He could see the SIN(E).
Wednesday, June 30, 2010
Trigonometric Break-Ups
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(C)Copyright 2010, C. Burke. All rights reserved.
He could see the SIN(E).
He could see the SIN(E).
Tuesday, June 29, 2010
Graduation Day 2010
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(C)Copyright 2010, C. Burke. All rights reserved.
These things happen.
Congratulations to everyone in the Class of 2010.
These things happen.
Congratulations to everyone in the Class of 2010.
Sunday, June 27, 2010
More on Pythagorean Triples
For those that have read my posts (and related comics) dealing with Pythagorean Triples, the blog Theorem of the Week has an entry about them.
Saturday, June 26, 2010
Self-Promotion, the Results
So I self-promoted my "Self-Promotion" comic because I wanted to either be ironic or be whatever it is that people call "ironic" but really isn't but makes English teachers rip their hair out.
I expected downvotes and negative reviews and comments from those that saw the URL and the user id of the poster (both containing "xwhy" in them) without clicking on the link to see that that was part of the joke. The jokes back on me.
The results: 260+ views on Stumbleupon, with no comments and no one listed as liking it; 150 visits from reddit, with 4 up votes and 3 down votes, and no comments; and no one saw it on digg, except me.
On the other hand, David Morgan-Mar posted a link on his Facebook page. Over 700 hits, 11 people liked it, with two comments.
Self-promoting doesn't pay. Especially when you have a small, select audience to begin with. I'm happy to have you.
I expected downvotes and negative reviews and comments from those that saw the URL and the user id of the poster (both containing "xwhy" in them) without clicking on the link to see that that was part of the joke. The jokes back on me.
The results: 260+ views on Stumbleupon, with no comments and no one listed as liking it; 150 visits from reddit, with 4 up votes and 3 down votes, and no comments; and no one saw it on digg, except me.
On the other hand, David Morgan-Mar posted a link on his Facebook page. Over 700 hits, 11 people liked it, with two comments.
Self-promoting doesn't pay. Especially when you have a small, select audience to begin with. I'm happy to have you.
Thursday, June 24, 2010
Self-Promotion
(Click on the cartoon to see the entire image.)
(C)Copyright 2010, C. Burke. All rights reserved.
Down-vote or bury, as long as you spell the URL right.
Down-vote or bury, as long as you spell the URL right.
Thanks, again, to David Morgan-Mar, of Irregular Webcomic, for allowing use of his material under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 Unported Licence.
As such, the comic above is also copyright and is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 Unported Licence.
Class Blog was a previous strip that was created under the same license.
Tuesday, June 22, 2010
Sending Out an S.O.S to the World Cup
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(C)Copyright 2010, C. Burke. All rights reserved.
I hope that someone gets my ... I hope that someone gets my ... I hope that someone gets my ...
I hope that someone gets my ... I hope that someone gets my ... I hope that someone gets my ...
Obligatory Educational Content: A soccer ball looks like a bucky ball, or vice versa.
Sunday, June 20, 2010
Saturday, June 19, 2010
Thursday, June 17, 2010
HEX
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(C)Copyright 2010, C. Burke. All rights reserved.
The character, 'Leven Hex, dates back to April 2008, but I held off because I had just done a comic book strip at the end of March, and I ran
hex-based 0'Factor instead.
And then I never got around to doing this one. Things happen.
I spent a lot more time on this one than I had expected to. And I probably could've spent even more, but I had to finally let it go. And then I updated it again this morning because I thought it was too tall and there was a lot of empty, blue sky. And I still didn't get around to adding any grass by the pond, or mixing any green in the water.
If you're curious, I looked through a lot of covers to find the right look.
The character, 'Leven Hex, dates back to April 2008, but I held off because I had just done a comic book strip at the end of March, and I ran
hex-based 0'Factor instead.
And then I never got around to doing this one. Things happen.
I spent a lot more time on this one than I had expected to. And I probably could've spent even more, but I had to finally let it go. And then I updated it again this morning because I thought it was too tall and there was a lot of empty, blue sky. And I still didn't get around to adding any grass by the pond, or mixing any green in the water.
If you're curious, I looked through a lot of covers to find the right look.
Monday, June 14, 2010
Friday, June 11, 2010
Thursday, June 10, 2010
Sums of Squares of Consecutive Numbers
Continuing what I started on Tuesday's post:
Giving the Pythagorean Theorem, a2 + b2 = c2, find three consecutive numbers for a, b and c.
The answer, of course, is everyone's favorite Pythagorean Triple, 3, 4 and 5.
But suppose instead of three consecutive numbers, we had five consecutive numbers, which were split with the three smaller values on the left and the two greater values on the right? That would give us:
a2 + b2 + c2 = d2 + e2
The answer is in the previous post. I'll omit it here in case you want to work it out.
Now, a couple approaches could work here. The first, and probably best if you plan on going further, is to replace the variables with n, n+1, n+2, etc., and then using FOIL (or a "FOIL"-free alternative if you hate "FOIL"), combining like terms and solving the resulting equation.
The other, which I can use on Day 1, is guess and check. Okay, stop laughing and rolling your eyes, and hear me out.
First of all, most of my students haven't handled a scientific calculator very much let alone a TI-83, 84, or N-Spire. (Yes, we had a bunch donated to the school as part of a technology initiative. Unfortunately, they aren't allowed to be used during the Regents exams, so we have to switch back to the older calculators. But that's a rant for another day.) An activity like this could be a simple and thoughtful first exercise.
Second, many of them have little or no Number Sense or Estimating skills. How would they approach the problem? Would they try 3, 4, 5, 6, 7 first? When that doesn't work, will they move to 4, 5, 6, 7, 8, or will they jump a little higher a little faster? But if they don't try every combination, how will they know if they went too far and passed the answer?
Then, after finding the answer and comparing it to 3, 4, 5, what would their first guess be for
a2 + b2 + c2 + d2 = e2 + f2 + g2 ?
Naturally, all of this occurs to me during the last week of classes, after the
final exam has been given.
Giving the Pythagorean Theorem, a2 + b2 = c2, find three consecutive numbers for a, b and c.
The answer, of course, is everyone's favorite Pythagorean Triple, 3, 4 and 5.
But suppose instead of three consecutive numbers, we had five consecutive numbers, which were split with the three smaller values on the left and the two greater values on the right? That would give us:
The answer is in the previous post. I'll omit it here in case you want to work it out.
Now, a couple approaches could work here. The first, and probably best if you plan on going further, is to replace the variables with n, n+1, n+2, etc., and then using FOIL (or a "FOIL"-free alternative if you hate "FOIL"), combining like terms and solving the resulting equation.
The other, which I can use on Day 1, is guess and check. Okay, stop laughing and rolling your eyes, and hear me out.
First of all, most of my students haven't handled a scientific calculator very much let alone a TI-83, 84, or N-Spire. (Yes, we had a bunch donated to the school as part of a technology initiative. Unfortunately, they aren't allowed to be used during the Regents exams, so we have to switch back to the older calculators. But that's a rant for another day.) An activity like this could be a simple and thoughtful first exercise.
Second, many of them have little or no Number Sense or Estimating skills. How would they approach the problem? Would they try 3, 4, 5, 6, 7 first? When that doesn't work, will they move to 4, 5, 6, 7, 8, or will they jump a little higher a little faster? But if they don't try every combination, how will they know if they went too far and passed the answer?
Then, after finding the answer and comparing it to 3, 4, 5, what would their first guess be for
Naturally, all of this occurs to me during the last week of classes, after the
final exam has been given.
Wednesday, June 09, 2010
Definition: Relative Change
(Click on the cartoon to see the entire image.)
(C)Copyright 2010, C. Burke. All rights reserved.
I guess it could also be "trading spouses", but then it could be "trading parents", "trading children" or even "trading crazy uncles in the cellar", as well.
I guess it could also be "trading spouses", but then it could be "trading parents", "trading children" or even "trading crazy uncles in the cellar", as well.
Tuesday, June 08, 2010
Martin Gardner (1914-2010)
I recently found out that mathematics and science writer, Martin Garnder passed away a couple of weeks ago.
I first discovered Gardner at Xaverian High School, browsing the library shelves, probably looking for a puzzle book. I found a copy of The Incredible Dr. Matrix, which was a fun book to read. Besides being the first place where I ever encountered the Lincoln/Kennedy connections (complete with corrections, such as Lincoln's secretary's name was John, not Kennedy), but it had some great puzzles that got me thinking (a dangerous pasttime).
One problem that I remembered was that Gardner listed
32 + 42 = 52,
which everyone knows, and then added that
102 + 112 + 122 = 132 + 142,
which I had to independently verify.
It hadn't occured to me that this progression might continue. The puzzle was to find four consecutive numbers which, when squared, have the same sum as the sum of the squares of the next three consecutive numbers after that.
Having already had Algebra under my belt by that point, it turned out not to be a problem at all.
My brother, Joseph, saw the book and mentioned that Gardner had puzzles in Asimov's Science Fiction, which he had a subscription to. The one story that comes to mind had this as the basic puzzle:
A family is riding a rocket ship from the Moon to Earth. A child looks out the front window and then runs to the rear window. He then tells his father that the Earth and the Moon appear to be the same size. The puzzle, which included some information that I'd have to look up, was find the position of the spaceship relative to the Earth and Moon.
I haven't read anything by Gardner in quite a while, but I should probably stop by the library and find a book or two of his and see if I can find some good puzzles for my students.
I first discovered Gardner at Xaverian High School, browsing the library shelves, probably looking for a puzzle book. I found a copy of The Incredible Dr. Matrix, which was a fun book to read. Besides being the first place where I ever encountered the Lincoln/Kennedy connections (complete with corrections, such as Lincoln's secretary's name was John, not Kennedy), but it had some great puzzles that got me thinking (a dangerous pasttime).
One problem that I remembered was that Gardner listed
which everyone knows, and then added that
which I had to independently verify.
It hadn't occured to me that this progression might continue. The puzzle was to find four consecutive numbers which, when squared, have the same sum as the sum of the squares of the next three consecutive numbers after that.
Having already had Algebra under my belt by that point, it turned out not to be a problem at all.
My brother, Joseph, saw the book and mentioned that Gardner had puzzles in Asimov's Science Fiction, which he had a subscription to. The one story that comes to mind had this as the basic puzzle:
A family is riding a rocket ship from the Moon to Earth. A child looks out the front window and then runs to the rear window. He then tells his father that the Earth and the Moon appear to be the same size. The puzzle, which included some information that I'd have to look up, was find the position of the spaceship relative to the Earth and Moon.
I haven't read anything by Gardner in quite a while, but I should probably stop by the library and find a book or two of his and see if I can find some good puzzles for my students.
Monday, June 07, 2010
What's Stranger Than Cows That Mu?
(Click on the cartoon to see the entire image.)
(C)Copyright 2010, C. Burke. All rights reserved.
I debated adding "aque" and "tape".
I debated adding "aque" and "tape".
Update: The cartoon was ready to go when I found out about this joke, which just appeared in the 66th Carnival of Mathematics.
It did provide me with a better title than what I had had.
Thursday, June 03, 2010
Behind the Fence
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(C)Copyright 2010, C. Burke. All rights reserved.
Sometimes you want to look when everybody calls your name...
But it might lead to a squirt in the eye
Or, if you're Brando, cider in the ear.
Sometimes you want to look when everybody calls your name...
But it might lead to a squirt in the eye
Or, if you're Brando, cider in the ear.
Wednesday, June 02, 2010
Just Frickin' Cool!
I went to check my blog today. Google was on the screen so I just started typing in "mrburkemath".
I got as far as "mrbu" when it not only showed up in the dropdown box, but it was listed FIRST.
Take that, Mrbubbles.org!! Take that, Mrbuttons.com!!
Just frickin' cool!
Tuesday, June 01, 2010
Near-Sighted
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(C)Copyright 2010, C. Burke. All rights reserved.
You wouldn't hit a guy with glasses, would you?
How's that for "subtle"?
You wouldn't hit a guy with glasses, would you?
How's that for "subtle"?