOP

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

The PiTOP: this beautiful brass cylinder has a radius of 1 inch, a height of 1/π inches, and displays the first 109 digits of π on its face. Spin this disk (best with sound on) and it will demonstrate some very interesting physics involving energy transfer and conservation of angular momentum. The edges of the cylinder are rounded and engineered to exhibit an optimum motion of a “spolling” coin, a motion that combines spinning and rolling (closeup shown in 240fps). As the disk’s angle of inclination decreases the speed of the rolling increases dramatically until the contact point with the mirror is moving in excess of 200mph. From the mind of physicist Ken Brecher, inventor of the PhiTOP. Note also that with the specified height, that the volume of this cylinder is exactly 1 cubic inch! 

Stomachion Puzzle

Get this 3-color laser cut acrylic version here:
From Kadon Enterprises: BUY NOW: Stomachion Puzzle

Also a very nice multicolor acyrlic version here:
From Etsy: BUY NOW: Stomachion Puzzle

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

Learn about the 1998 discovery of the lost writings of Archimedes (and the technology used to recover them) in this TED talk

Ancient Stomachion Puzzle: the oldest known puzzle, discovered in the writings of the great Greek physicist and mathematician Archimedes from some 2200 years ago. The puzzle is a dissection of a square into 14 polygons, where the areas of each piece are integer multiples of each other (a curious way to slice it up). In 2003 Bill Cutler showed that there are 536 district ways to configure these pieces to make the square (five are shown here), ignoring simple rotations and reflections. Swipe to see the most famous solution, attributed to Archimedes himself, that was found in an ancient manuscript discovered only in 1998- before this date historians knew the name of the puzzle, but no one knew what it looked like. Kate Jones, the maker of this particularly aesthetic version, found that when using only three colors for the polygons, there are only 6 solutions where no two pieces of the same color touch (four solutions shown here).

Frabjous Geometric Sculpture Puzzle

Get one here- five colors to choose from:

From MoMath: BUY NOW: Frabjous Sculpture Puzzle

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Frabjous Geometric Sculpture Puzzle: 30 identical laser cut acrylic pieces interlock into 12 interconnected five point stars (each with a spiral vortex center) in this puzzle based of the Frabjous sculpture by artist and professor of mathematics George Hart (Prof. Hart is now on Instagram, follow him at @george.hart.sculptor to see more of his amazing work.) Note that if one connects the tips of the stars one gets the outline of a dodecahedron, with its 30 edges and 12 sides, and if one considers the face planes of the linked pentagrams the underlying shape is a polyhedron called the “great rhombic triacontahedron”. A year or so ago I got to visit the National Museum of Mathematics in NYC where I bought this puzzle in the @momath1 museum shop. This puzzle was great fun to assemble- buy one to support this inspirational museum, and make a great sculpture for your bookshelf! 


Platonic Solids Dice Set

Get this nice set of regular polyhedra dice here:

From Etsy: BUY NOW: Polyhedra Dice Set

Less expensive sets of standard plastic dice here:

From Amazon: BUY NOW: Polyhedra Dice Set

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Platonic Solids Dice Set: The five famous convex regular polyhedra in the form of fair dice. This set is cast in metal with clean edges and makes for a great way to own these symmetrical objects that have fascinated thinkers ever since the ancient Greeks wrote about them circa 360 BC. Only these five forms meet these criteria (in 3D space) for each face: must be equal in size, be equal in number of sides, each side of equal length, identical in angle were any two sides meet, and have the same number of sides meet at each vertex point of the solid. 2000 years later the famous mathematician Euler determined that for these 5 shapes V-E+F=2, the number of corners (vertices), minus the number of edges, plus the number of faces, will always equal 2. 

Infinity Cube Sculpture

Get an infinity cube here (many colors and sizes to choose from):

From Ricardo Churchill (Etsy): BUY NOW: Infinity Cube
Note: this site contains affiliate links for which I may be compensated

Infinity Cube Sculpture: crafted from solid stainless steel and powder coated orange, the geometry of this mathematical sculpture is the perimeter of the faces of a cube traced by a nonintersecting connection of equal line segments. When viewed from a corner, a cube has a hexagonal cross section, and some may recall the famous logo of Silicon Graphics computers based on such an infinity cube (a design by Scott Kim). Rotating this “tubed cube” along a diagonal axis reveals the interesting symmetries of this geometric construction.

Aristotle's Wheel Paradox 

Get this demonstration puzzle here:

From Etsy: BUY NOW: Aristotle's Wheel

WIkipedia has some details on the Wheel "Paradox"

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Aristotle’s Wheel “Paradox”: How does the smaller attached disk travel the same length as the larger one if both disks only make one full rotation? Note the shorter path of the smaller disk, if rolled on its own. This beautifully made demonstration depicts an issue of geometry and motion that perplexed the best minds of humanity for 2000 years. The ancients knew the formula for circumference, and C=2πR for the large disk is clearly greater than C=2πr for the smaller- so how could the smaller disk, rotated once, still travel the distance of the larger one if attached? The great Galileo even offered a solution to the problem in his book Two New Sciences, where he approximated the situation as concentric hexagons and considered the limit as the number of sides increased. So what is the best answer to make sense of this situation?


Squaring a Circle Sculpture

This sculpture available as a 3D print:

From ShapeWays: BUY NOW: Square Circle Illusion

See other amazing geometric illusions here: Ambiguous Objects

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

Squaring a Circle: from one particular point of view this wireframe sculpture looks like a circle, from another it’s a square! From other viewing angles one can see that the underlying curve is comprised of four identical segments of a parabola. A wonderful example of how a single perspective can be misleading! A math sculpture available as a 3D print by Matt Enlow. 

RPSLK Dice

These dice are available here:

From Amazon: BUY NOW: Rock Paper Scissors Lizard Spock Dice

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RPSLK Dice: the famous Lizard Spock extension to the Rock, Paper, Scissors game expressed on 10 sided dice allowing the study of the non-associative nature of the game (Rock wins Scissors, and Scissors wins Paper, but Rock does not win Paper, etc.), and other interesting math. The original RPS game had three “weapons” and only three rules are needed to play the game. Adding Lizard-Spock makes for 5 gestures, but now 10 rules must be used, including “Spock vaporizes Rock”, “Lizard poisons Spock”, and my favorite “Paper disproves Spock” (swipe to see famous graphic). Interestingly, mathematical analysis shows a similar four weapon game with equal odds of winning is not possible. It was also found that the next possible game with 7 gestures would require 21 rules to play. The Lizard-Spock extension was invented by Sam Kass and Karen Bryla in 2005 and made famous on the sitcom Big Bang Theory. 

Soma Cube

The Soma Cube is available in a variety of materials and colors:

From Amazon: BUY NOW: Soma Cube

From Etsy: BUY NOW: Soma Cube

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

Soma Cube: Math toy invented by Danish scientist and artist Piet Hein, who claimed that this puzzle idea came to him as he was listening to a lecture on Quantum Mechanics by Werner Heisenberg (yes- that Heisenberg) in 1933. The seven pieces are all the ways 3 or 4 cubes can be joined, such that each piece has at least one inside corner. Amazingly there are 240 ways to make the larger cube from these 7 pieces- still not that easy!