Math Toys

Nova Plexus Interlocking Puzzle

Precision machined and available in brass or stainless steel:

From Art of Play: BUY NOW: Nova Plexus Puzzle

Nova Plexus Puzzle: 12 identical brass rods can create 4 interlocking triangles in a perfect symmetry- look carefully and you can see that each rod is in an identical configuration with the 5 others that connect with it. Precision machined notches on the ends of the rods allow them to interlock with elastic tension such that vector sum of the 5 forces on each rod is zero- creating this astonishing geometry as the equilibrium state. Unlock the ends of any two rods and the system instantly disassembles (swipe to view process in slow motion). Invented/designed by artist and computer scientist Geoff Wyvill in 1978, this puzzle has just recently been made available for sale with a limited production run.

Oloids: Solid and Anit-oloid

Order your Anti-Oliod today: available in three types of metal:

From The Matter Collection: ORDER NOW: Anti-Oloids in Brass, Copper, and Steel 

Oloids: “solid hull” and “ruled surface” types made from brass and copper- oloids are unique solids that roll in such a way that every point on their surface comes in contact with the plane. The basis of the oliod’s geometry is that of two connected circles, one perpendicular to the other such that the rim of each circle goes through the center of the other. The shapes you see here are the results of connecting the rims of these circles together with a family of straight lines, one method leads to the solid convex hull form, and another way leads to the ruled oloid (anti-oloid). 

The Random Walker

Galton Board version available here: 
From Amazon: BUY NOW 
Galton Board 

The Random Walker: second model of two Galton Boards designed and produced by this version is made to demonstrate probability in investment returns of a global stock market portfolio relating to risk capacity. Slow motion reveals the erratic path of each steel ball (second half of video). The red graph shows the distribution of 592 monthly returns (mean =1%, SD=5%) representing data from 50 years of an IFA Index fund- here the random “walk” of 3000 steel balls falling through 12 levels of branching paths always produce a close match, and both distributions tend toward the famous bell curve distribution. A wonderfully designed modern version of the Galton Box invented by Sir Francis Galton(1894) to demonstrate the Central Limit Theorem - showing how random processes gather around the mean.

Pythagorean Puzzle

Available here: 
From Creative Crafthouse: BUY NOW Pythagorean Puzzle

Pythagorean Puzzle: 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. This kit also allows at least two other ways to prove this theorem named after the famous Greek mathematician from 500 BC. One of the most used formulas when calculating vectors in physics classes ?

Reuleaux Rotor

This toy is availble from Amazon Japan and will ship to the US:

From BUY NOW: Reuleaux Rotor Wodden Toy

Reuleaux Rotor: this famous curve of constant width, the Reuleaux triangle, can rotate such that at all times it remains in contact with all four sides of a square. As demonstrated by this wooden toy from Japan, the rotor covers approximately 98.77% of the area of the square, missing only the sharp corners. The curves in the corners are in the shape of an elliptical arc. Fun fact: a Reuleaux triangle has a perimeter equal to pi times its width- just like a circle! 

Mirror Anamorphic Lenticular Cup & Saucer

Message Luycho on Instagram about this design. Other designs can be seen here: 
From Luycho: 
Luycho | A New world on Mirrors 

Somtimes available here:
From Amazon: BUY NOW: Anamorphic Cups & Saucers

Click here for more Mirror Anamorphic 

Mirror Anamorphic Lenticular Cup & Saucer: a flamingo sits in a nest of flowers, revealed 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 where turning the plate 180 degrees trades images- using my new photography turntable to nice effect. Art meets math and physics! 

Hexa Sphericon

Sphericon and Hexa-sphericon: order your set today! 
From the Matter Collection: BUY NOW The Sphericon (Hex and Regular) 

Hexa-Sphericon: Sphericons are unique solids that roll in such a way that every point on their surface comes in contact with the plane. Solids from the sphericon family all have one side and two edges. Each sphericon is based on a regular polygon, with the basic sphericon derived from a square, and here- a more interesting case with more complex rolling motion- from a hexagon. 

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. 


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. 

In-Feed Google 2

Steinmetz Bicylinder

Three choices of metal- order one today! 

From KickStarter: ORDER NOW: Steinmetz Bicylinder

Steinmetz Bicylinder: intersect two cylinders at right angles and the remaining confined space is the bicylinder- shown here machined from stainless steel. The bicylinder casts a circular shadow along two orientations, and a square shadow perpendicular to those. In addition the curve created along where the two cylinders meet is an ellipse- as seen with the object spinning along the intersection axis. Fun fact: the area and volume of this object are known to be A=16r^2 and V=16r^3/3. Thanks to Zac Eichelberger of Math Meets Machine for sending me one of his creations. 



The eTOP

Get this and other beautifully crafted math themed tops here: 

Fropm Etsy: BUY NOW: The eTOP

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. 

Novascope Kaleidoscope

The Novascope can be ordered from the artist here: 
From 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.

Mirror Anamorphosis

This image by István Orosz is available as a poster and as a puzzle: 
From Amazon: BUY NOW Mysterious Island Puzzle 
From BUY NOW Mysterious Island Poster 

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. 
Many books are available (with mirror cylinders) from Amazon: Anamorphic Art in Books 

Mirror Anamorphosis: this famous print by artist István Orosz has a hidden anamorphic image revealed by placing a mirrored cylinder over the depiction of the moon in the image. The work visualizes a scene from the book “The Mysterious Island” by the science-fiction author Jules Verne- whose portrait emerges in the reflection on the cylinder. The math describing this mapping is quite complex and was given in detail in a physics journal in 2000, but before that Martin Gardner described the math in 1975. Repost for this week’s theme as I head to G4G! 

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.

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 indeed oddly satisfying!

Tapered Mirrors Kaleidoscope

This design by Koji Yamami available here: 
From 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.