How do we know the genetic code? (Part 1)

Over the course of the next few posts, I hope to tell you the story behind one of the most important codebreaking efforts in history.  The code at the center of this story does not concern itself with assassination conspiracies or terrorist plots.  There is no political intrigue or corporate espionage.  No couriers are relieved of their parcels (or their lives) during a clandestine midnight ride.  The code of which I speak isn’t really much of a code at all; its message can be read in the very faces of those who carry it.  And every single one of us, and everyone we know or have ever known or will ever know, carries this code with us.

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How do we know that sin²&#952+cos²&#952=1?

I’m already late for this week’s post and I’m nowhere near done with the one I intended to post.  So here’s a really quick post for the time being.  You can probably already answer it yourself if you think a little bit about it.  The equation sin^2\theta+cos^2\theta=1 may or may not be familiar to you from geometry or trigonometry, but it’s dead easy to prove.  We use good old “soh cah toa.”  For those of you scratching your heads in bemusement at this point, soh cah toa is a mnemonic for “sine is opposite over hypotenuse, cosine is adjacent over hypotenuse, tangent is opposite over adjacent.”  A few of you may really be puzzled now.  What I’m referring to is the definitions of the sine, cosine and tangent functions.  They’re defined in terms of the lengths of the sides of a right triangle, as seen below:

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