See the Sun (Chromatically Abberated) Part II

I Want to See the Sun (Chromatically Abberated) Part II 

There is more to seeing than what meets the eyeball.

N. R. Hanson

Speaking of reducing chromatic abberation (in my last post) there is a device that actually increases it...on purpose! It's called a prism. We'll deal with sunlight, rather than the sun itself for now.

Here's a photo of an incredibly awesome prism that really separates the wavelengths of light really well. The craftsman that cut and wet sanded it is an incredible optician: me!

If the glass were perfectly, magically clear it wouldn't work as a prism. The differences in color absorption due to the refractive index, which in turn disperse the colors (breaks white light into a rainbow of its constituent colors). The speed of light changes in different media (air, water, glass) This is a dispersive prism.

If the surfaces are nicely polished and you blast a laser through it, it can act as a simple reflective prism. Lasers are a single wavelength and thus cannot be broken up into rainbows. They are one color only. 

Here's my same prism with a laser blasting through it. No dispersion-no rainbow. It does refract-changes directions at an angle. This is mathematically referred to using Snell's Law and Ray Tracing (computing the angles the laser will exit a prism, or a bunch of prisms and mirrors and lasers in a huge system like a knowing where the ball will go in a pinball machine before you fire it).

So pretty, but useless? Not by a longshot! 

In addition to aiming lasers (boring) you can use knowledge of dispersive refractive indices and wavelengths of light to investigate chemical properties of objects (and stars) you can see but not touch!

Above is a photo I took of a diffraction grating. It's a tiny, cheap $2 piece of plastic that disperses light. The white source light is at the top. The grating has zillions of tiny grooves that act like prisms. 

What is similar to that? A compact disk, which has zillions of pits in it that do the same thing. That's why you see a rainbow on the bottom of music CDs. So I took a CD and put it in a box with a tiny slit to let on light:

This my homemade spectroscope's readout from a fluorescent light bulb. Notice how there are lots of blank spaces in between the color lines? Newer light bulbs are more like the laser than sunlight: way fewer wavelengths to disperse. Here's the cooler part: see the green line? That corresponds to the element Mercury. We now have proven that this fluorescent light bulb contains Mercury in it! We didn't even have to cut it open or touch it at all. 

Astronomers point spectroscopes at stars to learn what elements are burning within them. Same exact principle.

Building a CD Spectroscope is easy. Here's a link to a nice set of instructions: https://www.cs.cmu.edu/~zhuxj/astro/html/spectrometer.html

Is there a way to take what we learned from the last post (PVC Telescope) and use it in spectroscopy? Yes, you can make a Slitless Spectrograph:

However, if you do the Ray Tracing in real life its not a straight line like my drawing above, it's like a downward curved line which is annoying to put into a box and more annoying to hook to a telescope which was my original purpose.

Anyway, I had so much fun with my homemade toys that I ordered a fancy store-bought Spectroscope from Amazon for all of $9 including postage. 

The readout was identical to the ones i made, except that it has a scale to show you the actual wavelengths (in nanometers). Fancy!

On the right you can see the white nanometers scale above the colors. This is pretty even with no black missing lines, so this was probably sunlight on a nice day with no clouds. 

Man has closed himself up till he sees all things

 through the narrow chinks of his cavern.

William Blake

The only difference between my free CD spectroscope, my $2 diffraction grating Spectroscope and my $9 spectroscope is that the $9 one had a nanometer scale. Same readout on all. 

Now, is there a device that melds spectroscopes with prisms? Yes. They're called prism spectrographs. They also make use of Snell's Law and Ray Tracing to get light to pass through a few (usually three) prisms.

In the above pic notice the trapezoid formed by 3 prisms smooshed together. The scribbling is me feebly trying to start figuring out what shape prisms I needed to grind. I wrote "Snell's Law" but it's just part of calculating total internal reflection. I wisely decided manual Ray Tracing would be easier: shine a laser through the prisms and see where it goes, which is what the red laser photo at the beginning of this post shows...so finally, for the first time in human history lasers actually did something useful: lasers kept me from having to calculate inverse trigonomic functions for the angles of incidence. 

As an aside, in not bothering with Snell's Law (named after a guy named Snellius but discovered by Ibn Sahl in the 900s) and playing with Ray Tracing I can also find and deal with any bits of light that doesn't confirm to Snell's Law. Specifically: Newton Rings!

Newton Rings are those weird rainbows that occur when you lay to almost flat pieces of glass on top of each other. They were of course discovered by one of my heroes...Robert Hooke. Isaac Newton played with them over half a century after Hooke wrote about them, so that's where the name comes from. That was almost exactly 300 years ago. The rainbows come from diffraction, not of the glass but because of tiny air pockets between the glass. Shown are two microscope slides I randomly selected: Rings! Actually these look more like wavy lines, but as I squeeze the lines move and change. Interference also plays a role: like throwing two rocks into a pond, the waves from each will eventually touch and mess with the patterns of each alone.

An even weirder aside: Hooke was the first to build a Gregorian Reflector Telescope. It was designed (by James Gregory) before another guy built a reflector telescope, but wasn't made until a little after the other guy did, which is why most reflector telescopes are now called Newtonian Reflectors. Yep, good old Issac cheated Hooke yet again! Gregorian telescopes still mostly survive in very nice, easy to design and build Schmidt-Cassegrain telescopes. Isaac Newton did invent calculus all by himself, or at least he claimed to have done so a few years after Gottfried Leibniz published a paper on the new math of calculus he (Leibniz) invented. In fact we still use Leibniz notations to this day!

Newton is often quoted, "If I have seen further it was because I was standing on the shoulders of giants." This would seem to be a fair acknowlegement and reconciliation-except that he ripped that quote off from Bernardus Carnotensis. Newton: pickpocket of science.

Is that all? Not by a long shot! In addition to identifying burning elements in laboratories and in stars you can do something else with a spectroscope. Calculate Radial Velocity! If an object space shows a slight increase in red wavelengths it is receding away from us, blue means it's floating towards us! Neat. It is the color wavelength version of The Doppler Effect for sound waves.  A passing police car's siren is high pitched when it's coming at you and then goes to a lower pitch (at least it seems to for you) as it passes.

As the car approaches and passes you standing still:
eeeeeeeeee-aaaaaaahhhh. 

To the police officer in the car the siren doesn't change pitch: eeeeeeeeeeeeeeeeeeeeeee.

Shhh...I'm analyzing the sunlight. Ten nanomices and rising-meow!

PVC Telescope: A Modular Optics Lab in a Tube!

PVC Telescope: A Modular Optics Lab in a Tube!

Reflector telescopes use mirrors, refractors use lenses. To make a reflector you precision grind a mirror, for a refractor you need to play with at least two lenses-more of you want color correcting and distortion minimizing qualities.

It's quite simple really. Light gets focused between two lenses: the main objective lens at the end of the tube that gets pointed into the sky and the eyepiece. However different colors of light are different wavelengths. Different wavelengths focus at different places. 

This makes your telescope into a prism: colorfully blurry!

When a nice focused green wavelengths falls perfectly on the eyepiece that means the red and blue waves are a little too in front of and too past the eyepiece to be on focus. This problem is called chromatic abberation and some really expensive refractor telescopes have it. It's something that you can: get used to; hate and buy a reflector (mirror) telescope; or pay even more money to correct. Adding additional lenses can bring the red and blue to the same focus point, this is called an achromatic len(s).

Now, to be clear "blurry" isn't exactly accurate as a description of chromatic abberation. The views is very crisp, but tripled slightly: you'd see the moon with a red moon slightly misaligned with a blue moon slightly misaligned with a yellow moon. All very crisp but distracting.

Many telescopes that are refractors (lenses not mirrors) show this tripled misalignment just along the edges of bright objects as color fringes and flares. Even really, really, really expensive refractors can have a little color fringing from chromatic abberation.

If you want to see chromatic abberation on your own just aim a pair of binoculars at an electrical power line hanging from a telephone pole. Of you hey just the line in focus with a bright, clear sky behind it you'll notice yellow and purple highlights along the edges of the line. Shiny highlights on the line may also have weird color aberrations. The better the optics, the less color fringing.

The glass of the lenses absorbs and passes light waves through at different rates. Reflector telescopes (mirror) bounce light off a mirror-the mirror reflects the light, but doesn't absorbs it. The light bounces and isn't passing through it so reflector telescopes don't have problems with chromatic abberation. 

I wanted to build a refractor of my own design that allowed me to swap different lenses in and out to experiment with correcting various flaws including chromatic abberation. A modular optics laboratory in a tube! I decided to use PVC and headrd to Home Depot with calipers, pad, pencil and a tape measure.

But first I needed a nice lens. I bought a cheap one for $7 on Amazon. It was an Ajax Scientific Polished Glass Bi-Convex Spherical Lens, 100mm Diameter 500mm Focal Length. Nice lens!

1x 3" PVC flat top cap (not the domed/rounded bubble top)

3x 3" PVC 3x3 repair couplings (that are smooth inside, not with an internal ridge)

1x 3" PVC 3"x2 foot foam core pipe

1x 4" PVC 4"x2 foot foam core pipe

A big objective lens

Wood saw to shorten both pipes (hack saws don't cut straight with PVC easily)

Telescope eyepiece or bi-convex lens or eyepiece from binoculars

Black spray paint

A big ring cutter drill bit to cut a hole for eyepiece or lens (.965", or 1.25", or 2" or whatever your focuser needs if you're using a focuser instead of just plunking an eyepiece into the hole in the end cap).

At Home Depot I bought a 4" PVC white pipe and painted the inside black to reduce glare and increase contrast. One insert (repair coupling) with hole in the center pushed in followed by this lens followed by another insert. These trap the lens in the tube.

Another insert with hole at other end of pipe allows a 3" PVC pipe to slide in and out to adjust focus. At the end of the 3" pipe pit a 3" end cap with a hole in it to hold an eyepiece of to fit a telescope rack focuser.

Extend the tubes for close focus like neighbor's house, push them in (shorten) for father focus like the sky, moon and stars. All with so much chromatic abberation they looked like a psychodelic Andy Warhol print! My first view was of a street light a couple blocks away. The abberation was so bad it looked like a bunch of multicolored poles barely touching, not merely "misaligned" slightly. 

Medium distance focus is about 20" from lens to eyepiece (focal length is 500mm f/5). So you'll have to cut the tubes to short lengths. This shows the effects of differing focal lengths on telescope designs: magnification (greater or less zoom with the same eyepiece), brightness (f-stop/speed) and field of view (wide angle).

The magnification (zoom-in) of a telescope equals its focal length divided by the focal length of whatever eyepiece you have in it. Every time you double the magnification you loselose 50% of the sharpness of focus and 25% of the brightness! 

If you're looking at something bright like a planet or the moon that's fine-but for faint nebulae and galaxies it might make you unable to even find your target in the sky. 

Useful magnification is twice the diameter of the objective (lens or mirror) in millimeters. 50mm lens x 2 = 100x top magnification.

1000mm focal length ÷ 100x = 10mm eyepiece needed.

Remember though: my design slides in and out so I can change my focal length slightly, but not my objective diameter (unless I swap out the front lens). I can change my magnification by changing eyepieces.

My telescope has a 100mm diameter objective lens. Twice 100mm equals 200x maximum magnification. 

Its 500mm focal length ÷ 200x desired magnification = 2.5mm eyepiece needed. Those are expensive, but I've got a wonderful 3mm eyepiece that gets me close enough. However, in my larger telescope that same eyepiece will give me 400x magnification! Everything effects everything else in the optical chain.

Too close...zoom out or claws out!

Once you've played with focal length and eyepieces you can add a concave lens in between to try and correct for chromatic aberration, etc. Alternatively you can use a double or bi-concave lens instead of an eyepiece. This is really a telescope laboratory in a conveniently simple modular package!

So less than ten bucks for the lens and about thirty-five for the pvc if you don't have it around the house compared to big bucks for a 4" refractor astrograph telescope (plus you'll have to scrounge up a focuser and maybe some other lenses to experiment with correction).

It's quite a large and heavy beast! 

Here it is mounted on top of a rather long, metal, 1970s Tasco. PVC is incredibly heavy, but if you take care and balance it well it moves easily. Even on a terrible mount. Tasco had the worst mounts in the business, but an even bigger tragedy were their eyepieces. They were the small 0.965" size and atrocious! 

I bought an adapter for $9 on Amazon that is a 90° elbow: one end fits into the 0.965" opening in the telescope; the other side has a 1.25" hole that accepts professional 1.25" eyepieces (but not 2" Diameter ones). If you have an old Tasco buy the adapter and some cheap 1.25" eyepieces and you'll be blown away! A 20mm, 12mm and 9mm are a fine set for most Tascos. The mount will still be criminally terrible: jerky, wobbly, prone to falling, etc.

I also took some old slide and film projector lenses and converted them to use as eyepieces. They have varying outside diameters so some had to be spun up on a metal lathe and smallerized, others were too narrow and needed tubing or duct tape wrapped around them for a snug fit.

You can find old lenses like this cheap or free all over the place. Even if you're using a store bought telescope it's neat to increase your eyepiece collection for free and have fun doing it!

At dead center of the photo above you can see the 90° adapter on the Tasco and upper right is the eyepiece simply stuck into the end of my PVC telescope.

Woah, the colors! Chromatic-Cat says meow!

See The Sun Part I

I Want To See The Sun Part I

Much like my other series of posts about seeing atomic particles, this is the first in a sporadic series of posts about using different devices to "see" the sun. From a simple radio telescope to solar viewing filters to a purpose-made solar telescope I'm going to do what you were always warned not to do: stare at the sun! I'll probably throw in some info about my homemade UV and infrared goggles too.

So, what do you need to make a radio telescope? An old satellite TV dish, 8 AA batteries with holder, an rf choke, a satellite finder, and some other odds and ends like solder, tape, a tripod, coax cable and coax terminators. Less than twenty dollars worth of stuff from Radio Shack (and your neighbor's garbage).

Simple instructions from the NRAO (National Radio Astronomy Observatory) are available here: 

http://www.aoc.nrao.edu/epo/teachers/ittybitty/procedure.html

Big caveat: the 0.1Mhz rf come on all the online plans don't seem to exist. Use any smallish RF choke. They may have meant milli or microHenrys (mH) but not Megahertz (Mhz). It's an honest mistake considering Mr Hertz is the guy that discovered radio waves. He used a spark gapped radio antenna, like a bug zapper for radio waves! So many of the things I experiment with are like bug zappers. Alpha particle on my spark detector-zap! Gamma or X-ray on a Geiger tube: zap! On or off electrically. Zap or no zap. 

With this radio telescope we're dealing with something more subtle: quantity. Not just yes or no, but how much? One decibel or two? A flat or peaked curve? Twenty MHz (yes we actually are taking Hertz now) means a solar flare. Ten to forty MHz and you could be looking at Jupiter, but Jupiter's magnetic storms are best monitored between eighteen and twenty-eight MHz. A wide swath between forty and eighty MHz with a plan around sixty MHz? That's Saturn my friend! Two and a half GHz-that's my Hot Pockets in the microwave oven. Of course you add voltage to the mix when interpreting too: frequency, an amplification, amplitude,  voltages, standing wave ratio...all sorts of things used in everyday devices like stereos, phones, cb radios, etc. It's all just electromagnetic waves. 

Setup is to aim at blue sky, dial decibel knob just barely to zero. Point at sun and itll6read around 6. How to aim at sun? Get the shadow of the LMB (pointy part) just barely onto the disk. Trace shadow on dish with marker once needle jumps up:

I ditched the dangerously unbalanced mounting bracket and spun the dish upside-down. There was a hole there that allowed the standard camera mounting screw to fit through, and as luck would have it the nuts from the dish bracket fit the screw. Mounting was easy!

I'm pondering getting a longer coax cable to attenuate the signal and help the RF smooth noise away. It might be possible to coil it on the tripod to create a balun. A balun is just a coil that helps a system cross from a balanced state to an unbalanced on (such as coax cabling).

Update: I did rearrange everything farther from the dish and coiled up a make-shift balun.

The red plastic cup holds the 8 AA battery pack. The second output from the LNB (low noise block converter) is capped off with a gold-plated coax terminator. The LNB is the brains of the dish which is basically a radio received. The actual dish is just a waveguide-badically an receiver in your car, only this received and translates microwaves from satellites instead of AM/FM waves. Simple!

So what am I looking at? Radio waves from our Sun. It turns out that the huge nuclear inferno above our heads melting 600 million tons of hydrogen into helium every second makes quite a lot of radiowaves! Here's a nice video of me aiming at the Sun and then slightly away a few times.

If I tame all the RF interference (probably by just moving the battery pack away) and plug this into my oscilloscope it should be easy to detect other things: like people walking past the dish or cars driving by. According to the NRAO a cellphone signal is a billion times more powerful than the cosmic rays detected by larger radio telescopes, so a radio-people-detector is very plausible (I've seen it done actually) even though this design is referred to as an Itty Bitty Radio Telescope.

My set up procedure now is to point to clear sky and dial up the gain on the meter until it almost squeals. Then I point out at the sun. If I really crank it up I can tell when the telescope scans past the sun, to the quieter open sky and then much quieter on the neighbor's tall chimney.

With the tripod locked the sun moves out of the dish's narrow focus rather quickly. The moon would do the same as it slides into the path of the sun's light the moon will get brighter in the sky-and on the radio telescope's meter. Think about it, when the moon is dark its surface is -243° Fahrenheit but when the sunlight hits it the surface rapidly heat up to a little over +250° Fahrenheit! Wow! It happens whether we can see the moon or not in the sky, on bright days you could search for the moon in a blue sky. I found it:

I'll revisit this with the oscilloscope data at some point, but lugging this weird device around my neighborhood during the day is embarrassing enough without an additional wheeled cart hauling crazy looking electrical boxes and wires. 

It will give me something more productive to at oscilloscope practice than just trying to write my name with it...cause that's what oscilloscopes are for right? M I K E!

Itty Bitty Radio Telescope? Looks more like an Itty Bitty Kitty Detector to me! I'll just mash my face all over it to be sure. Can it see me? Does it know it's mine now? Meow!

See Atomic Particles With Your Own Eyes Huh, Part 3: Unleashing the fury of the alpha particle spark detector!

So You Wanna See Atomic Particles With Your Own Eyes Huh, Part 3: Unleashing the fury of the alpha particle spark detector!

When working with high voltage make sure to start by lighting a candle to St. Artemy of Verkola!    -Michael Logusz

Unleash the fury!!! My new toy: an alpha particle spark detector with an 8000 volt negatively charged ungrounded plate and extremely thin wires that are grounded. It's like a bug zapper for radioactive particles!

So far I've used: Geiger Counters, nuclear cloud chambers and a spinthariscope/radioscope to detect,  and visually see the paths various radioactive particles (alpha, beta, gamma and x-rays) leave in supercooled alcohol vapor and I've seen the flashes of light their impacts cause when smashing into a thin coating of zinc sulfide.

When an alpha particle passes in-between the wire and the plate of this alpha particle detector it ionizes the air in between: ZAP! The disk I'm holding with tweezers is 0.7 microcuries of the radioisotope Americium-241.

Every ZAP causes an avalanche: electrons start smashing there way into the electromagnetic field while ionizing the air gap between the plate and wire creating a plasma. The dielectric breakdown strength is exceeded by the electrical field's power. This rips a conductive path in the air. It's what causes lightening bolts to get all spikey, inside a sealed Geiger Counter tube is called the gas multiplication effect, but the result is the same: ZAP!

I bought this simple, but amazing device from Scientifics Direct. The first arrived with a blown out power supply. They rushed me out a replacement that works fantastically as you can tell from the videos.

In the diagram above to the upper right is an idea: layer many of these in a stack and that would give you the speed and direction of the particle!

My visceral "need to see" is met with these devices, unlike understanding through theory via mathematical formulae-which can have its own, equally powerful eureka moments. I still remember seeing Saturn for the first time at 2:22am with my telescope set up in the middle of a freezing Michigan road. Simple seeing: nowadays astronomers use telescopes that measure rather than simply look and see. In contrast, my activities are utterly primitive, but they're really fun!

This video shows a larger 0.9 microcurie source that is better insulated with protective plating: it will degrade slower, but has slightly fewer particles zinging off of it. Still plenty of fun! And all it took was 8000 volts of electricity that was negative (below the voltage of the ground point, in this case the wires).

High Voltage / Highly Weird

High voltage electricity (even without ionizing radiation) is fascinating. So are the electromagnetic fields that high voltages create. Many household devices feature transformers.

A transformer is basically two diffetent coils of wire that don't touch. The first coil gets powered by the electricity from the wall outlet plug. The electricity flowing through the coil creates an electromagnetic field. This field radiates outward and creates electricity in the nearby (but not touching) secondary coil.

Weird! But it gets weirder: if the second coil has more loops of wire it will receive/create more electricity than was pumped into the first coil from the wall outlet! That's a step up transformer. Less coils mean lower power is magically captured: a step-down transformer.

If both coils have the same amount of loops, the same amount of electricity jumps to the second coil as was pumped into the first coil. This of called an isolating transformer: all it does is isolated the wall outlet power from the device since at no time do the coils ever physically touch! Since all transformers isolated, only the ones that don't step up or down are called isolating transformers.

Here's a transformer I just got that will step up 120 volt wall outlet electricity to 7,500 volts. At the bottom left is a tiny first (primary) coil. It is not attached in any way to the rest of the transformer. The field of creates bleeds over onto the huge coil to the right: stepping up the voltage.

I was given this transformer for free yesterday, along with a bunch of other high voltage toys. I would have made an alpha spark detector with it, but since I already have one maybe this will end up as a Tesla Coil or Jacob's Ladder or who knows what.

Whatever I make will probably be a visceral seeing device, as opposed to a subtle sensing one. First I look, then I go back and visit the theory. My first love is seeing but I always (eventually) get to the theory.

Forget seeing particles, I'm working on a new string theory: I think this string might taste good! Meow.

The Power of Cold (and Hot)

The Power of Cold (and Hot)

What we have here is video of my new Stirling Engine. As shown it is sitting on top of a hot glass of water. This heats the bottom plate. Room temperature air (and sometimes an ice cube) cool the top. This creates a temperature differential which starts the engine spinning.

This is not a steam engine! Hot air expands and pushed the piston to the cold side. The hot air leaks past the piston to the cold side too which makes the gas contract, pulling the piston back down. It's a sealed system so the now cold air heats again and the piston goes up and down over and over again. It's seems very simple, yet probably is the most complex thing I've had on my blog! 

So, if you supply heat and cold to the top and bottom it outputs power/work. With hot water out of a coffee maker this particular engine ran ran for over an hour at about 200 rpm. After it started slowing down I added an ice cube to the top plate and it sped back up for another half hour or so.


But, of you supply power/work with an electric motor it outputs cold/heat. Tiny versions of this are actually used to cool microchips in imaging and night vision systems. Although a similar invention called the Peltier Cooler is rapidly replacing it. Peltier Coolers are solid state devices with heat sinks that transfer heat from one side to the other using electricity (power/work).

Another use for these subtle, quite, simple engines is in submarines. My other blog is the devoted to my model submarines. I love subs! 

(http://mikelogusz.blogspot.com) 

Anyway,  stealth and air are a concern for submarines. Recently Saab (under the name Kockums Naval) debuted a Stirling Engine for sub propulsion: quite and no need for air/diesel/nuclear replenishment. Russia's attack on nearby Ukraine had seen more focus on the Swedish manufacturer's efforts on the realm of quieter than stealth subs powered by these AIP (air independent propulsion) systems. No more surfacing to get air for the electric and diesel systems of old: the 1816 brain child of the Reverend Stirling has come of age big time. With the renewal of Cold War antagonisms we'll see cutting edge efforts to incorporate this old technology anew.

Segway inventor Dan Kaman is researching then for augmenting our power grid, solar power companies are researching them for the same reasons. Kaman has come up with a Stirling Engine called the Beacon 10 which can generate electricity (power/work) from natural gas for a home or can be used in the reverse to heat water (for a laundromat for example).

You'll notice a clacking noise in my Stirling Engine: it has metal on metal connecting points with no bearings. A little bit of graphite powder lubricant or a simple set of roller bearings would make this thing almost completely silent. There is a little slop in the system that can be taken out by tightening the length of the piston arms. That alone would probably diminish the slight noise by about 90%.

Stealth beyond stealth.

A hot mess on the bottom pushes your eye up to the cool cat on top, then back down again. Thank goodness for moody lighting and PhotoShop! Meow.

Flexagon, Folding Paper Machines

Flexagon, Folding Paper Machines

This is my flexagon. It is a tetra-tetra flexagon. Or has four faces and four sides. By folding, and sometimes pinching and flexing, these little paper devices you can check change numbers or colors or patterns. Numbers or colors or patterns well up from seemingly flat dimensions in an (almost) never ending succession like a mobius-strip come alive! Although instead of creating a 3D shape from a flat piece of paper and then making it 1D this mobius-strip "snake", the flexagon takes a flat piece of paper and cycles of into the realm of 3D momentarily and then end with a 1D/2D changed first world.

Each flex, pinch, fold or flip can change the image, pattern or number by a little or a lot. Flip, meow, flip!


In 1939 Arthur Stone, Bryant Tuckerman, Richard Feynman and John Tukey published a paper of their mathematical findings after Arthur Stone discovered the hexa-flexagon. Flexagons can have as few as three sides up to an infinite number: whatever your brain can come up with, provided you have a big enough  piece of paper.

Here is my humble collection of flexagons. There are various shapes, which necessitate different maneuvers-not just flipping like the first video.

Pinch, flex, pinch, flex...

This last hexa-hexa-flexagon has six sides and six faces, so many in fact that I stopped flexing it at just the 5th face/side...I just got lost between dimensions and couldn't find the sixth.

I'm stuck in dimensions too-meow!

Jacob's Ladder Toy

Something very similar to a paper flexagon is this Jacob's Ladder Toy I made from some La Florentine candy boxes that my boss gave me.

There are tons of great instructions online on how to make these. My two tips: don't make the ribbon attachments too tight; and use heavy boxes. I ate the candy, so my boxes are too light and don't flip as fast as they could.

Although it's "automatic" and quite impressive looking in action, the Jacob's Ladder Toy is much less sophisticated than a flexagon. Add we've seen previously, a flexagon can have many phases it can cycle through. My Jacob's Ladder Toy can only flip the boxes upside down or right-side-up.

I'll probably throw some pennies into the boxes to weight them better.