## Monday, August 12, 2013

### How much Trig does your governor know?

How much math should our public officials know? Basic probability and statistics so they can follow the arguments that their science advisers give them. And they should hire good objective science advisers and listen to them.

How much Trigonometry should a Governor know? Should a Governor know the angles of a 3-4-5 triangle? The following true story is paraphrased from Somewhat more than Governors need to know about Trigonometry by Skip Garibaldi.

In June 2004 Governor Jeb Bush of Florida was giving a talk to promote state-wide annual testing of students in public schools. A high school student asked him What are the angles in a 3-4-5 triangle? He responded I don't know. 125, 90, and whatever is left to add up to 180. Note that (1) he knew that 3-4-5 triangle has a 90 degree angle, (2) he knew that the angles of a triangle add up to 180, but (3) he didn't realize that 125+90 > 180. Still, I suspect most governors would do worse. The real answer is 90, 53.1 (approx), 36.9 (approx). A retired math professor was later quoted as saying I would not expect many mathematicians to know that.

The paper then proves the following:

The Governors Theorem: If a right triangle has integer
side lengths then the acute angles are irrational when measured
in degrees.

When politicians say things that contradict current science (e.g., on evolution or global warming) I wonder if they know the truth and are lying to please their voters, or if they honestly don't know the truth.I also wonder which one is worse. In the case above I think Jeb honestly didn't know, and that's fine.