Friday, July 27, 2012

Coffee Cups and Doughnuts

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(C)Copyright 2012, C. Burke. All rights reserved.

When you need coffee that badly, you'll try anything.

And whether it worked or not, it would definitely be an eye-opener!

Thursday, July 26, 2012

Book Review: The Pleasures of Pi,e and Other Interesting Numbers (Y E O Adrian)

Every now and then, I like to pick up a book about math (rather than a generic "math book"). I'm not sure what I'm looking for, and what I might find that I haven't seen before. One thing I know: I usually get lost or bogged down halfway through when I get to long series of equations that I possibly could get through if I bothered. The problem is that after a while I don't want to bother.

Readability is the first factor in favor of The Pleasures of Pi,e and Other Interesting Numbers (2006) (Note: I'm not sure if there is supposed to be a space between the comma and the "e" or not. There is a picture of a pie on the cover, so I suspect no space.)

Y E O Adrian, M.A., Ph.D. (Cambridge University), keeps the tone of the book light and interesting for the first 140 pages or so. In each chapter, the reader will be shown a series on the left-hand page, and a passage with some explanation, interesting fact or even encouragement for the reader to figure something out on the right-hand page. The first few series tend to infinity (with an explanation of what that means), but soon the sums start to converge on 1 or 2 or some multiple or fraction of e or pi.

Are there proofs of these sums? Sure. They're just let for later. The back 100 pages lists the proofs from easy to advanced, relying on things previously established, and explaining in a way that's easy to comprehend. I think high school students (ones who have had trigonometry) will be able to follow along.

It was a nice little diversion from my usual summer fare. I enjoyed reading it, and I would recommend it to anyone looking for a "fun" math book to read. Yes, some of those actually exist. It's not a null set.

One final note -- and this was almost the lead, but I held off out of respect -- if you were to remove the interesting number, e, from the author's name, what would you have left?

YO Adrian!

A Rocky finish to my review, to be sure.

EDIT (7/28): Forgot to mention: library book, softcover. Sometimes when looking over the books I've read, I like to keep track of the ones that I bought (new or used) or borrowed (from friends or libraries) and for that matter, if they're even printed on paper anymore! Five of the last six books I read were e-books, but I've still read fewer that a dozen of those.

Monday, July 23, 2012

Smoking Area

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(C)Copyright 2012, C. Burke. All rights reserved.

ObMath: How can we increase the population density of the smoking area without increasing the number of icky smokers?
What can we maximize the area of the pen without exceeding the limited amount of barbed wire available to fence them in?

Wednesday, July 18, 2012

Concave Polygons

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(C)Copyright 2012, C. Burke. All rights reserved.

Decamom is proud of her two octakids, regardless of concavities.

Monday, July 16, 2012

Mean Value Theorem

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(C)Copyright 2012, C. Burke. All rights reserved.

I guess somewhere in-between there should be some kind of intermediate value theorem.

Monday, July 09, 2012

Welcome STEM Classmates

Greetings and good evening to anyone from my STEM (Science, Technology, Engineering and Math) Vertical Math workshop who copied down my URL in class today and decided to check out the site. Thank you for stopping by.

Keep in mind that the earliest posts on the blog date back to the time when I was trying to get my students involved, and before that period of time when was blocked from schools. The comics start a bit later.

Feel free to leave a comment to let me know you were here. Anonymous is fine!

Also: I just want to add, if you start reading from the most recent comic, you might be a little confused. That's the 700th strip and it contains references to jokes and events and topics and characters from the previous 699 strips.

Saturday, July 07, 2012

Problem of the Day: Factorials

I was going through old papers and torn magazine pages stored in folders that I hadn't looked at in years, finding stuff to recycle. I happened to glanced at a calendar of daily problems, most of which were either too advanced for the classes I was teaching at the time, or just a little too involved. However, one simple problem jumped out at me, and I decided to file that one away for next year. It's definitely a question that needs the solver to explain how he arrived at the answer, and would give me insight into their thinking.

I made a second problem based on the original. Here they both are:

1. Find the largest prime factor of (87!)(88!).

2. Find the largest prime factor of 87! + 88!

Why I love the problems: first, students needed to know something about factors, prime numbers and factorials. Second, seeing a number like 88!, that student whose first instinct is to reach for the calculator will have to put it down and find a new approach.

Answers below. Stop reading here if you didn't figure them out yet.

The answer to problem 1 is fairly straightforward. The factors of 87!*88! are
1 * 2 * 3 * ... * 87 * 1 * 2 * 3 * ... * 87 * 88.

There is no need to make factor trees to find the prime factorization (an approach students might take). The largest prime factor would be the largest prime number not greater than 88. That would be 83.

(If a student guessed 87, show them that 8+7 = 15, which is divisible by 3, so 87 is divisible by 3. Or just have them divide 87 / 3 and see that they'll get 29.)

The answer to problem 2 requires a little work. We want a factor of the sum, but factors are for products, not sums. No problem. Let's make a multiplication problem out of it.

87! + 88!
= 87! + 87!(88)
= 87!(1 + 88)
= 87!(89)

The largest prime factor of 87! is still 83. But 89 is a prime number, so it's the largest prime factor, which is another reason why this is such a neat little problem: 89 isn't in the initial problem, but every whole number less than 89 is!

I think that this is a great journal-type question to assess their understanding of concepts and their ability to communicate a solution. And it will fall in nicely with whatever they're calling "differentiating of instruction" this semester. (Yes, they mentioned a new term at the last department meeting, but I neglected to write it down or even really care.)

P.S. The first problem is mine. The second is the original.

Friday, July 06, 2012

A Funny Thing Happened ...

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(C)Copyright 2012, C. Burke. All rights reserved. A funny thing happened on the way to my class blog ... The students weren't using it, so I made some bonus comics. I doodled and diddled, and threw in some old jokes. Next thing I know I have recurring characters, both human and numerical, all developing personalities, in my own geeky version of "Sesame Street" where such could exist side-by-side. (Except that they're never actually existed side-by-side, I think.) This was definitely the most ambition thing I've done to date -- and those last two words scare the hell out of me. There were other things that I left out of this. Not just illustrations to go with the text, but other text that didn't fit. And I wanted as many characters as I could squeeze in, but some were just faces and the stick figures wouldn't blend in well. That's enough for today. I need a break. It's hot. -- Chris Burke

Wednesday, July 04, 2012

Declaring Independence

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(C)Copyright 2012, C. Burke. All rights reserved.

It's a fact: i can declare as much as i will, but i will never be completely independent of others.

Monday, July 02, 2012

Watch Where You're Walking

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(C)Copyright 2012, C. Burke. All rights reserved.

One does not simply tell ten-year-old jokes when one has filler to fill.

... Or does One?