On Not Proving The Twin Prime Conjecture With AutoCAD

November 3, 2012 by Brian Benchoff 28 Comments

As an HVAC engineer by trade, [Carlos Paris] spends a lot of time in AutoCAD designing all those hidden pipes, tubes, and ducts hidden in a building’s rafters. One day, [Carlos] read of an open contest – the prize was over a million dollars – to generate a prime number with a billion digits. [Carlos] misheard this as, ‘a prime number greater than one billion’ and of course said this was a trivially easy task and opened up his favorite tool – AutoCAD – in an effort to discover the largest prime ever. [Carlos] never generated a remarkably large prime, but he did come up with a very, very cool visualization of prime numbers on a number line, as well as a great justification of the twin prime conjecture, a problem in mathematics that has remained unsolved for several generations.

[Carlos] started his investigations into the properties of prime numbers by drawing a series of circles on a number line in AutoCAD. These circles were of diameters of all the integers, and going down the number line, these circles started to have an interesting, chaotic pattern (see above picture). [Carlos] found that whenever two circles intersected, that position was a prime number. It’s really nothing more than a Sieve of Eratosthenes, but it’s a very cool-looking visualization nonetheless.

Looking deeper into his graph, [Carlos] discovered there were certain primes that had another prime number just two places down the number line. For example, the numbers 3 and 5, 29 and 31, and 41,and 43 are twin primes, as the difference between the primes is only 2. The idea there are infinitely many twin primes is a famous unsolved problem in mathematics – it’s obvious it must be true, but no mathematician has yet come up with a proof of this conjecture.

[Carlos] looked at his number line and simplified it to a generic prime number. By taking a generic number line and overlaying the multiples of other prime numbers on this graph, [Carlos] had a very, very clever way of understanding exactly how twin primes come into existence.

In the end, [Carlos] is no closer to proving the twin prime conjecture than anyone else. We’ve got to hand it to him, though, for nerding out with an engineer’s favorite tool – AutoCAD – and managing to derive some fairly obscure mathematics on his own.

After the break you can see [Carlos]’s videos describing the though process that went into his creation. Very, very cool work.

Continue reading “On Not Proving The Twin Prime Conjecture With AutoCAD” →

Pull-string Most Useless Machine

November 2, 2012 by Mike Szczys 18 Comments

The mechanical simplicity of this pull-string controlled most useless machine is delightful. You can see the metal gripper which is reaching up to tug on a light-fixture-style pull chain. This is how it turns itself off after you’ve pulled the string to power it up.

The device is [Alex555’s] entry in the 7400 Logic competition. We do hope that he ends up posting a schematic because we’d love to see the gritty details of how it works. After the break you can watch two doors open, allowing the arm to raise up and the gripper to grab the chain. This takes just four servo motors, which are controlled by the signal from a 555 timer and some accompanying hardware.

Apparently the chain is a fake, as the servos didn’t provide enough force to actuate that type of switch. It’s not a surprise as those pull chains do require quite a tug. An optical sensor was used to trigger the movement when your hand reaches for the chain.

Continue reading “Pull-string Most Useless Machine” →

Computer Tracking Of Billiard Balls

October 31, 2012 by Brian Benchoff 15 Comments

The folks at the London-based startup GoCardless have a pool table at their office. Being the techies they are, they decided to build a system that automatically scores games. The results, while not fully complete, are still pretty impressive for something whipped up during a 48 hour hackathon.

The automated score keeper uses a webcam duct taped to the ceiling right above the center of the pool table, The balls – red and yellow balls replace the rainbow of solids and stripes to make things easier – are found using OpenCV.

This build isn’t quite finished yet. The people at GoCardless are looking to improve the accuracy of their setup by using a camera with a higher frame rate and possibly moving on to physics simulation to predict where the balls should be. If these guys get the time, they could add something like augmented reality pool table to improve shot accuracy.

Vidia after the break.

Continue reading “Computer Tracking Of Billiard Balls” →

Launching A Balloon And Not Landing In The Ocean

October 24, 2012 by Brian Benchoff 32 Comments

In just a few short hours, the Yale Undergraduate Aerospace Association will launch their 4th high altitude balloon project into the rarefied air of the stratosphere and with any luck bring back pictures of the view high above Connecticut Long Island, Rhode Island, and Martha’s Vineyard.

Inside their surprisingly strong unibody chassis is two GoPro cameras and a triple-redundant telemetry system consisting of a custom radio system capable of transmitting over 40 miles, a cell-phone based comms system and a SPOT satellite tracker.

There is one very large problem the Yale Aerospace team has had to cope with; Because they’re launching their Skyview balloon from the eastern seaboard of the US, it’s very likely their payload could end up taking a drink in the Atlantic. To solve this problem, the team developed a novel cut-down solution: a piece of nichrome heater wire is wrapped around the line tying the payload to the balloon. If the hardware receives a signal from the ground, or has a software problem, or runs out of battery power, the nichrome circuit will release the balloon from its launch vehicle to hopefully return it to solid ground.

The Yale Aerospace team has also written a custom iOS app allowing the chase cars to track the balloon in real time – a great feature if you’re trying to communicate with several cars going down the highway. You can check out the live data from the balloon on the Yale Aerospace tracking site or just head over to their twitter to read the latest news about the flight.

Scratch-built Motor Uses A Clever Design

October 23, 2012 by Mike Szczys 17 Comments

[Lou] is on a hot streak when it comes to interesting builds. This time around he made his own motor using wood, PVC, some fasteners, and a bunch of enameled wire.

His method of building a commutator is intriguing. He first builds a rotor by cutting two opposing sides off of a PVC four-way connector and pushing a short galvanized pipe through what’s left. After adding two PVC nubs with caps and nails as pivot points he wraps the PVC and metal pipe with a continuous length of enameled wire. The enamel is then sanded off the windings around the PVC, and half is covered with electrical tape. The spinning rotor will cause the brushes to contact the bare wire during half of the rotation, and be insulated by the tape during the other half. The video after the break shows the motor in action, then walks you through each step of the build.

If you liked this video you should check out [Lou’s] water bottle rocket launcher, or his automated Ping Pong table topper which stores the game in the ceiling.

Continue reading “Scratch-built Motor Uses A Clever Design” →

Exploring The Mandelbrot Set In Real Time

October 23, 2012 by Brian Benchoff 33 Comments

The Mandelbrot set – the fractal ‘snowman turned on its side’ seen above – has graced the covers of magazines, journals, and has even been exhibited in art galleries. An impressive feat for what is nothing more than a mathematical function, and has become something of an obsession for [Chiaki Nakajima].

Even on modern computers, generating an image of a portion of the Mandelbrot set takes a good bit of time. When [Chiaki] discovered this fractal in the mid-1980s, the computers of the day took hours to generate a single, low-resolution image. Real-time zooming and scrolling was impossible but [Chiaki] made the best of what he had on hand and built Pyxis, a Mandelbrot set generator made entirely out of TTL logic chips (Google Translate here).

The original Pyxis connected to a desktop computer via a breakout box. while a special program toggled the bits and registers inside the Pyxis to generate pictures of the Mandelbrot set a thousand times faster than the CPUs of the day could muster.

Time marches on, and the original logic chip Pyxis is can be easily surpassed by even the slowest netbooks. There is, however, another way to build a hardware Mandelbrot set generator: FPGAs.

A few years ago, [Chiaki] began work on the Pyxis2010 (translation), an FPGA-based Mandelbrot set generator able to dynamically zoom and pan around the world’s most popular fractal. Built around an Altera Cyclone III FPGA he picked up from Digikey for $600 (no, not a dev board, just a bare chip), [Chiaki] began deadbugging his circuit directly onto the pins of the hugely expensive FPGA. A man with a steady hand and no fear if there ever was one.

Instead of connecting his Mandelbrot generator to a computer and using it as a co-processor, [Chiaki] decided he wanted something more portable. He found an old Sony PSP, removed the LCD screen, and integrated it into his circuit. After a careful bit of dremeling and fabrication, [Chiaki] had a hand-held Mandelbrot generator that is able to display images of the world’s most famous fractal faster than any desktop computer.

It goes without saying this build is incredible. The technical skill to build an insanely fast Mandelbrot generator on an FPGA is astonishing, but basing it off a logic-chip based build reaches into the realm of godliness. You can check out a video of this amazing build after the break.

Props to [Ian Finder] for sending this one in.

Continue reading “Exploring The Mandelbrot Set In Real Time” →

Most Useless Machine: Building Elevator Edition

October 18, 2012 by Mike Szczys 41 Comments

[Niklas Roy] calls it his Perpetual Energy Wasting Machine, but we know it for what it truly is: a building-sized most useless machine. You’ll remember that a most useless machine is a bobble that uses clever design to turn itself off once you have turned it on. This does the same thing with the elevator of the WRO Art Center in Wroclaw, Poland. The one difference is that it continually turns itself on and off.

He rigged up a pulley system that travels through the stairwell of the building. Whenever the elevator door on the top floor opens it causes the call button on the bottom floor to be pressed. The same thing happens when the elevator reaches the ground floor. But he didn’t stop there. Since the device is just wasting electricity whenever the elevator moves without passengers in it, he added a meter to track the loss. It’s the guts of a printing calculator strapped to the inside of the car. Every time the doors open it adds to the total.

You can see the installation in the video clip after the jump.

Continue reading “Most Useless Machine: Building Elevator Edition” →