### Hyperbola Clock

This amazing clock available here:

From Maths Gear: **BUY NOW **

Hyperbola Clock

Hyperbola Clock: a straight rod glides through a curved hole in this unconventional clock based on the hyperboloid, the 3D ruled surface traced by rotating diagonal line. In this creation by Robert Darwen of Fibonacci Clocks, the rod serves as the hour hand with a smaller minute hand above the center of the base disk. (The time adjustment dial of the clock mechanism was connected to a small motor to produce the sped up motion in this video so that 1 second = 1 hour)

### Trammel of Archimedes

Get similar devices here:

From Etsy:** BUY NOW **

Trammel of Archimedes

From eBay:** BUY NOW **

Trammel of Archimedes

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 **

From Amazon (Japan):** BUY NOW set of four ambiguous objects with booklet **

This kit contains four white plastic illusion objects (including the arrow) and a booklet. I used the translate feature in the Chrome browser to place my order and it shipped to California in a few days.

The math and physics are described here in this technical journal article by Prof. Sugihara.

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.

### Pocket Scintillator Kinetic Art

Logan sometimes has items for sale here:

From Etsy: **BUY NOW: PocketScintillators**

Pocket Scintillator Card: three sheets of seemingly random arrays of translucent colored pixels produce words and images when stacked- shift the stack of sheets and a second images appears! Innovative kinetic optical art by inventor, artist, software developer Logan Kerby @thanksplease who kindly sent me these cards encoded with @physicsfun themes.

### Novascope Kaleidoscope

The Novascope can be ordered from the artist here:

From novascopes.com: **Order here Novascope by David Sugich **

Novascopes can sometimes be found on eBay

From eBay:** Search NOW Novascope Kaleidoscopes **

Novascope: tapered mirror kaleidoscope by David Sugich uses three mirrors to create an image of geodesic spheres. Three mirrors in an equilateral triangle configuration will produce a plane of tiled triangles, but if they are tapered the repeated reflections curve to infinity creating the spherical geometry. In this design there are thin gaps etched into one mirror which allows in colored light from a flashlight (on the white side of the pyramid shaped scope) to produce the hexagon lattice. Shining a light through the view portal reveals where the colored lines come from as a flashlight moves from top to bottom and back. Invented by the famous Scottish physicist Sir David Brewster (1781-1868), the kaleidoscope is an ultimate physics toy and entire field of artistic endeavor.

### Hyperbolic Holes

This inexpensive kit available here: From eBay: ** BUY NOW**

Hyperbolic Holes Kit

Hyperbolic Holes: a straight rod, in this case a pencil, glides through a symmetrical pair of curved holes. The design is based on the hyperboloid, the 3D ruled surface traced by an offset rotating diagonal line. This device is sold as an inexpensive kit to assemble yourself, and includes a motor with geared drive and pre-cut pieces. The pencil is my addition- just the right size to clear the curved openings.

### 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**

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.

### Cone of Apollonius

Similar models available here:

From Amazon: **BUY NOW: Cone of Apollonius**

From Etsy: **BUY NOW: Cone of Apollonius**

Cone of Apollonius: Slicing a cone with a plane will produce the famous curves known as the conic sections, as demonstrated with this beautiful vintage wood model by Nasco. Slicing at a right angle to the cone’s axis of symmetry produces a circle, and tilting the intersecting plane a bit produces an ellipse. When the plane is tilted parallel to the side of the cone the curve produced is a parabola, and tilting even further creates a hyperbola. The discovery of the mathematics demonstrated here are attributed to Apollonius of Perga from about 250 BC- thousands of years later Kepler, Newton, and others showed these conic sections to be intricately connected to many branches of physics such as planetary orbits and the optics of telescopes.

### Shadow Stereographic Projection

These mathematical art objects are created by Henry Segerman and available here:

From Shapeways:** BUY NOW Mathematical Art **

Wikipedia has a nice introduction to the math and applications of stereographic projection.

Shadow Stereographic Projection: 3D printed sculptures that cast geometric shadows. When illuminated by a point source of light (placed at the top pole of the sphere) the shadow cast by the rays of light represent a one to one mapping of the points on the sphere to points on the plane- creating a square grid, and a honeycomb of regular hexagons. Stereographic projection is often used in representing the geography of the globe of our planet on to a flat map. Mathematical art by Henry Segerman.

### Equilateral Triangular Kaleidoscope

This inexpansive kaleidoscope is available here:

From increadiblescience: **BUY NOW: Moire Tube Kaleidoscope**

Click here for affordable, precision made scopes with angled mirrors: **Kaleidoscope Symmetries Explored**

See more kaleidoscopes in my collection: Kaleidoscopes

Equilateral Triangular Kaleidoscope: three mirrors arranged in a 60-60-60 degree triangle creates the appearance of a plane filled with triangles (or equivalently a honeycomb lattice)- perhaps the most common mirror configuration design, this inexpensive kaleidoscope produces an excellent example of the reflection pattern. As a bonus the exterior tube on this scope incorporates a kinetic Moirè pattern. The kaleidoscope was invented by the famous Scottish physicist Sir David Brewster (1781-1868), and has become an entire field of artistic endeavor.

### Beaded Kaleidocycle

Get similar beadwork geometric art here:

From Etsy: **BUY NOW: Beadwork Kaleidocycle**

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.

### Tapered Mirrors Kaleidoscope

This design by Koji Yamami available here:

From kaleidoscopeshop.com: **BUY NOW Space Teleiedoscope **

Click on this link for details on the physics and symmetries of two mirror kaleidoscopes.

Tapered Mirrors Kaleidoscope: the unique design of this teleidoscope uses three mirrors to create an image of a geodesic sphere. As can be seen through the semi-transparent acrylic tube, the three mirrors are tapered, with their smaller ends near the ball shaped lens. Three mirrors in an equilateral triangle configuration will produce a plane of tiled triangles, but if they are tapered the repeated reflections curve to infinity creating the sphere. In this design by Koji Yamami there are small gaps between the mirrors which allows in colored light from the iridescent tube to produce the radiant streaks of light. Invented by the famous Scottish physicist Sir David Brewster (1781-1868), the kaleidoscope is an ultimate physics toy and entire field of artistic endeavor.

### 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**

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.

### Pencil Hyperboloid

Choose your color and get one here:

From Etsy: **BUY NOW **

Hyperboloid Pencil Holder

don't forget a set of pencils:

From Amazon: **BUY NOW **

Colored Pencil Sets

Better yet- get some thermochromic color changing pencils!

From Educational Innovations: **BUY NOW **

Heat-Sensitive Pencils

Pencil Hyperboloid: a perfect gift for any math teacher- the precisely oriented holes in this base direct 16 pencils to reveal a hyperboloid, the 3D surface traced by revolving a diagonal(skew) line, the outline of which is the conic section of the hyperbola. A doubly ruled surface for any desktop!

### 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**

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.

### 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**

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.

### In and Out Illusion

Similar objects available here- from Etsy:** BUY NOW**: ** Ambiguous Objects**

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.

### 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?