Today is March 14th, or Pi Day because 3.14 is March 14th rendered in month.day date format. A very slightly better way to celebrate the ratio of a circle’s circumference to its diameter is July 22nd, or 22/7 written in day/month order, a fractional approximation of pi that’s been used for thousands of years and is a better fit than 3.14. Celebrating Pi Day on July 22nd also has the advantage of eschewing middle-endian date formatting.
But Pi Day is completely wrong. We should be celebrating Tau Day, to celebrate the ratio of the circumference to the radius instead of the diameter. That’s June 28th, or 6.283185…. Nonetheless, today is Pi Day and in the absence of something truly new and insightful — we’re still waiting for someone to implement a spigot algorithm in 6502 assembly, by the way — this is a fantastic opportunity to discuss something tangentially related to pi, the history of mathematics, and the idea that human knowledge builds upon itself in an immense genealogy stretching back to the beginning of history.
This is our Pi Day article, but instead of complaining about date formats, or Tau, we’re going to do something different. This is how you approximate pi with the Monte Carlo method, and how anyone who can count to a million can get a better approximation of one the fundamental constants of the Universe than Archimedes.
The trouble with being an incidental witness to the start of something that later becomes world-changing is that at the time you are rarely aware of what you are seeing. Take the Acorn Archimedes, the home computer for which the first ARM processor was developed, and which has just turned 30. If you were a British school pupil in 1987 who found a pair of the new machines alongside the row of BBC Micros in the school computer lab, for sure it was an exciting event, after all these were the machines everyone was talking about. But the possibility that their unique and innovative processor would go on to spawn a line of successors that would eventually power so much of the world three decades later was something that probably never occurred to spotty ’80s teens.
[Computerphile] takes a look at some of the first Archimedes machines in the video below the break. We get a little of the history and a description of the OS, plus a look at an early model still in its box and one of the last of the Archimedes line. Familiar to owners of this era of hardware is the moment when a pile of floppies is leafed through to find one that still works, then we’re shown the defining game of the platform, [David Braben]’s Lander, which became the commercial Zarch, and provided the template for his Virus and Virus 2000 games.
We see the RiscOS operating system booting lightning-fast from ROM and still giving a good account of itself 20 years later even on a vintage Philips composite monitor. If you were that kid in 1987, you were in for a shock when you reached university and sat down in front of the early Windows versions, it would be quite a few years before mainstream computers matched your first GUI.
The Archimedes line and its successors continued to be available into the mid 1990s, but faded away along with Acorn through the decade. Even one being used to power the famous Trojan Room Coffee Cam couldn’t save it from extinction. We’re told they can still be found in the broadcast industry, and until fairly recently they powered much of the electronic signage on British railways, but other than that the original source of machines has gone. All is not lost though, because of course we all know about their ARM joint venture which continues to this day. If you would like to experience something close to an Archimedes you can do so with another computer from Cambridge, because RiscOS is available for the Raspberry Pi.
Sit back and enjoy the video, and if you were one of those kids in 1987, be proud that you sampled a little piece of the future before everyone else did.
3D-scanning seems like a straightforward process — put the subject inside a motion control gantry, bounce light off the surface, measure the reflections, and do some math to reconstruct the shape in three dimensions. But traditional 3D-scanning isn’t good for subjects with complex topologies and lots of nooks and crannies that light can’t get to. Which is why volumetric 3D-scanning could become an important tool someday.
As the name implies, volumetric scanning relies on measuring the change in volume of a medium as an object is moved through it. In the case of [Kfir Aberman] and [Oren Katzir]’s “dip scanning” method, the medium is a tank of water whose level is measured to a high precision with a float sensor. The object to be scanned is dipped slowly into the water by a robot as data is gathered. The robot removes the object, changes the orientation, and dips again. Dipping is repeated until enough data has been collected to run through a transformation algorithm that can reconstruct the shape of the object. Anywhere the water can reach can be scanned, and the video below shows how good the results can be with enough data. Full details are available in the PDF of their paper.
While optical 3D-scanning with the standard turntable and laser configuration will probably be around for a while, dip scanning seems like a powerful method for getting topological data using really simple equipment.
Simple machines are wonderful in their own right and serve as the cornerstones of many technological advances. This is certainly true for the humble lever and the role it plays in manual transmissions as evidenced in this week’s Retrotechtacular installment, the Chevrolet Motor Company’s 1936 film, “Spinning Levers”.
This educational gem happens to be a Jam Handy production. For you MST3K fans out there, he’s the guy behind shorts like Hired! from the episodes Bride of the Monster and the inimitable Manos: The Hands of Fate. Hilarity aside, “Spinning Levers” is a remarkably educational nine-ish minutes of slickly produced film that explains, well, how a manual transmission works. More specifically, it explains the 3-speed-plus-reverse transmissions of the early automobile era.
It begins with a nod to Archimedes’ assertion that a lever can move the world, explaining that the longer the lever, the better the magic. In a slightly different configuration, a lever can become a crank or even a double crank. Continuous motion of a lever or series of levers affords the most power for the least work, and this is illustrated with some top-drawer stop motion animation of two meshing paddle wheels.
Next, we are shown how engine power is transferred to the rear wheels: it travels from a gear on the engine shaft to a gear on the drive shaft through gears on the countershaft. At low speeds, we let the smallest gear on the countershaft turn the largest gear on the drive shaft. When the engine is turning 90 RPM, the rear wheel turns at 30 RPM. At high speeds using high gears, the power goes directly from the engine shaft to the drive shaft and the RPM on both is equal. The film goes on to explain how the gearbox handles reverse, and the vast improvements to transmission life made possible through synchromesh gearing.
Wielding the power to melt glass or instantly ignite most day to day materials can be intoxicating pretty fun. With a little math, a lot of patience, and 5,800 1cm pieces of mirror, this build requires welding glasses just to look at the 1-2cm focal point. With an idea rumored to date back to Archimedes, this more portable parabolic project is perfect for your home burning needs. Unfortunately, this setup seems to have burnt itself to death at some point, though that makes room for version two, which will reportedly bump the mirror count to 32,000 or so.
There are plenty of other ways to make a death ray out there as well, including using lasers or lenses. Think you have a better tool of destruction? Be sure to tell us about it.
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