I’m Perfect!

Happy Birthday to Mr. Chase, today!

Today, I think I can safely say, is the last time my age will be a perfect number. The last time my age was perfect was when I was 6 years old. For those that forget the definition of a perfect number:

A number is perfect if it is the sum of its proper divisors (that is, the sum of its divisors, excluding itself).

For example, 6 is perfect because 1+2+3=6.

I’m not 6. How old *am* I?

So, how old am I?

If you’re a consummate mathematician, you have the first couple perfect numbers memorized, and this is an easy question. If you’ve never thought about perfect numbers, or you forget what the next one is, I challenge you to figure it out for yourself. I challenged my students today to figure out my age, and two of them got it out without my help.

For a real challenge, prove that there are infinitely many perfect numbers. (open problem!)

Go Rockets!

Just had to share my Easter Egg honoring the school at which I teach:

(front) Richard Montgomery

(back) Ritchie the Rocket

Compare with the eggs from last year. I think I’m improving my egg-decorating skills!

Happy π day!

Today at our school we had to have the obligatory π day celebrations. Here are the ways we observed π at RM:

• To raise money for the math honors society, students purchased π-grams for one another and a piece of pi with a note were delivered to the recipients during first period.
• There was a pie eating contest on “main street”, also sponsored by the math honors society, and guess who won? Check out my crown!!

Get the joke?? On the back it says "We are the 3.14%."

Action shot

Mr. Chase wins!

• In each of my classes kids bring in food and we have a π day party. I pass out a sign up sheet a few days before and kids agree to bring all sorts of round food. Here’s the sign up sheet. Feel free to use it, steal it, modify it. Also available in pdf format. Here’s one of my favorite food items from this year:

• I showed these youtube videos.
• I did a mini lecture on the history of π and gave some interesting facts about the number.
• Students got to find out at what digit of π their birthday appears. You can too!

One more thing you can still do, if you haven’t yet observed π day:

• Send one of six different π day cards to your friends today, courtesy of NCTM.

 

 

Also, on an unrelated note, today’s Google logo is great. If you’re interested in the mathematics of origami, you probably know who Robert Lang is. Today’s Google logo is an origami piece created by Lang in honor of the late Akira Yoshizawa, world famous origami artist.

Stellated Icosahedron

I’ve been motivated by George Hart and Zachary Abel to make my own mathematical sculpture with found objects . A few former students dropped by to visit me this afternoon and I put them to work making this (they had no where to be, right!?):

A cardboard stellated icosahedron

It’s a stellated icosahedron, made out of these little triangular pyramids. I did not make the pyramids, they came to me this way. Can you guess what their original purpose was?

Pop quiz: What do you think this is??

My wife and I redid our kitchen a few years ago, and I saved twenty of these from (did you guess it yet?) the packaging our cabinets came in. For each cabinet, there are 8 of these keeping the corners safe. The construction process was pretty straight forward, but here are some photos documenting the event.

Construction begins

Every vertex looks like this on the inside.

Almost done!

The last piece goes on.

Here are some more views of the icosahedron. The icosahedron has a symmetry group of size 60.

There are 15 pairs of opposite edges, each with 2-fold symmetry (for a total of 15 orientations, not counting the identity)

There are 10 pairs of opposite faces, each with 3-fold symmetry (for a total of 20 orientations, not counting the identity)

There are 6 pairs of opposite vertices, each with 5-fold symmetry (for a total of 24 orientations, not counting the identity)

So (1 identity) + (15 edge symmetries) + (20 face symmetries) + (24 vertex symmetries) = 60 total orientations.

Now I just need to find a large enough Christmas tree upon which to put this giant star!

9999

Happy 9999th day of life to Mr. Chase!

I’d like to see 9999 candles on a cake!

Actually, I guess tomorrow is the big day. Maybe I’ll post again then .

Bonus points for:

1. calculating my age (easy)
2. calculating my birthday (a bit harder)

What graphing calculators are really used for

from graphjam.com, as usual

At least, this is true for students that don’t go to RM. I’m sure most students at RM use their calculators for exclusively academic purposes. Right? Right?

First Day of School!

I just wanted to let everyone know that I’m back, and excited for the new school year.  I took a little summer break from blogging, just like I did from teaching .

Today was our first day of school at Richard Montgomery High School, where I teach. (And we actually did have school today, even though we had both a 5.8 earthquake and an ‘historic’ hurricane in the last week.) So welcome back to all my current and former students!

Happy Spring Break!

Here’s an RM-spirited Easter egg I painted and thought you’d like . Hope everyone had a great spring break!

Obligatory π Day Post

Happy π-day.

 

We had lots and lots of pie, cookies, chips, cheese balls, and other ’round’ snacks today. A fun excuse for a party . I showed them a powerpoint with some interesting facts about π. One of my classes even got to whoop and holler at 1:59:26.

I showed some of my classes this:

 

And I showed one of my classes this, which was put up just today by Vi Hart (bonus: see if you can find the small error in this video):

 

I’m not sure where I stand on the whole Tau thing. I do think it helps with learning the unit circle and trig values. But I’m not convinced it makes most formulas simpler. And history is a force to be reckoned with. There is lots of mathematical notation that could use some revision, I suppose.

 

Congratulations, Ray!

In follow up to my post from Tuesday,

Congratulations to Raynell Cooper who won big last night in the final match of the Jeopardy Teen Tournament!!

From Jeopardy.com

Here’s an excerpt from the press release on the Jeopardy website, at which you can also watch a video interview with Ray:

CULVER CITY, CALIF. (March 2, 2011) – Raynell Cooper, a senior at Richard Montgomery High School from Rockville, Md., has won the “Jeopardy!” Teen Tournament, earning the $75,000 grand prize.

Regarding his win, Cooper said, “It was unreal. I honestly didn’t think I’d make it that far.” He added, “I’m so happy that all my hard work paid off.”

One of the major highlights for Cooper was seeing Alex Trebek in person. He said, “I don’t get the chance to see celebrities often, so it was pretty amazing.” He also enjoyed meeting his fellow contestants. “We all got along wonderfully. They were excellent players and incredible people.”

Cooper, 16, hopes to attend George Washington University and will use his earnings towards tuition. He also plans to buy a car and donate to charity to help underprivileged youth in his community.

In his spare time, Cooper enjoys participating in his school’s drama club. He is also captain of the academic team and student government vice president.

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