Math Toys

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Symmetry Sculptures

These amazing scluptures from Bathesheba Grossman available here:

From Etsy: BUY NOW: Math Sculptures

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Symmetry Sculptures: the Quintrino with 12 identical interlocking starfish, and the Metatrino with 6 identical connected four armed stars- based on the symmetries of the dodecahedron and the cube. Two examples of the amazing work of artist Bathsheba Grossman, a pioneer in creating such intricate mathematical forms.

Levitating Cube Tensegrity

Get the 3D print files here: Levitating Cubes

Similar fun tensegrity prints often available on Etsy

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Levitating Cube Tensegrity: connected only by four segments of fishing line! An amazing 3D print creation by @heliox_lab where the beautifully symmetric configuration is stable in all orientations. Another fun take on the tensegrity concept, invented by Kenneth Snelson and made famous by the architect Buckminster Fuller in 1949. 

Ambiguous Suits & Hearts 

Get this ambigous object illusion here:

From SEO Magic: BUY NOW: Heart Metamorphosis by Kokichi Sugihara

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

See other: ambigous object illusions in my collection

Ambiguous Suits & Hearts: I first discovered and posted the work of mathematician Kokichi Sugihara’s amazing ambiguous object illusions in 2017. Here is one more really nice example of his original work that was sent to me by my good friend Tim Rowett.

Hosono Kaleidoscope

Fine Art Kaleidoscopes by Tomoo Hosono:
From Nellie Bly: Hosono Precision Kaleidoscopes 

Check out this: afffordable yet amazing tapered mirror teleidoscope

See more Kaleidoscopes in my collection.

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

Two Mirror Kaleidoscope: this unassuming stainless steel cylinder holds within one of the most beautiful kaleidoscopic mandalas I’ve seen. The colors seen come from polarizing filters and thin films encased in oil, and the two mirrors are precisely aligned at a 60 degree angle to produce the sixfold symmetry.

Puzzle Proofs

Get these and many other interesting puzzles here:

From Etsy: BUY NOW: Puzzles from Jeux Efce

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

Puzzle Proofs: three mathematical proofs in a physical form that use equivalent areas to make the case. The first video illustrates one of the most famous equations concerning the sides of any right triangle, the Pythagorean Theorem. 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. One of the most used formulas when calculating vectors in physics classes! In the second video, similar comparisons of areas illustrate two special binomial products (a+b)² and (a+b)(a-b), and connects these famous algebraic equations to simple geometry. 

Squirclusion (Square Circle Illusion)

Get this sculpture here:

From Etsy: BUY NOW: Squirclusion

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

Squirclusion (Square Circle Illusion): from one particular point of view this sculpture looks like a circle inside a square, from another, a square inside a circle- a matter of perspective! From other viewing angles one can make out that the underlying curves for each circle/square component are four identical segments of a parabola conjoined. Another reminder of how a single perspective can be misleading. This math sculpture is available as a 3D print, expertly designed and produced by Pyrigan Puzzles. 

Curta Calculator 

These vitiage items are available here, but are a bit pricey:

From eBay: BUY NOW: Curta Calcualtor

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

Here is an amazing article about the inventor and the device by Cliff Stoll

Curta Calculator: before the electronic calculator there was this device that was portable, powered by hand, and could calculate to a precision of 15 decimal places! This is the Type 2 model and it was made in 1962 and still works beautifully. Demonstrated here is how to multiply two large numbers- for fun let’s pick 3803 x 32463. Although the process is not as simple as pressing buttons, the steps are intuitive: First, set in the largest number using the sliders on the side. Next we now multiply that number using each digit of the smaller number and move the top “carriage” to note the place values of each digit. Placing the carriage on 4 will multiply the side number by 1000 for each turn, so we turn the crank 3 times. Following this pattern we then place the carriage on 3 and turn the crank 8 times to multiply by 800, and finally we place the carriage on 1 and turn the crank 3 more times. The number 3803 now appears on the top silver readout, and the result, 123,456,789 is read off the top black output register. From this demonstration we see that the number of crank turns needed is just the sum of the digits of the smaller number (14 for this calculation)- some effort but better than multiplication long hand and with much less chance of mistakes! The device is cleared by lifting the carriage and swinging the clearing ring around once. Invented by Curt Herzstark and manufactured from 1947-1972, these devices are mechanical wonders with over 700 precision components. 

Invisible Ink and UV LED Pen

This item came to me in my Winter 2022 Curiosity Box subsciption:
Get (or give!) a Curiosity Box subscription here: JOIN NOW: The Curiosity Box

Get this amazing and inexpensive version of the Spirograph here:
From Amazon: BUY NOW: Spirograph Animator

Get a similar pen and UV light here: 
From Educational Innovations: BUY NOW UV Pen

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

Invisible Ink and UV Pen: this pen utilizes a clear ink that when dry is barely noticeable, but contains fluorescent compounds that reveals its presence under long wave ultraviolet light. This cool pen with UV LED light came in my @thecuriositybox yesterday where I applied it to make some hypotrochoid roulette curves with this pocket Spirograph set. 



Dendritic Quartz

Available here:

From Etsy: BUY NOW: Dendritic Quartz

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

Dendritic Quartz: Fractal patterns are found throughout Nature- but few are in as pure a fractal form as these manganese dendrite inclusions, found in quartz and other mineral compounds where they grow along the cracks and joint planes of crystals. The fractal dimension of these delicately branched structures is about D=1.8 as estimated by the famous “box counting” algorithm. I picked up this beautiful fractal quartz freeform cabochon from @rareearthminingco (thanks Curtis!) at the Tucson gem, mineral, and fossil show. 

Stellated Dodecahedron of the Sagrada Familia

Similar 3D printed form:

From Etsy: BUY NOW: Stellated Dodecahedron

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

Stellated Dodecahedron of the Sagrada Familia: another amazing application of aesthetic geometry encountered in my travels to Barcelona. The latest addition to the continued construction of Antoni Gaudi’s design was placed upon the Tower of the Virgin Mary in 2021, an illuminated stellated dodecahedron made of glass. Swipe to see a photo and the impressively detailed model of the spire featured in the on-site museum. I purchased this 3D printed model of the star in the museum gift shop

Magnetic Soma Cube

Get this inexpensive SomaCube here:

From Amazon: BUY NOW: Magnetic Soma Cube

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

Magnetic Soma Cube: a new fun variant of the famous math toy invented by Danish scientist and artist Piet Hein, who claimed that this puzzle came to him as he was listening to a lecture on Quantum Mechanics by Werner Heisenberg (yes- that Heisenberg). The seven pieces of this puzzle are all the ways 3 or 4 cubes can be joined such that the piece has at least one inside corner. In this version small magnets are encased in cleverly designed cavities such that they will always flip over to attract a counterpart in another puzzle piece, allowing the puzzle to stick together- or hang from the side of the refrigerator. Amazingly there are 240 ways to make the cube from these 7 pieces- still not that easy! 

Spirograph Animator

Get this amazing and inexpensive toy here:

From Amazon: BUY NOW: Spirograph Animator

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

Spirograph Animator: a turntable adds an ingenious embellishment to this classic math toy. When the centerpiece is put into rotation a strobe light turns on and the cyclic designs spring into a complex dance. Spirographs produce mathematical roulette curves called hypotrochoids, cyclical designs that repeat at varying integer multiples. When the strobe light frequency, and rotation frequency, match up with an integer multiple of one of the patterns, that roulette curve appears stationary while the other patterns stay in motion. Shown here is but one combination of many possible overlapping patterns that can be produced by the supplied set of gears and colored pens. 

Fractal Tree Ornament

Get this and other mathematical creations by George Bell:

from Etsy: BUY NOW: Koch Snowflake Ornament

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

Fractal Tree Ornament: four iterations of the famous Koch Snowflake fractal are ingeniously combined as the four symmetry planes of a cuboctahedron. A very seasonal mathematical object to hang on the tree! Designed and 3D printed by artist and maker George Bell. 

Tapered Mirror Kaleidoscopes 

These precision kaleidoscopes are crafted from front surface mirrors and other specialty materials, many with innovative design and construction techniques:

From Etsy: BUY NOW: Kaleidoscopes by Marc Tickle

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

See more kaleidoscopes in my collection.

Tapered Mirror Kaleidoscopes: hidden within these colorful tubes are tapered mirrors, 2 rolling glass spheres, and 1 dichroic glass reflector. These elements combine to produce the dynamic and magical images seen through the view window as the device is slightly tilted back and forth and brought in and out of a bright light source. The first design uses 3 mirrors to create the hexagonal symmetries, the second design uses 4 mirrors to produce the infinite cylinder effect. These unique teleidoscope designs are but two of many creations by artist Marc Tickle. Invented by the famous Scottish physicist Sir David Brewster (1781-1868), the kaleidoscope is an ultimate physics toy and entire field of artistic endeavor. 

Fruit Basket Hyperboloid

Get this affordable math art here:

From Amazon: BUY NOW: Hyperboloid Fruit Basket

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

Take a look at other featured hyperbolid art and toys

Fruit Basket Hyperboloid: 14 straight rods are arranged 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. An affordable doubly ruled surface for any table- great for fruit or mathematical holiday decor!