## Monday Morning Math: 24

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Instead of a mathematician today, we’ll look at the number 24.  (Thanks to Kevin Laley for the suggestion to revisit  Adam Spencer’s Book of Numbers: A bizarre and hilarious journey from 1 to 100!  Wolfram Alpha was also a nice resource.)

• 24 =4!
• 24 can be written as $2^2+2^2+4^2$, which is the same thing as $2^2+2^2+2^4$ and also $2^2+2^2+2^{2^2}$
• 24 is the smallest number that can be written as a sum of 2 primes in three different ways.  (Can you find them?)
• It is possible to draw a regular icositetragon (that’s a 24-gon and yes I had to look it up) using a straightedge and compass.  I don’t think it would be too hard, either – I’d start with a regular hexagon, which you can draw using equilateral triangles, and which happens to be part of the homework assignment for the Geometry students this past weekend.
• There are 24 hours in a day.  This apparently comes to the United States from a path starting with Egypt (via Babylon, where the hour was then divided into 60 minutes) although China also had 24 hours in a day.
• There are 24 letters in the Greek alphabet, alpha to omega.  Omicron is the 15th letter, in case you were wondering.
• Pure gold is 24 karat.   If you want to make fancy desserts like on The Great British Baking Show then you want  your gold to be 22-24 karats.