Fun Facts: Numbers and Measurement
"Infinity is a fathomless gulf into which all things vanish"
- Marcus Aurelius
For number puzzles and games, see the Number Games
More mathematics topics can be found on our sister site, the Math Lair
Names for numbers prior to 1974
|Trillion ||1012 ||1018
|Quadrillion ||1015 ||1024
|Quintillion ||1018 ||1030
|Sextillion ||1021 ||1036
|Septillion ||1024 ||1042
|Octillion ||1027 ||1048
|Nonillion ||1030 ||1054
|Decillion ||1033 ||1060
|Undecillion ||1036 ||1066
|Duodecillion ||1039 ||1072
|Tredecillion ||1042 ||1078
|Quattuordecillion ||1045 ||1084
|Quindecillion ||1048 ||1090
|Sexdecillion ||1051 ||1096
|Septendecillion ||1054 ||10102
|Octodecillion ||1057 ||10108
|Novemdecillion ||1060 ||10114
|Vigintillion ||1063 ||10120
Before 1974, a billion in the United States of America was different from
a billion in Great Britain.
An American or short scale billion was a thousand million (1,000,000,000), but a
British or long scale billion was a million million (1,000,000,000,000).
Other names for large numbers also differed between the two countries. Starting in 1974, however, the short scale numbers started to be used exclusively in Great Britain.
The original usage is the former British usage
(around 1484, N. Chuquet invented the words billion through nonillion to denote the second through ninth powers of a million, while around the middle of the seventeenth century, French arithmeticians began using these words to denote the third through tenth powers of a thousand).
A googol is the name for the number 10100, or 1 followed by 100 zeroes. (source)
The largest number in the English language with a word naming it is a googolplex. This number is equal to 10 to the power of a googol, or 10 to the power of 10100. This number would be written as 1 followed by 10100 zeroes (except that, as there are far fewer particles in the universe than there are zeroes in a googolplex, the number could never be written out in full). The names "googol" and "googolplex" were both suggested in the 1930s by Milton Sirotta, the nine-year-old nephew of mathematician Dr. Edward Kasner.
The first apparent record of counting dates from 30,000 years ago.
A leg-bone of a wolf was found in Czechoslovakia containing fifty-five cuts,
arranged in groups of five. It is not known what the cuts represented.
The earliest known standard of weight is the beqa,
an ancient Egyptian unit which equals from
6.66 to 7.45 ounces.
It is still generally used in weighing gems,
precious metals, and stones in troy weight.
The Piraha tribe in the Amazon jungle has no words to describe "one" or other numbers. While they have words for "some" or "more", specific numbers are not useful in their culture.
The classic work Principia Mathematica by Bertrand Russell and Alfred North Whitehead aimed to put mathematics on a solid foundation of logic. It is not until page 379 of volume 1 that enough of a foundation has been laid to prove that 1 + 1 = 2.
The ounce is most familiar as a unit of weight equalling 28.35 grammes
(avoirdupois measure), but in troy measure, it equals 31.1 grammes. As a
unit of length, an ounce equals 0.016 inches, and in volume it equals
2/3 of a whiskey jigger.
In 1266, Henry III of England decreed that "an English penny,
called a sterling, round and without any clippings, shall weigh
32 wheatcorns in the middle of the ear. Twenty pence do make an
ounce, and 12 ounces a pound". The English kings used troy
(named for the French town Troyes) weight for currency measurements,
and in 1527 it became the legal standard for minting coins.
One of the administrative changes that Edward I (1239-1307)
introduced during his reign as King of England (1272-1307) was to
recognize and legalize, in 1303, units of weight such as the ounce,
pound, wey, stone, and hundredweight.
Later, in 1335, these weight units were grouped together under the name
avoirdupois, a French word meaning "goods of weight", intended
mainly for use in trade.
A pound of feathers weighs more than a pound of gold. Precious metals
like gold are weighed using troy weights, in which a pound consists of 12
ounces (5,760 grains). Objects such as feathers are weighed using
avoirdupois weights, in which a pound consists of 16 ounces or 7,000 grains.
The foot as a unit of length is defined today as 0.3048 metres, but
during the time of Edward VI (1547–1553), the foot was defined as
follows, according to a book published during his reign:
"Stand at the door of a church on Sunday and bid sixteen men
to stop, tall ones and small ones, as they happen to pass out. Then make
them put their left feet one behind the other, and the length thus obtained
shall be a right and lawful rood to measure the land with, and the
sixteenth part of it shall be a right and lawful foot."
In 1852, the first official calculation of the height of Mount
Everest was performed. All six measurements that were made were
different. Averaging the six results (between 28,990 feet
and 29,026 feet), the result was 29,000 feet exactly. Unwilling to
publish a figure that just looked like an estimate, the people who
made the calculation arbitrarily added 2 feet to the value, giving
a value of 29,002 feet.
A "light year" is a measure of distance, not time.
It is defined as
the distance light travels in one year. Light moves at a velocity of about 300,000 kilometres each second, so in one year, it travels about 9,500,000,000,000 kilometres.
The word "mile" comes from the Roman milia, "thousands".
The Romans measured distances in paces, which were about five feet.
So, milia passum, 1,000 paces or about 5,000 feet, was the
length of a mile.
The length of a mile used to be 5,000 feet. However, in 1575
the British Parliament added 280 feet to this measurement, declaring the
mile to be 1,760 yards or 5,280 feet, so that it could be divided
evenly into furlongs. One furlong is 660 feet long, giving 8 furlongs
to the mile.
Until 1959, when the avoirdupois pound was established as 453.59237
grammes, the United States and Great Britain had different values for the
pound. The American version was 453.5924277 grammes and the British pound
453.592338 grammes. Similarly, the British and American inches differed
slightly (with the American inch 2.540005 centimetres, and the British
inch 2.539998 centimetres).
The carat was derived from the weight of a seed of the carob tree.
The weight of each bean is quite consistent, with about 142 beans to
Many European advances during the Middle Ages were made possible by
the Moorish occupation of Spain. The most important was the use of
Arabic numerals. The Moors also brought other discoveries to Europe,
which is reflected by the fact that words such as "algebra", "lute",
and "magazine" are of Arabic origin. The Moors also
introduced the game of chess into Europe.
Arabic numerals are not Arabic. While Europe obtained this system
from the Arabs, the Arabs in turn obtained this system from the Hindus
around the middle of the eighth century. The Hindu writer Aryabhata
first described the new system in the year 499. The invention of the
sign for zero made arithmetic computation much easier. In contrast,
calculation was more awkward in the Roman numeral system.
Napoleon was not particularly short. He was 5 feet 6½ inches tall,
which was a typical height at the time. This height is equal to 5 feet 2
inches in old French feet (pieds du roi), which led to confusion as
to his true height.
The number 10 is used as a convenient base to count with, but the
Gauls of ancient France, the Mayas of Central America, and other
peoples used a base of 20. The Sumerians, the Babylonians, and
others after them used a base of 60—convenient because 60 can be
evenly divided by 2, 3, 4, 5, 6, 10, 12, 15, 20, and 30. The use
of base 60 survives in the division of hours into minutes and minutes into
seconds, and the division of the circle into 360 (60 × 6) degrees.
The earliest known unit of length was used around 2,300 B.C. by
megalithic tomb builders in ancient Britain. Called the megalithic yard,
the name used by the builders is unknown, but its length was about 2.722 feet.
A portion of the Rhind Mathematical Papyrus containing the work's title.
The oldest surviving work about mathematics (the Rhind Mathematical Papyrus,
written by the ancient Egyptian scribe Ahmes around 1650 B.C.) is entitled
"The Entrance Into the Knowledge of all Existing Things and all Obscure Secrets".
Euclid is the most successful textbook writer of all time. His
Elements, written around 300 B.C., has gone through more
than 1,000 editions since the invention of printing.
Euclid worked out virtually none of the theorems of "Euclidian"
geometry, but rather collected the works of others. His great
accomplishment was that he arranged the theorems in such a logical
manner that the arrangement can barely be improved on.
Syracuse's leading citizen in the third century B.C. was the greatest
scientist and mathematician of ancient times, Archimedes, nine of whose
famous treaties on geometry and hydrostatics survive. When the Roman
consul Marcellus conquered Syracuse, he instructed his men that
Archimedes was not to be harmed. But Archimedes was run through by a
sword when he begged a Roman soldier not to destroy geometrical figures
he had drawn in the sand.
Gerbert of Aurillac, who became Pope Sylvester II (999–1003),
tried to introduce Arabic numerals into Christian Europe.
While calculation can be performed much easier with Arabic numerals than
with the Roman numerals in use at the time, Arabic numerals did not catch on
for a few more centuries.
King Richard I the Lion-Hearted passed the first law requiring
standards for length and volume. These standards were made from iron
and were kept by sheriffs and magistrates.
Leonhard Euler (1707-1783) was probably the most productive
mathematician of all time, publishing enough mathematical papers to
fill 90 volumes of books. Even though he became completely blind
at the age of 60, he still published over 400 mathematical papers,
most of which he dictated to a servant untrained in mathematics.
A theory put forward by Polish mathematicians Steven Banach and
Alfred Tarski in the early 20th century states that there
is a way of dividing a sphere into separate parts and rearranging them
so that they fill all of a larger sphere without leaving any gaps.
Girolamo Cardano, a sixteenth-century Italian physician and mathematician,
asserted that each face of a die will turn up exactly once in any given
six rolls, despite the fact that he was a notorious gambler and should
have observed quite the opposite at the gambling tables.