### Impossible Knot

Follow the link below for full explanation and instructions.

From mathematician/artist George Hart: Tying the Knot Puzzle

Impossible Knot: how did this overhand knot get into this closed continuous band of rubber? It did not get there by cutting the loop, tying a knot, and rejoining it. Amazingly this band was once a rubber o-ring. How was it cut to produce a knot? An “impossible object” related to the Möbius strip by mathematician and artist George Hart- a brain teaser puzzle he calls “Tying the Knot”.

### Impossible Bottle with Arrow

Get an impossibe object from this artist here:

From Etsy: **BUY NOW: Impossible Bottles and Objects**

Impossible Bottle with Arrow Sculpture Puzzle: a new seemingly impossible object in my collection- Created with clever engineering, this “impossible” syrup bottle contains a wooden arrow that should not fit through its neck. The wood of the arrow is notably one uncut piece, and yet a metal washer is also somehow trapped on the shaft of the arrow. The puzzle aspect is to consider how the bottle was produced (I personally have some theories- but I do not know the secrets of this artist). I can tell you with high certainty that the bottle was never cut or altered in anyway, and it was not somehow formed around the objects. This bottle by Brad Byers is an expertly crated example of the impossible object genre.

### 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.

### Balance Stacking Sculpture

Another wonderful desing by BinDesign- get one here in black or natural wood:

From Etsy: **BUY NOW: Bin Design Balancer Puzzle**

Balance Stacking Sculpture: a series of torques in unstable equilibrium complete this Calder-esque structure. As each component is added its weighted end balances all the others before it, with the initial small piece weighing about a gram or so. Remove the end piece and the whole structure comes down. Another wonderful design by artist Bin Xu.

### Aperiodic Monotile

Learn more about this recent math dicovery here: An aperiodic monotile (arXiv)

Althogh the math says they can tile the plane, getting them to do so is more challenging than one might think!

Get a set of laser cut hat tiles here:

From Etsy: **BUY NOW: "the Hat" monotile set**

See other aperoidic tilings in my collection.

Aperiodic Monotile: this newly discovered 13 sided shape, named “the hat”, will tessellate a plane to infinity, similar to how squares or hexagons can tile out with no gaps. However the hat tiles the plane aperiodically- if one tries to shift a part of a hat tiling, the shifted part will not align or match up with any other part of the same tiling- all the way out to infinity! The fact that aperiodic tessellations exist at all is pretty amazing, and Sir Roger Penrose (Nobel prize in physics 2020) is also famous for discovering a pair of regularly shaped polygons that tile in this aperiodic way. However it was not clear until a few weeks ago if a single shaped tile could tessellate aperiodically when the hat was described in a paper by Smith, Myers, Kaplan, and Goodman-Strauss uploaded to arXiv March 20.

### Penrose Aperiodic Rhombs

A nice version of Penrose Tilings is available here:

From Etsy:** BUY NOW Penrose Tiles **

Penrose Aperiodic Rhombs: a famous aperiodic tiling with just two shapes- a pair of rhombuses with equal sides, but with the ratio of their areas made to equal the golden ratio. Note that although the starting pattern of 10 tiles is symmetrical, adding any further tiles breaks the symmetry, as highlighted by the path of the double curves. Sir Roger Penrose- who just won the Nobel prize in physics for his contributions to General Relativity- also discovered tessellations (tilings) that are aperiodic even though the two tile types are regularly shaped polygons. If one tries to shift a part of a Penrose tiling, the shifted part will not align or match up with any other part of the same tiling- all the way out to infinity! In this construction, single and double line patterns must align such that the tiles can only connect in specific ways to ensure the non-repetitive nature of the Penrose tiling structure. Shown here is one way these two tile types will fill the plane.

Wikipedia has the details on Penrose Tilings and their inventor Sir Roger Penrose (Recently won Nobel Prize!)

### Penrose Tiling Puzzle

This puzzle was produced and sold in the 1990s.

The individual tiles can be found on eBay (and sometimes the whole puzzle):

From eBay: **Search NOW Penrose Pentaplex Puzzle **

Wikipedia has the details on Penrose Tilings and their inventor Sir Roger Penrose (Recently won Nobel Prize!)

A nice basic version of Penrose Tilings is available here:

From Etsy:** BUY NOW Penrose Tiles **

Penrose Tiling Puzzle: a challenging puzzle with pieces that come in only two shapes. Sir Roger Penrose- who just yesterday won the Nobel prize in physics for his contributions to General Relativity- also discovered tessellations (tilings) that are aperiodic even though the two tile types are regularly shaped polygons. If one tries to shift a part of a Penrose tiling, the shifted part will not align or match up with any other part of the same tiling- all the way out to infinity! This puzzle, entitled “Perplexing Poultry”, created and sold by Penrose himself, uses polygons modified into crazy looking birds such that the tiles can only connect in specific ways to ensure the non-repetitive nature of the Penrose tiling structure. Shown here is one way these two tile types will fill the plane.

### Gravity Drop Challenge

Get this well made demonstration here:

From Etsy: **BUY NOW: Gravity Path Demo Puzzle**

Gravity Drop Challenge: starting at the same height, and ending at a same lower height, which path will take the shortest amount of time? The straight line (red marble) or the wavy longer path (blue marble)? The weird thing is that both marbles will have identical speeds at the finish line- yet one gets there quicker. The physics problem of finding the curve of fastest descent is called the brachistochrone problem- from the Greek words brakhistos ‘shortest’ and khronos ‘time’- and it is not a straight line. The fastest curve turns out to be the cycloid- a topic for a future post.

### Impossible Bolt

Only available from these aritist/craftsmen:

From Art of Play: **BUY NOW: Impossible Bolt & Nuts**

Impossible Bolt: one nut threads on clockwise as normal- the other threads on counterclockwise on the same bolt! Not impossible- but carefully engineered and machined. Swipe for partial hint on mechanism. This puzzling curiosity was inverted by Scott Eliott and machined in solid brass by puzzle crafters Steve Nicholls and Ali Morris of TwoBrassMonkeys.

### Perspective Puzzle

Vintage puzzles in this series are sometimes available on eBay:

From eBay: **Search NOW Virtual Illusion 3D Puzzle**

Perspective Puzzle: twelve flat images, when ordered and spaced correctly, combine to produce this 3D illusion of structure and depth. This vintage toy by Mattel was sold as “Virtual Illusion 3D Puzzle” where the challenge is to scramble/shuffle the 12 sheets and then place them in the correct orientation and order to complete the image. A fun application of the math and physics of anamorphosis and perspective.

### Trisected Cube

Get this puzzle here:

**BUY NOW: Trisected Cube Puzzle**

This puzzle came in my Curiosity Box subscrition. A great way to start collecting your own physics toys (and other brain food):

From the Vsauce team: **BUY NOW: The Curiosity Box**

Trisected Cube Puzzle: three identical pieces interlock to form a cube in this ingenious dissection puzzle. The cube is sliced following a helical path along a corner to corner diagonal, creating a smooth disassembly, and a smooth but surprisingly challenging initial reassembly. Invented by Robert Reid and designed by puzzle master Oskar van Deventer.

### Impossible Bottle Sculpture Puzzle

Mr. Evans makes a variety of amazing impossible bottle sculptures:

From impossiblebottle.co.uk: **Buy NOW Impossible Bottles by Philip Evans **

Nice Impossible bottles are often available on Etsy:

From Etsy:** BUY NOW Impossible Bottles**

Impossible Bottle Sculpture Puzzle: seemingly impossible, but created with clever engineering, this “impossible” bottle contains a padlock and full deck of cards still in the wrapper (a cut out in the side of the box reveals that all the cards are inside). The puzzle aspect is to consider how the bottle was produced (I personally have some theories- but I do not know the secrets of this artist). I can tell you with high certainty that the bottle was never cut or altered in anyway, and it was not somehow formed around the objects. This bottle by Phil Evans is one of the best I’ve seen.

### Aristotle's Wheel Paradox

Get this demonstration puzzle here:

From Etsy: **BUY NOW: Aristotle's Wheel**

WIkipedia has some details on the Wheel "Paradox"

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?

### Impossible Arrow

One of many creative illusions and curiosities of Victoria Skye. See her work here:

**Visit Now: Victoria's Illusion Art**

Click here for to explore more **"impossible objects"**

Impossible Arrow: an arrow made of wood through the center of standard steel hex nut. The arrow was carved and somehow placed through the nut- neither the wood nor the steel nut was cut or glued to produce this object. Not impossible, but creating this does depend on the use of some obscure physical properties of wood (similar to the impossible nail sculpture).

### Ring Catch Chain Trick

Get a set here:

From eBay:(best selecton)** BUY NOW Ring Chain Catch**

From Amazon:** BUY NOW Ring and Chain Set **

The physics of this trick in great detail with more slow motion: Ring Falling into a Chain: No Magic — Just Physics

Ring Catch Chain Trick: a solid ring will be caught by a loop of chain if it tumbles during its fall. By Newton's Third law, when the ring twists into and hits the chain, the impact transfers momentum to the end of the chain, which rises up and over the ring- seen here in 480 fps slow motion.

### Anti-Gravity Puzzle

This particular puzzle by puzzlab.com is no longer in production.

However (spoiler), it's possible to creat a version of this puzzle with these:

From Educational Innovations:** BUY NOW Growing Spheres **

"Anti-Gravity" Puzzle: a physics brain teaser- what's the trick here? Four glass marbles can move but stay separated in this liquid filled tube no matter the orientation- why do they not touch?

### Frabjous Geometric Sculpture Puzzle

Get one here- five colors to choose from:

From MoMath: BUY NOW: Frabjous Sculpture Puzzle

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!