Cool Math: Is Pi Outdated?

Pi is one of our oldest and most recognizable math accomplishments.  Fancy-pants mathematicians think we should move away from using it because there are numerous counter-intuitive features of Pi as the math gets more advanced. Tau v. Pi is a battle to reconceptualize circle math in terms of motion rather than in terms of solids. Continue reading Cool Math: Is Pi Outdated?

Cool Math: Lucas Numbers

I was torn between posting a video explanation of how they found the recent super-massive Mersenne Prime and this shorter bit on Lucas Numbers, which is how they found it.  Since this video has more explanation–and some very cool commentary on the nature of mathematics toward the end–I went with it.  I’ll save the super-Mersenne for another day.

Lucas Numbers are related to the Fibonacci Sequence.  Both are related to the Golden Ratio, which I definitely need to post on at some point.  Like many Numberphile videos, this one does a good job conveying infectious love of numbers.  Enjoy! Continue reading Cool Math: Lucas Numbers

Cool Math: (IR)Regular Polygons

I am a huge fan of Greek geometry.  That’s the real stuff.  Real geometry involves an unmarked straightedge and a compass.  If it has numbers, you are doing it wrong.  One of my colleagues is a geometrical genius–he’s actually one of the most famous origamists in the world (that’s right, I name-dropped an origami master!).  I like to tease him when they get into “analytic” stuff late in the year after the proofs are all done.  “Oh look, Algebra!  I thought you were teaching Geometry this year!”

Doubling the Cube?  Squaring the Circle?  Neusis Constructions?  Now we’re talking.  The Greeks thought geometrically in a way that borders on the mystical.  Come to think of it, they actually did make a religion out of it. Continue reading Cool Math: (IR)Regular Polygons

Cool Math: A New Prime!

So they found a new Mersenne Prime.  Mersenne Primes have the form (2^n) − 1.  For the newest prime, n = over 74 million (!).  That is an astronomically large number–actually, that’s not right.  It’s an unimaginably large, universe-busting number.

Of interesting note is that it would have been utterly impossible to find this number without computers, the internet, and a ton of people.  It was basically an enormous, crowd-sourced, brute-force method of discovery.  Given how far beyond the previous prime this number was, we may never find another in our lifetimes unless some super-spooky algorithm is discovered.

Then again, the magnitude of the primes does not grow in any predictable way.  The next one might not be too many thousands of powers of 2 beyond this one!

How cool is that?

Cool Math: Infinitesimals

I have a complicated relationship with infinity as used in mathematics, which is very possibly explained by a math deficiency on my part.  I enjoy following proofs but I find myself questioning the moves that bring about some of the more counter-intuitive results of mathematical infinities.  Still I keep coming back for more!

Here’s a fun one on a topic directly connected to infinities: infinitesimals (infinitely small numbers).  Queue up some Leibniz and Newton, limits, and hyper-reals!

Math puts me in strange realms of thought.  Sometimes I think the Church saved me from being a theosophist or something.

Cool Math

I love YouTube series on math.  My wife asked me over the dinner table if I could prove that pi is irrational.  After a quick peek at the internet, the answer is, “No.”  Meaning very intelligent people can, but I cannot.

However, there is good news!  I can prove that e is irrational.  Or at least I can follow the proof.  If your algebra is sharp, you can too.  Check this cool video.

Math is…neat.  I almost went into math in college, but it was too much work for me.  I’m more of a dabbler.