# Liberal Arts Blog — Geometry V: Hymn to the Pentagon

Liberal Arts Blog — Monday is the Joy of Math, Statistics, and Numbers Day

Today’s Topic — Geometry V: Hymn to the Pentagon

So far: the triangle, the circle, the square, and the hexagon. Next week, the octagon. The week after the parabola. Today, the pentagon. Most famous for being the shape of the headquarters of the US Department of Defense, it is also the shape of the starfish, the morning glory, and the cross-section of an okra, The sum of all the internal angles is 540 degrees. Experts — please chime in. Correct, elaborate, elucidate.

THE PENTAGON — Five sided, five floors, five concentric rings

1. With 6 MM square feet of space and 17.5 miles of hallway, the largest office building in the world.

2. Ground broken in 1941, dedicated in 1942. In charge of project: Leslie Grove, later more famous as the guy in charge of the Manhattan Project.

3. The five acre central plaza is nicknamed ‘ground zero.’

NB: Do you believe in the magic of the number five? I do. Five fingers on the right hand, five on the left, five on the right foot, five on the left. A great way to remember anything important is to reduce the problem to five dimensions and assign each a finger. Examples: the five keys to a good society or the five keys to being a good person. Then draw a pentagon and assign each vertex a virtue. The most important challenge: which to put at the apex (ie. the middle finger)?

PENTAGONAL FLOWERS INCLUDE THE MORNING GLORY

1. The morning glory blooms for only one day.

2. But the plants are prolific and a new flower will soon take the place of the last one.

3. The cross section of an okra is pentagonal.

NB: The five carpels of the gynoecium of an apple form a five-pointed star as does the starfruit. Among animals, you have, of course the starfish.

HOME PLATE AND THE SOCCER BALL

1. First, second, and third base are square. Home plate is a pentagon. But not an equilateral one. It is an irregular isosceles pentagon. The two parallel sides are 8.5 inches in length, the angled sides 12 inches, and the base 17 inches.

2. A standard soccer ball has 12 black pentagons and 20 white hexagons.

3. A little math challenge to end this post: what are the measures of the central angles of an equilateral pentagon? Check out the last link for a cool way to figure it out.

YOUR TURN

Any thoughts on pentagons? Please share the coolest thing you learned this week related to math, statistics, or numbers in general. Or, even better, the coolest or most important thing you learned in your life related to math. This is your chance to make someone else’s day. And to consolidate in your memory something you might otherwise forget. Or to think more deeply than otherwise about something dear to your heart. Continuity is key to depth of thought.