Slide Rules were the Original Personal Computers

Unless you are above a certain age, the only time you may have seen a slide rule (or a slip stick, as we sometimes called them) is in the movies. You might have missed it, but slide rules show up in Titanic, This Island Earth, and Apollo 13. If you are a fan of the original Star Trek, Mr. Spock was seen using Jeppesen CSG-1 and B-1 slide rules in several episodes. But there was a time that it was common to see an engineer with a stick hanging from his belt, instead of a calculator or a cell phone. A Pickett brand slide rule flew to the moon with the astronauts and a K&E made the atomic bomb possible.

Slide rules are a neat piece of math and history. They aren’t prone to destruction by EMP in the upcoming apocalypse (which may or may not include zombies). Like a lot of things in life, when it comes to slide rules bigger is definitely better, but before I tell you about the 5 foot slide rule in my collection, let’s talk about slide rules in general.
Continue reading “Slide Rules were the Original Personal Computers”

On not proving the twin prime conjecture with AutoCAD

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”