# Square Root Day? How about Pythagorean Day?

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 ?

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.

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. ;-)

You mean 2025?

Oh. my bad. yeah. 2005.

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 …

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.

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

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

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

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: so and so and the angles are 30-60-90….

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

Not August 8?

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

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…)

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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Aw, this was a very good post. Taking the time and actual effort to make a very good article… but what can I say…

I put things off a whole lot and don’t manage to get anything done.

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