16 (
sixteen) is the
natural number following
15 and preceding
17.
16 is a
composite number, and a
square number, being
4^{2} = 4 × 4. It is the smallest number
with exactly five
divisors, its proper
divisors being , , and .
In speech, the numbers 16 and 60 are often confused. When carefully
enunciated, they differ in which syllable is
stressed: 16 vs 60 . However, in dates
such as
1666 or when contrasting numbers in the
teens, such as
15, 16, 17, the stress shifts to the first
syllable: 16 .
Sixteen is the fourth
power of two. For
this reason, 16 was used in weighing light objects in several
cultures. The British used to have 16 ounces in one pound, the
Chinese used to have 16 liangs in one jin. In old days, weighing
was done with a beam balance to make equal splits. It would be
easier to split a heap of grains into sixteen equal parts through
successive divisions than to split into ten parts. Chinese Taoists
did finger computation on the trigrams and hexagrams by counting
the finger tips and joints of the fingers with the tip of the
thumb. Each hand can count up to 16 in such manner. The Chinese
abacus uses two upper beads to represent the 5's and 5 lower beads
to represent the 1's, the 7 beads can represent from a hexadecimal
digit from 0 to 15 in each column.
In mathematics
As a power of 2 it has an
aliquot sum
one less than itself;
15, and is the fifth
composite member of the 3-aliquot tree having the 7 member aliquot
sequence (
16,
15,
9,
4,
3,
1,0).
Sixteen is the second number to be the
aliquot sum of a lesser number;
12, it is also the
aliquot sum
of the greater discrete
biprime 26. It is the fourth
power of
two.
Sixteen is the only integer that equals
m^{n} and
n^{m}, for some unequal integers
m and
n (
m = 4,
n = 2, or vice versa). It has this property
because 2
^{2} = 2 × 2. It is also equal
to
^{3}2 (see
tetration).
15 and 16 form a
Ruth–Aaron
pair under the second definition in which repeated prime
factors are counted as often as they occur.
Since it is not possible to find sequences of 16 consecutive
integers such that each inner member member shares a factor with
either the first or the first member, 16 is an
Erdős–Woods number. The
smallest such range of 16 consecutive integers is from 2184 to
2200.
16 is a
centered pentagonal
number.
16 is the base of the
hexadecimal number
system, which is used extensively in
computer science.
16 appears in the
Padovan sequence,
preceded by the terms 7, 9, 12 (it is the sum of the first two of
these).
In science
Age 16
- Sixteen is the minimum age for being allowed
an official beginners driver's
license with parental consent in many U.S. states and
in Canada.
In
Australia, Iceland and Norway, it is the
age one can begin to get a learner's licence.
- In
some states in the U.S, and some provinces in Canada, it is the
age one can obtain a learner's permit.
- Sixteen is the minimum age for getting an adult job in most
states and provinces across the globe.
- Sixteen is the minimum age that one can drop out of school in
most states of the US (however, restrictions apply and vary
depending on state).
- In the United States, female sixteen year olds earn the right
to privacy laws surrounding OBGYN practices.
- In the
Netherlands, Belgium and Italy, it is the
legal minimum age for a person to purchase any tobacco
product.
- Sixteen is the age of consent for
many jurisdictions around the world.
- For its "coming of age" significance, this age has inspired the
titles of many songs, such as "Happy Birthday Sweet
Sixteen", "You're
Sixteen", "Sweet Sixteen",
"U16 Girls" "Sweet Little Sixteen" and
"Sixteen Candles", the last of
which was borrowed as the title of a John Hughes movie. (This last one was
also parodied in a novelty song by The Mothers, titled "Eddie Are
You Kidding?", a tribute to the Los Angeles clothing store Zachary All; the tag line is
"Sixteen Tailors...")
- Sixteen is the minimum age to get married
with parental consent in many countries and without parental
consent in Scotland.
- Sixteen is the legal drinking age in France, Germany, Belgium, Austria, Italy, The
Netherlands and Portugal.
- In
The
Netherlands, sixteen is
the age when all adult rights are granted, but the age of majority is 18.
- Minimum age at which one can buy, rent, purchase, buy tickets
to, or view a 16+ rated movie in the province of Quebec. It is also
the minimum age at which one can accompany a minor under 13 while
buying, renting, or purchasing tickets to a 13+ rated movie in the
province of Quebec.
- Minimum age at which one can donate blood with parental consent
in many states.
- Minimum age at which one can obtain a 10 year passport in the
U.S.
In sports
Football
Baseball
Hockey
- The number 16 is retired by the Philadelphia Flyers in honor of
Bobby Clarke.
- Also, not used by any Detroit Red Wing player, in honor of
Vladimir Konstantinov.
Auto Racing
- Greg Biffle is currently the driver of the number 16 car in the
NASCAR Sprint Cup Series.
In other fields
- "The Sixteen" is an English choir
performing early religious music.
- Sixteen is a
Polish band that represented Poland in the
1998 Eurovision Song
Contest.
- The Cadillac Sixteen.
- There are sixteen different personality types in the Myers-Briggs classification system.
- A note played for one-sixteenth the duration of a whole note is called a sixteenth note or a semiquaver.
- In the 16-bit era, 16-bit microprocessor ran 16-bit applications.
- Sixteen Kingdoms, part of
Chinese history.
- Canada's Yellowhead Highway is designated as
Highway 16.
- Interstate 16
is the designation for a US interstate highway in Georgia.
- The fighter jet, the F-16
Fighting Falcon.
- 16 mm film was originally an amateur
movie format, but is now used by
professionals.
- 16 is a song by Green Day on their
album 39/Smooth.
- 16 is one of The
Numbers - 4, 8, 15, 16, 23, and 42 - featured in Lost.
- The M16 rifle.
- The number 16 is the symbol of the Day of solidarity with
political prisoners and victims of the Lukashenka regime in
Belarus, which is commemorated on 16th of every months by
demonstrations and flash mobs worldwide.
- A sixteen is a slang term for a verse in a hip hop song, which
are often written in sixteen-bar
stanzas.
- Android
16 of the Dragonball Z television
series.
- The amount of waking hours in a day in an "8 hours of sleep"
schedule.
- In the story of the Sleeping
Beauty, a spell is placed on the princess that when she reaches
her 16th birthday, she will "prick her finger on the spindle of a
spinning wheel and die."
- 16 is
the number of the French department Charente
- Many bank card numbers are 16
digits long.
References
- R. K. Guy,
Unsolved Problems in Number Theory New York:
Springer-Verlag (2004): B28
- Lesson plan explaining the reasoning behind the
hip-hop slang "sixteen"