### Polarized Light Cell Kaleidoscope

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

See more kaleidoscopes in my collection: Kaleidoscopes

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.

### 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.

### 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.

### 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.

### Vsauce Mirror Anamorphosis

Currently this mirror and image set comes to you (in the Summer 2020 box) with any subscription:

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

The Curiosity Box is an excellent way to start your own physics toy collection- reccomended highly!

For those who want to see the math behind this art, here is an initial paper on the topic published in 2000 in the American Journal of Physics: Anamorphic Images by Hunt et al.

Vsauce Mirror Anamorphosis: the warped printed image is restored only with a mirror in the form of cylinder- when placed carefully in the center of the image, Kevin, Michael, and Jake appear in their true form. This mirror (along with a set of images and DIY templates) came to me last week in the most recent @thecuriositybox- a fantastic way to start your own physics toy collection. The math describing this anamorphic mapping is quite complex and is nicely detailed in a physics journal article from 2000.

### Mirror Anamorphic Lenticular Cup & Saucer

Direct message Luycho on Instagram about this design. Other designs can be seen here:

From Luycho:** **

Luycho | A New world on Mirrors

Click here for more Mirror Anamorphic

Mirror Anamorphic Lenticular Cup & Saucer: a toucan sits in a nest of flowers, revealed only when the cylindrical mirrored cup is put in place. This beautiful design by Luycho uses both mirror anamorphic reflection and an accordion type lenticular dual image. Art meets math and physics! @luycho for details.

### 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.

### Tessellating Geckos

These laser cut hardwood geckos are available here:

From Etsy:** BUY NOW Tessellating Geckos **

Tessellating Geckos: MC Escher inspired lizard cutouts interlock precisely to tile a surface with no overlaps or gaps. Laser cut from maple, walnut, and cherry wood by maker/artist Craig Caesar and inspired by MC Escher’s “Study of Regular Division of a Plane with Reptiles” 1939. G4G week: Martin Gardner wrote about the art and math of Escher in 1961- which helped create the popularity that his work has experienced ever since.

### Arrow on Mobius Strip

Get this 3D printed object of math topology here:

From Etsy: **BUY NOW: Mobius Strip with Arrow**

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.

### Logarithmic Spiral Gears

Amazing creations made here:

From Etsy:** BUY NOW **

Spiral Gear Set

Original 3D print files available here:

From Thingverse:** Spiral Gear Set **

Logarithmic Spiral Gears: an extreme example of non-circular gear sets. This set is based on the famous Fibonacci spiral and evokes the cross section of nautilus shell with internal chambers. If one gear of this set is turned at constant speed, the other will turn with an varying speed. A kind gift laser cut at @hsvsteamworks and based on 3D prints of Misha Tikh and the research of Balint et al.

### 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)

### Coins of Constant Width

These triangle coins are often available on eBay.

Fron eBay: **Search NOW: Bermuda Triangle Coin**

The silver proof versions can be expansive, but sometimes the circulated coins (like those in the video) are available at a lower price.

Click to see more: **shapes of constant width**

Coins of Constant Width: the only coins produced in the shape of the Reuleaux triangle, issued in 1997 and 1998 by Bermuda. The special convex shape of the Reuleaux triangle 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 here how two straightedge rulers remain parallel as the coins rotate between them, just as one would expect circles to behave! Bermuda triangle (ha!) coins were only produced for two years and featured Elizabeth II on the front and shipwrecks on the back- this one depicts the wreck of the Sea Venture.

### Pentominoes

Get this set here:

From Etsy: **BUY NOW Hardwood Pentominoes **

Many versions available here:

From Amazon:** BUY NOW Pentominoes **

The book by mathematician Solomon Golomb that started the polyonomo recreational math craze:

From Amazon: **BUY NOW: Polyominoes **

Pentominoes: The 12 possible arrangements of five identical squares joined edge to edge. Since 5x12=60, the pentominoes can tile a 6 x 10 rectangle with no gaps (2339 ways to do this- yet even finding one solution is a challenge). I love this beautiful set from artist/woodworker Ron Moore where each pentomino is made from a different kind of hard wood.

### Holoscopes: Dodecahedron and Cube

Order a holoscope from the artist's gallery here:

The artwork of Gary Allison: **BUY NOW Holoscopeworld.com **

Look through other holoscopes in my collection here: Holoscope Kaleidoscopes

Holoscopes: polyhedra of mirrors (dodecahedron and cube) with the interior viewed from one corner and illuminated by light entering from glass spheres placed at all of the other vertices. A type of kaleidoscope based on mirrored polyhedra by artist Gary Allison @holoscope2000, and future posts will include tetrahedron, octahedron, and icosahedron holoscope forms as I complete my Platonic solids set. Each holoscope has stained glass on the exterior and front surface mirrors on the inside which create the amazing and seemingly impossible spaces within.

### 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.

### Satisfying Hexagons

Get this 3D print here (your choice of colors):

From Etsy: **BUY NOW: Satifying Hexagons**

Satisfying Hexagons: this delightful kinetic art manipulation toy features 19 nested hexagons within a hexagonal frame. Embedded magnets allows one to move the central hexagon from behind creating interesting visual effects. A 3D print created by @i.am.the.lazy.engineer- indeed oddly satisfying!

### 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.

### 3-Shuttle Trammel of Archimedes

This device 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**

Get similar (two shuttle) devices here:

From Etsy:** BUY NOW **

Trammel of Archimedes

3-Shuttle Trammel of Archimedes: as the shuttles take turns completing their straight line journeys, the end of the crank arm traces an ellipse. This precision 3-shuttle version by the VSauce team came in my @thecuriositybox - made with high quality molded plastic parts that produce very smooth movement- a wonderful addition to my collection! 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.