Math, A Cappella

I came across this video the other day, and even though I suspect it will not appeal to most of my readers, I could not resist posting it. This is the Klein Four performing their original composition, “Finite Simple Group (of Order Two)”.

I’m already a big fan of a cappella music; that is, people singing unaccompanied by musical instruments. It’s a great form of music for several reasons. And the math humor was just too good to pass up, even if my math training is not sufficient for me to understand many of the references. It makes me smile nonetheless.

This song was recorded back in December, 2004; the group is no longer together as members have graduated (the group was based at Northwestern University). Still, you can watch or download videos of other songs (or this one) at their web site, or even purchase their CD if you like.

Equations on WordPress

WordPress.com just added support for using inline [Wikipedia], a freely available protocol for using typesetting and displaying mathematics and other technical information. It is powerful and not too difficult to learn the basics. Equations can now be placed within a paragraph, such as Einstein’s famous and world-changing . Of course, one could use regular HTML to display such an equation (E=mc²), but where really shines is for more complex formulas. For instance, the volume of a sphere (using a cylindrical coordinate system) is . This is a very useful feature and I’m quite impressed that WordPress.com has offered it.

Update: WordPress.com has been busy! has now been enabled in comments as well. Furthermore, by using the\displaystyle command, one can have the equation display separately on its own line, instead of the vertically compact inline style used above. For instance, the volume equation I previously discussed would be displayed as follows:

For those unfamiliar with , it is really quite easy to learn. For reference, the code I have used here is as follows:

• $latex \textrm{\LaTeX{}} $
• $latex E=mc^2 $
• $latex V=\int_0^{2\pi} \int_0^R \int_{-\sqrt{R^2-r^2}}^{\sqrt{R^2-r^2}} r \, dz \, dr \, d\theta = \frac{4}{3}\pi R^3 $
• $latex \displaystyle V=\int_0^{2\pi} \int_0^R \int_{-\sqrt{R^2-r^2}}^{\sqrt{R^2-r^2}} r \, dz \, dr \, d\theta = \frac{4}{3}\pi R^3 $

Finally, is pronounced with a hard k sound at the end; it comes from the Greek letter Χ (chi). See Wikipedia for more information.

Any questions?

NASA Finally Switches to Metric

Countries primarily using non-metric systems of measurement (Liberia, Myanmar, Thailand, and the United States). Source: Wikipedia.

As reported in Space.com,

When NASA returns astronauts to the Moon, the mission will be measured kilometers, not miles.

The agency has decided to use metric units for all operations on the lunar surface, according to a statement released today.

(continue reading at Space.com)

Zero Divided by Zero

I was quite disappointed to read a BBC news story about the a new “theory” that supposedly solves the difficulty of dividing zero by zero (thanks to the blog “Web Pruned by Dawdling Monkeys” for pointing it out). The article discusses a Dr. James Anderson from the United Kingdom who has declared that this value should be called “nullity” and that with this definition, he has solved a “1,200-year-old problem.” While I was annoyed enough to write about it myself, I would actually recommend you read more about this incident at “Good Math, Bad Math,” which is much better written than what I could do.

First, some background. In mathematics zero divided by zero is considered indeterminate (and is undefined, as well). In approximate lay terms, this is because if we try to evaluate it in different ways, we get different results. In general, division by zero is not defined in mathematics. One way to look at this is to think of division as the inverse of multiplication. When we ask what twelve divided by three is, another way to word it would be to ask what number, when multiplied by three, gives twelve.