I’ve been taking a blogging break this week to get caught up at work, but I wanted to say a few words on the passing of Apple CEO Steve Jobs. Those of us who are lifeless Apple fanboys follow Apple news know that Steve had been very sick for some time now. His passing is not unexpected, but it is still a shock now that it’s happened, and it’s a sad day.

My first experience with an Apple product was using an Apple IIe while I was an undergraduate psychology major. The psych department had a small computer lab with some Apples in it, and I used one to run statistical analyses of an experiment I was doing. I hated the Apple IIe. To me, it was a computer for English and art majors, or perhaps for elementary school children. All those cutesy graphics! And music! Hard-working and self-respecting science nerds such as myself shouldn’t stoop to such devices. But, it was the only machine in…

I learned the following trick for memorizing the value of e from my colleague, Gene White. It never fails to impress calculus students (given a wide enough definition of “impress”).

Start by carefully looking at this picture:

That’s a 20 dollar bill, so memorize “2″ and put down the decimal point.

The picture on the bill is of Andrew Jackson. He was our seventh President, so put a “7″ after the decimal point to get 2.7.

Jackson was elected in 1828, so put down “1828″ next. Since there’s a 2 in front of the decimal place, put “1828″ a second time. We’re now up to 2.718281828.

Now look at the red square over Jackson’s face. The diagonal creates two congruent right triangles with angle measures 45, 90, and 45. So, add on 459045 to get 2.718281828459045. And that’s e to 15 places.

Students and faculty at University Preparatory School in Redding, CA have created the world’s largest Sierpinski triangle constructed entirely out of Doritos. (Well, it’s probably the only one, but still.) It is 64 feet long and made out of 12,000 Doritos. This was done as an entry to the Doritos Crash the Superbowl contest. Watch, and be awed:

Can a 128-, 256-, etc. foot long Dorito Sierpinski triangle be far behind? I bet the parent company for Doritos would seriously consider some corporate sponsorship.

Thanks to Cory Poole, math and physics teacher at U-Prep, who sent this in. That’s a great, creative way to get students interested in math. (And you can eat it when it’s done.) There’s more on the video here.

The story left off with me giving up trying to justify spending $399 for the 32 GB model, even though I’d saved up for it. Cheapness is in my DNA, and I’ve never been able to spend money on anything without feeling like I should have stuck it in a savings account instead. But, one day, my wife comes home and informs me that the daughter of one of her co-workers works at the Apple Store in Indy and gets a 15% “friends and family” discount. After trading a few emails, the deal was set up, and a few days later I had my grubby hands all over it (you see just how grubby your hands really are with this thing) with $60 knocked off the price. So, you see? It pays to wait.

I’ve been using it basically nonstop for a week now, and here are my overall impressions:

It’s incredibly thin and light, yet it also feels very sturdy, and despite having an all-shiny-aluminum back I haven’t…

The numbers believed to be the 45th and 46th Mersenne primes have been proven to be prime. The 45th Mersenne prime is \(2^{37156667} -1\) and the 46th is \(2^{43112609} – 1\).Full text of these numbers is here and here.

Of course what you are really wanting to know is how my spreadsheet models worked out for predicting the number of digits in these primes. First, the data:

Number of digits actually in \(M_{45}\): 11,185,272

Number of digits actually in \(M_{46}\): 12,978,189

My exponential model (\(d = 0.5867 e^{0.3897 n}\)) was, unsurprisingly, way off — predicting a digit count of over 24.2 million for \(M_{45}\) and over 35.8 million for \(M_{46}\). But the sixth-degree polynomial — printed on the scatterplot at the post linked to above — was… well, see for yourself:

Number of digits predicted by 6th-degree polynomial model for \(M_{45}\):…

At the end of this post, I made a totally naive guess that the recently discovered candidate to be the \(M_{45}\), the 45th Mersenne prime, would have 10.5 million digits. There was absolutely no systematic basis for that guess, but I did suggest having an office pool for the number of digits, so what I lack in mathematical sophistication is made up for by my instinct for good nerd party games. On the other hand, Isabel at God Plays Dice predicted 14.5 million digits based on a number theoretic argument. Since I am merely a wannabe number theorist, I can’t compete with that sort of thing. But I can make up a mean Excel spreadsheet, so I figured I’d do a little data plotting and see what happened.

If you make a plot of the number of digits in \(M_n\), the nth Mersenne prime, going all the way back to antiquity, here’s what you get:

Here’s a great illustration from George Gamow’s classic book One Two Three… Infinity which shows two things: just how big \(10^{20}\) really is, when thought of as a scaling factor; and also the power of a good illustration to drive home a point about math or science. The picture shows a normal-sized astronomer observing the Milky Way galaxy when shrunk down by a factor of \(10^{20}\).

That’s a big number, folks.

Gamow’s book is one of several on my summer reading list, and there’s a reason it’s a classic. In particular, it’s chock full of cool illustrations like this that convey more information about a science concept than an hour’s worth of lecturing.

I am a mathematician and educator with interests in cryptology, computer science, and STEM education. I am affiliated with the Mathematics Department at Grand Valley State University in Allendale, Michigan. The views here are my own and are not necessarily shared by GVSU.

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September 26, 2008, 10:11 am

## Some programmer needs to make this a reality

By Robert Talbert

From the always-inventive xkcd: