Aristotle's Wheel Paradox
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WIkipedia has some details on the Wheel "Paradox"
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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?
RPSLK Dice
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From Amazon: BUY NOW: Rock Paper Scissors Lizard Spock Dice
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RPSLK Dice: the famous Lizard Spock extension to the Rock, Paper, Scissors game expressed on 10 sided dice allowing the study of the non-associative nature of the game (Rock wins Scissors, and Scissors wins Paper, but Rock does not win Paper, etc.), and other interesting math. The original RPS game had three “weapons” and only three rules are needed to play the game. Adding Lizard-Spock makes for 5 gestures, but now 10 rules must be used, including “Spock vaporizes Rock”, “Lizard poisons Spock”, and my favorite “Paper disproves Spock” (swipe to see famous graphic). Interestingly, mathematical analysis shows a similar four weapon game with equal odds of winning is not possible. It was also found that the next possible game with 7 gestures would require 21 rules to play. The Lizard-Spock extension was invented by Sam Kass and Karen Bryla in 2005 and made famous on the sitcom Big Bang Theory.
Soma Cube
The Soma Cube is available in a variety of materials and colors:
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Soma Cube: Math toy invented by Danish scientist and artist Piet Hein, who claimed that this puzzle idea came to him as he was listening to a lecture on Quantum Mechanics by Werner Heisenberg (yes- that Heisenberg) in 1933. The seven pieces are all the ways 3 or 4 cubes can be joined, such that each piece has at least one inside corner. Amazingly there are 240 ways to make the larger cube from these 7 pieces- still not that easy!
Sphere Sticks Geometric Puzzle
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Sphere Sticks Puzzle: 30 identical wood pieces, each with two notches as shown, can create 12 interlocking pentagons in a perfect symmetry- look carefully and you can see that each rod is in an identical configuration with the 4 others that connect with it. Precision cut notches on the rods allow them to interlock with elastic tension such that vector sum of the 4 forces sum to zero in this tensegrity type equilibrium. The dodecahedron, with its 30 edges and 12 sides, is the basis of this puzzle sculpture.
Penrose Aperiodic Rhombs
A nice version of Penrose Tilings is available here:
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Penrose Aperiodic Rhombs: a famous aperiodic tiling with just two shapes- a pair of rhombuses with equal sides, but with the ratio of their areas made to equal the golden ratio. Note that although the starting pattern of 10 tiles is symmetrical, adding any further tiles breaks the symmetry, as highlighted by the path of the double curves. Sir Roger Penrose- who just won the Nobel prize in physics for his contributions to General Relativity- also discovered tessellations (tilings) that are aperiodic even though the two tile types are regularly shaped polygons. If one tries to shift a part of a Penrose tiling, the shifted part will not align or match up with any other part of the same tiling- all the way out to infinity! In this construction, single and double line patterns must align such that the tiles can only connect in specific ways to ensure the non-repetitive nature of the Penrose tiling structure. Shown here is one way these two tile types will fill the plane.
Wikipedia has the details on Penrose Tilings and their inventor Sir Roger Penrose (Recently won Nobel Prize!)
Ambiguous Object Illusion Set
This wonderful and afffordabe set includes four illusion objects and a mirror:
From curiositybox.com: BUY NOW: Inq's Ambiguous Illusion Kit (sold out)
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Ambiguous Object Illusion Set: This kit comes with four objects (three shown here) invented by mathematician Kokichi Sugihara of Meiji University in Japan. Polygons appear as circles in a mirror and vice versa, and the famous “stubborn arrow” that will only point to the right (or, in a mirror, to the left). I like how the base is also an ambiguous pentagon/circle, which like all these objects, is a result of a clever combination of reflection, perspective, and viewing angle. Thanks to the Vsauce team for producing this kit!
The Holoscope : Icosahedron
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The artwork of Gary Allison: BUY NOW Holoscopeworld.com
Look through other holoscopes in my collection here: Holoscope Kaleidoscopes
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The Holoscope Icosahedron: the intricate beauty of multiple internal reflections from 20 triangular mirrors in the shape of this famous platonic solid. The interior is viewed from one corner and illuminated by light entering from glass spheres placed at all of the other 11 vertices. A type of kaleidoscope based on mirrored polyhedra by artist Gary Allison, (swipe to see the dodecahedron and cube) and future posts will include tetrahedron and octahedron 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.
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 (New box will ship soon- get a great deal now)
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Trammel of Archimedes
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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.
Satisfying Hexagons
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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!
Mirror Anamorphic Lenticular Cup & Saucer
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See all the amazing illusions and art avaialble from Luycho: Luycho | A New world on Mirrors
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Mirror Anamorphic Lenticular Cup & Saucer: a toucan 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 (turning the plate 180 degrees trades images). Art meets math and physics!
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
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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.
Scutoids
This set of 3D printed scutoids available here:
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Scutoids: a recently recognized form of geometric solids discovered in 2018. Scutoids have a different polygon on each end, and when packed together maximize stability and minimize energy when forming a boundary layer- such as the membranes around organs in living tissue. These 5-6 scutoids have pentagons on one end and hexagons on the other. Discovered by a collaboration of biologists and mathematicians in 2018, this set is sold by Recep Mutlu of 3DPrintBase.
Uphill Roller
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Uphill Roller: a double cone (like two funnels connect by their tops) will roll up a set of inclined rails. Although the bi-cone rolls toward the higher end, its center of mass descends due to the geometry of the rails. This curious construction was first published in 1694 by the noted surveyor William Leybourn to promote “recreation of diverse kinds” towards the “sublime sciences”. Physics fun from three centuries ago!
Cone of Apollonius
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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.
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
Note: this site contains affiliate links for which I may be compensated
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.
Sphere and other Orbiforms
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Sphere and other Orbiforms: pi day special post- volumes of constant width made from solid brass. These shapes have constant diameter no matter their orientation and will roll like spheres between two planes- note how the acrylic plate stays parallel to the table as the sphere and other orbiforms roll underneath. The first orbiform is based on the Reuleaux triangle and the second on a Reuleaux pentagon. Fun pi fact- the perimeter of any shape of constant width is alway equal to the diameter(width) multiplied by pi: P=πd.
Pocket Scintillator Kinetic Art
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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.
Reuleaux Rotor
This toy is availble from Amazon Japan and will ship to the US:
From Amazon.jp: BUY NOW: Reuleaux Rotor Wodden Toy
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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!