yellowpigs.net

Seventeen

Seventeen is the most interesting number. It is far superior to the number 23. It is, of course, the number of eyelashes on a yellow pig. Being such an interesting number, David Kelly, a math professor at Hampshire College gives a lecture on it every year. The following notes were taken from the lecture he gave on July 17, 1995.

• The modern Italians foolishly think that 17 is unlucky, and they are very superstitious concerning it. For instance, Air Italia has no 17th row, Italian buildings do not have a seventeenth floor, and when the Granault R17 went to Italy, it's name was changed to R117. Part of the reason that Italians do not like 17 is that XVII rearranged spells vixi, which means "I am dead."
• The Bible, disappointingly, contains only 16 references to 17, mostly numbers of troops or days or books. The shortest book of the Bible is the 17th, Obadiah. The shortest verse of the Bible is in Psalm 117, which is also the midpoint. The great flood started on the 17th day of the month, and the ark landed on the 17th day of a different month on Mt Ararat (elevation approximately 17000 feet).
• The Pythagoreans, being number-obsessive, doubtless had much to say about the number 17. Plutarch records "The Pythagoreans also have a horror for the number 17, for 17 lies exactly halfway between 16, which is a square, and the number 18, which is the double of a square, these two, 16 and 18, being the only two numbers representing areas for which the perimeter equals the area".
• The 17th triangular number is 153. The 17th tetrahedral number is 969, the greatest tetrahedral number less than 1000. The 100th tetrahedral number is 171700.
• The ancient Greek architects also knew the sanctity of the number 17, and put 17 columns on the long side of the Parthenon.
• The Alhambra, a Moorish castle in Spain contains 17 different tiling patterns, which is actually the total number of possible tilings with triangles by translation and rotation patterns. Also, there are 17 distinct ways to fit polygons around a point.
• The 17th century was a time of great importance in history. Shakespeare wrote plays. His 17th was Much Ado about Nothing, and Hamlet was king for 17 years. The 17th century also marked the height of Haiku poetry (17 syllables) in Japan.
• Gauss started a journal 200 years ago with "We discovered that a circle is geometrically divisible into 17 parts."
• There are 17 non-Abelian groups of order less than or equal to 17.
• Any sequence of fewer than 17 consecutive positive integers contains one number relatively prime to all the other terms.
• A complete graph of 17 points can be colored along edges with three colors such that there is no monochromatic triangle. In other words, the Ramsey number (3,3)=17.
• A hypercube must be cut along 17 faces to unfold into a three-dimensional cross.
• The White House has 17 bathrooms. There are 17 miles of corridors in the Pentagon.
• The world's largest pie was 17 feet in diameter.
• Ohio was the 17th state admitted to the Union, the first one not admitted in the 1700s, has 17 exits on its turnpike, and boasts a town called Seventeen. (Really, I've been there.)
• There are 17 species of penguins, and among penguins, the divorce rate is 17%. Penguins are the fastest swimming birds, and can swim with bursts of over 17mph.
• In The Glass Menagerie (17 letters) by Tennessee Williams (17 letters), Amanda had 17 gentleman callers in one day. At age 17, Jack London wrote the first of his 17 books.
• Benjamin Franklin, born January 17, was one of 17 children and moved to Philadelphia at age 17. There were 17 women among the 117 colonists who settled at Roanoke, and more than 17% of them disappeared.
• The average giraffe's tounge is 17 inches long. There are 17 muscles in a horse's ear. A camel can go 17 days without water. A three-toed sloth moves up to 17/100 of a mph.
• It takes 17 muscles to smile and 43 to frown. The average person breathes 17 times per minute and turns in their sleep once every 17 minutes. The average teenage male has a sexually related thought every 17 seconds.
• 17 feet diameter is believed to be the limit of what is practical.
• On Yellow Pigs Day (July 17) in 1717, Handel's Water Music was first performed. On Yellow Pigs Day in 1901, the Wright brothers began testing. Wilbur (some pig) did all of the flying for the 17 glides. The Apollo-Soyuz handshake was on a Yellow Pigs Day, and there were 17 Apollo missions. On Yellow Pigs Day in 1969, seven polar bears in the Chicago Zoo broke out and swam through a moat to raid a refreshment stand.
• There are almost 17 ounces in a pound.
• Leonardo DaVinci painted more than 17 paintings.
• 17 is the only prime exactly equal to 17.
• A map of the thirteen original colonies cannot be colored with 17 colors.

See also this paper by another HCSSiM alum on the properties of 17.