What’s a Sadness Gap, You Ask?

I almost don't even want to tell you if you're studying for the SAT, because you really shouldn't worry your pretty little head about this.

They're rare -- in fact, so rare that I couldn't even find a single one in the entire Blue Book.  Not one.

UPDATE: Ok, one.  Stacey Howe-Lott found one in the Blue Book: Test 1, Section 7, Question 7 on page 415.

So what is a "sadness gap?"

It's officially known as the "Triangle Inequality Theorem," though when I heard it referred to as a "sadness gap" in PWNtheSAT's SAT Math Guide Beta Access, I thought, huh, how apropos. I've shed tears over this triangle question. In fact, I believe I gave up on math entirely in the 10th grade because of this "theorem."

When I say I've spent hours pouring over SAT books 30 years later in an attempt to finally understand this theorem in a way that will stick for more than a minute, I am not exaggerating.

Ok, here it is, Sadness Gap Explanation:

The basic thrust is this: if one side were longer than the sum of the other two, then how would those two shorter ones connect to form the triangle? They couldn't. And if one side was equal to the sum of the other two, would you have a triangle? No, you'd just have a straight line.

To drive this home: imagine your forearms (apologies to my armless friends) are two sides of a triangle, and the imaginary line that connects your elbows is the third side. If you touch your fingertips together and pull your elbows apart, eventually your fingertips have to disconnect...that's when the length between your elbows is longer than the sum of the lengths of your forearms. Neat, huh?

Do you get it?

I do.  For a second.  And then I don't.  But I will.  Because I want my 800.  And they could serve one up.  In fact, I've heard they have (though have yet to verify with my own eyes).*

Now go have fun, unless you want an 800.  And then it's better to be safe than sorry, but I feel your pain.

And if you haven't ordered PWNtheSAT's SAT Math Guide Beta Access, do it.  It's got the funny, which makes "sadness gaps" much more bearable.

And, it's filled with gems like this, The Pythagorean Triple.....

......which I can verify, having just finished all Blue Book triangle problems today, are prevalent.

*UPDATE: No sooner than I wrote that I hadn't seen a Sadness Gap with my own two eyes, then I saw one with my own two eyes:

I'm sort of surprised this is a #10.  Feels like a #19 to me.

Illustrations by Jennifer Orkin Lewis