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Yesterday the whole world seemed to be discussing square root day. I ran a related activity in algebra, and was pleased by how the kids engaged.

So I went back to the well. Over at 360, TwoPi had suggested Pythagorean Day. I ran with it.

Today I wrote on the board,

Yesterday we found all the days in your lifetime for which the month times the day equaled the last two digits of the year. Today, a related question. For how many days in your lifetime $month^2 + day^2 = year^2$ ?

And I left it up. We worked on other things. The bell rang. And then some kids came up to discuss the problem. And other freshmen filtered in. They dismissed anything in the 1990’s. And then one kid found March 4, 2005. And it took almost 10 more minutes for them to find the second solution. I was surprised how long it took. And only one kid really got it.

1. March 6, 2009 am31 5:13 am 5:13 am

Takes me back to 9th grade Geometry when we had to memorize the formulas for 45 degree and 30-60-90 triangles. 3-4-5 is a 30-60-90, and that’s about the only one I remember. ;-)

March 6, 2009 am31 11:51 am 11:51 am

You mean 2025?

March 6, 2009 am31 11:56 am 11:56 am

March 6, 2009 pm31 10:06 pm 10:06 pm

I disagree with the first comment that a 3-4-5 triangle is the same as a 30-60-90 triangle. The small angle in a 3-4-5 triangle is the inverse tangent of 3/4, about 36.87 degrees …

• March 6, 2009 pm31 10:53 pm 10:53 pm

It’s a very easy mistake to make – most of us only learn about a few special right triangles, and easily conflate the fact about the sides and the fact about the angles.

4. March 7, 2009 am31 2:24 am 2:24 am

In their lifetime so far, or in their projected lifetimes — there are more in the future

• March 7, 2009 pm31 10:50 pm 10:50 pm

I meant lifetimes so far… I should have been more precise… thanks for the catch!

5. March 7, 2009 am31 8:33 am 8:33 am

Well, then you need to call Mr. Combs and tell him he was wrong. :-)

• March 7, 2009 pm31 10:49 pm 10:49 pm

You may be misremembering, or, and it seems unlikely, but it’s possible, he could have goofed. But use a ruler, draw a 3-4-5 right triangle, and then measure the angles with a protractor. Doesn’t work.

Or, consider an equilateral triangle with 2″ sides. That’s 60-60-60, right? Drop an altitude from one vertex to slice the triangle in half. Look at one half. The base is one. The hypotenuse is 2. We use Pythagoras to find the other side: $a^2 + b^2 = c^2$ so $1^2 + b^2 = 2^2$ and $1 + b^2 = 4$ so $b = \sqrt{3}$ and the angles are 30-60-90….

6. March 7, 2009 pm31 8:24 pm 8:24 pm

Someone needs to put up a counter to June 8, 2010!

• March 7, 2009 pm31 10:44 pm 10:44 pm

Not August 8?

March 9, 2009 am31 5:10 am 5:10 am

Help me improving the Wikepedia article, so we can keep it.

8. March 10, 2009 am31 6:22 am 6:22 am

My brother wanted to know why I didn’t mention anything about “Squares” Day on 3/3/9. I told him that I used Squares Day back on Jan 4 of this year.

My other favorite used to be telling students it was a “prime day for learning”, but I’m taking a bit of a break on that one. (Not that I had much choice…)

9. June 20, 2009 pm30 11:54 pm 11:54 pm

about the 3-4-5, 30-60-90 thing: there’s a blurb somewhere on cut-the-knot.com that says that an equilateral triangle is the ONLY triangle whose side lengths and angle measures can both be rational. Cool!

and i am so happy that you brought up 6/8/10…because that’s my birthday next year!!!

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11. June 26, 2013 pm30 9:17 pm 9:17 pm

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