A Sal Khan Proof

Now why would I post on my blog this video showing (proving) that perpendicular lines have negative reciprocal slopes? Why a mathematical proof, and why this one? Well this one happened to arrive in my inbox just today and I had the time to look at it. And in this video it was Sal himself doing the proving. That’s important. I pretty much avoid listening to KA videos when it’s not Sal himself doing both video and audio. Khan Academy is still for me the original videos of Sal Khan, himself at the time a young graduate of MIT.

When was that, when did Sal begin doing his thing? Well it was years ago, that I know. In fact, it was 2006 as I learn from doing a quick Google search. A bit earlier, in late 2003, Khan had begun tutoring his cousin, Nadia, in mathematics over the internet using Yahoo!‘s Doodle notepad.

I was “with” Sal from the start, one of his first viewers. I was teaching myself the Calculus (once again, because like the solution to Rubik’s Cube I never seem to remember all the steps and need to be continually reminded as I try once again to walk through them) and Sal’s 10 min videos were always just about perfect for my needs and abilities, in additional to their being in Sal’s own inimitable manner always delightful. Now of course there are millions of us, tens of millions (hundreds of millions throughout the world?) who make use of Khan Academy, probably all like me, for their own purposes.

But about my question, why would I post this video on my Blog. There are hundreds/thousands of other KA proofs there for the borrowing, many probably more beautiful and interesting than this one. Well this one just happened to be there today in my inbox. And this proof like so many others is thing of beauty, and that’s why the post.

Mathematics itself if a thing of beauty but only a few are aware of this. Most don’t make it beyond halting first steps in highschool algebra, and wouldn’t even have even been there if they hadn’t been compelled by adults. In fact, for many mathematics is what drove them to leave school or later change careers. And this was and still is too bad. For I believe that everyone is capable of knowing the beauty of mathematics, the beauty of a mathematical proof such as the slopes of perpendicular lines are negative reciprocals of one another, but very few ever do. The proof is on my blog for that reason alone. Would that others might share with me this thing of beauty.

Maybe in another blog I’ll talk about the Calculus and some of Sal’s calculus proofs. Sal himself never tires of saying how overwhelmed he is (he says he’s “tingling”) as he reaches yet again the final steps of this or that proof on the board that we’re seeing on our computer screens.

And one can sense the beauty of the calculus without being totally fluent, much as one can sense the beauty of a second or third language without  yet being fluent in that language. For all my own inability, for my countless stumbling steps in mathematics, and in particular in the calculus, I’ve never doubted the beauty of the subject matter, and I’ve always, well not always, but since becoming an adult, positioned it right up there with all the greatest artistic and scientific achievements of mankind.

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