Friday, July 7, 2017

Cavalieri's What?

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Here is question 27 from the New York State Geometry Regents exam of June 2016.

One thing specifically stands out in this question. Cavalieri's Principle.

Students in New York do not have to remember the quadratic formula, how many feet in a mile, or even the Pythagorean Theorem. Those items are all on the Common Core High School Math Reference Sheet with which each student is supplied. 

But Cavalieri's Principle? That stands out. After all, everyone should know the main success of Felix Cavalieri, lead singer of the Lovin' Spoonful.

Oh, sorry, Wrong Cavalieri.

This Cavalieri is actually the gentleman who proved the formula for the volume of a general prism (which can be found on the reference sheet). 

I will admit that when I first read this question, I said to myself "what the heck is Cavalieri's Principle?" After a little research I was reminded that I had confronted it somewhere in my mathematical meanderings.

It does please me that NY has risen its standards and now expects students to remember and be able to apply Cavalieri's Principle. Now if they could only do that with the other items on the reference sheet...

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