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Trammel of Archimedes
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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.
From Amazon: BUY NOW Skew Dice
Skew Dice: these unusually shaped dice are completely fair- roll them and the probability of outcomes are identical to a standard set of dice! The odd shapes are a special type of polyhedra called asymmetric trigonal trapezohedra which come in right and left handed versions- this set has one of each (mirror images of each other). What allows this shape to be fair like a cube has to do with the property of being isohedral, where each face of an object will map onto all other faces via a symmetry of the object. Manufactured by The Dice Lab.
The Soma Cube is available in a variety of materials and colors:
From Amazon: BUY NOW: Soma Cube
From Etsy: BUY NOW: Soma Cube
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!
This and other beautiful and well made puzzles are available on Etsy:
From Etsy: BUY NOW 10 Hex Puzzle
Two great resources about these polyhexs: polyform puzzler page and puzzleworld page
10 Hex Puzzle: this puzzle is comprised of pieces which are the set of all ways three and four hexagons can be joined with a common edge. There are 3 trihexs and 7 possible tetrahexs, and similar to pentominoes, these 10 polyhexs can assemble into a large hexagon. Amazingly there are exactly 12,290 solutions to this puzzle- but it’s still a challenge to find just one!
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.
The set I used for this video is called Pocket Katamino and is available here
From Amazon: BUY NOW Pentominoes
3D Pentominoes: the 12 possible arrangements of five identical squares, joined edge to edge, form the set of all pentominoes. Since 12x5=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). This set of colorful pentominoes is made so that the height of each piece is the same as the width of the constituent squares, such that 3D constructions can be made. Since 3x4x5=60 one can build a box with these dimensions (amazingly, 3940 ways to do this- but again, finding one is still a fun challenge).
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From Art of Play: BUY NOW: Dymaxion Folding Globe
Dymaxion Map: today some math fun with this unique mapping of the Earth where the globe is projected onto an icosahedron and then unfolded onto two dimensions. Invented by the famous architect R. Buckminster Fuller, the Dymaxion projection map is designed such that it does not have a “right way up” and showing the continents as “one island Earth”. This mapping also produces less distortion of relative areas and shapes- note here that Greenland looks, correctly, much smaller than Africa- unlike what is seen on many world maps where they look the same size. This version, designed by Brendan Ravenhill, uses flat magnets to allow a very satisfying transformation between the flat 2D net and the 3D icosahedron “globe”.
This sculpture available as a 3D print:
From ShapeWays: BUY NOW: Square Circle Illusion
See other amazing geometric illusions here: Ambiguous Objects
Squaring Circles: from one particular point of view these wireframe sculptures looks like a circles/squares, from another it’s a square/circle! From other viewing angles one can see that the underlying curves are four identical segments of a parabola conjoined. Further examples of how a single perspective can be misleading! Math sculptures available as a 3D print by Matt Enlow.
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).
Galton Board version available here:
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The Random Walker: second model of two Galton Boards designed and produced by IFA.com- 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.
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 ?
A nice version of this tensegrity icosohedron is sold as a toy for tiny tots:
From Amazon: BUY NOW Tensegrity Toy
I constructed this version by referring to the images and descriptions of tensegity on Wikipedia
Tension Integrity Icosohedron: Six brass struts float isolated from each other but held in a stable configuration by a net of 24 connecting cables. I made this sculpture using hollow brass tubes and weaving through them a single strand of fishing line, which is connected after passing through each tube exactly four times. This configuration of three sets of parallel struts forms a Jessen’s icosahedron under tension, and was invented by the famous architect Buckminster Fuller in 1949.
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.
Well engineered brass spinning toys by SiriusEnigmas:
From Etsy: BUY NOW: The iTOP
From Etsy: BUY NOW: The PhiTOP
From Etsy: BUY NOW: The eTOP
From Etsy: BUY NOW: The PiTOP
The iTOP: inverting spinning disk- the equilibrium state for a spinning thing is often different from that of the same object when stationary. When spun, the iTOP almost instantly inverts to raise its center of mass (shown in slow motion because it happens so fast). However, when the rotation speed decreases to a certain rate the system becomes unstable (shown again in slow motion) and flips again before going into a rolling/spinning motion like a coin. This top completes the set of four spin tops by astrophysicist Kenneth Brecher, all made of polished brass and themed on a mathematical constant. Swipe to see a demonstration of each: iTOP (square-root of -1), PhiTOP (golden ratio, φ), eTOP (base of the natural log), and the PiTOP (C/D of a circle, π).
Well engineered brass spinning toys by SiriusEnigmas
From Etsy: BUY NOW: The PiTOP
From Etsy: BUY NOW: The PhiTOP
The PiTOP: this beautiful brass cylinder has a radius of 1 inch, a height of 1/π inches, and displays the first 109 digits of π on its face. Spin this disk (best with sound on) and it will demonstrate some very interesting physics involving energy transfer and conservation of angular momentum. The edges of the cylinder are rounded and engineered to exhibit an optimum motion of a “spolling” coin, a motion that combines spinning and rolling (closeup shown in 240fps). As the disk’s angle of inclination decreases the speed of the rolling increases dramatically until the contact point with the mirror is moving in excess of 200mph. From the mind of physicist Ken Brecher, inventor of the PhiTOP (swipe for video). Note also that with the specified height, that the volume of this cylinder is exactly 1 cubic inch!
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.
Message Luycho on Instagram about this design. Other designs can be seen here:
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!