Get these and amny other designs here:
From Shapeways: BUY NOW: 3D printed Illusions
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Ambiguous Circles and Squares: two more examples of the Sugihara ambiguous object illusion, with “impossible” mirror reflection. Thanks to Gerardo Ortega for sending me these 3D prints of his designs.
This item came to me in my Summer 2023 Curiosity Box subsciption:
Get (or give!) a Curiosity Box subscription here: JOIN NOW: The Curiosity Box
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Sonic Photonic Visualizer: a laser reflects from a small mirror mounted on a stretched rubber membrane which allows the projection of complex curves produced by the deformation of the membrane from sound waves. Yet another amazing kit from the VSauce team at @thecuriositybox which uses a balloon as the membrane for the top of the “drum”. The membrane is most sensitive to sound waves in the bass and midrange frequencies and I got the best reaction with my Bluetooth speaker playing Moon Flower by Tahüm- a snippet of which is featured here.
This vintage card is from the 1980s.
Click here: to find more Anamorphic Images and Devices
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Mirror Anamorphosis: perspective often depends on the lens (or in this case, mirror) that is looked through. This vintage card from 1984 contains a cylindrical mirror anamorphic image. Lady Liberty is revealed by bending the flexible Mylar mirror in to a half cylinder.
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.
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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.
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.
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.
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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.
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
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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.
Available here:
From Etsy: BUY NOW: Dendritic Quartz
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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.
Similar 3D printed form:
From Etsy: BUY NOW: Stellated Dodecahedron
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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.
Get this amazing and inexpensive toy here:
From Amazon: BUY NOW: Spirograph Animator
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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.
Get this affordable math art here:
From Amazon: BUY NOW: Hyperboloid Fruit Basket
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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!
Get this inexpensive 3D printed set here:
From Etsy: BUY NOW: Nautilus Gear Set
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Nautilus 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 3D print of Misha Tikh and the research of Balint et al.
These mathematical art objects are created by Henry Segerman and are available here:
From Shapeways: BUY NOW Mathematical Art
US Flag projection can be obtain here (Support MoMATH!);
From MoMATH: BUY NOW: US Flag Stereo Projection
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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 1) the US Flag, 2) a honeycomb of regular hexagons, and 3) a square grid. 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.
Get the files (or order one printed) here:
From MakeAnything's MyMiniFactory: BUY NOW: Illusion Cube 3D Print Files
From Shapeways: BUY NOW: Ambiguous Cube Illusion
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See the other illusions my collection: Ambiguous Objects
Wireframe Ambiguous Cube: another innovation of the ambiguous object illusion invented by mathematician Kokichi Sugihara of Meiji University- this time a 3D frame of a cube transforms to a cylinder! A new 3D print design from @make.anything.