## Numbers and Measurement Facts

"Infinity is a fathomless gulf into which all things vanish"
- Marcus Aurelius

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Names for numbers prior to 1974 Name | U.S. | U.K. |
---|

Millard | — | 10^{9} |

Billion | 10^{9} | 10^{12} |

Trillion | 10^{12} | 10^{18} |

Quadrillion | 10^{15} | 10^{24} |

Quintillion | 10^{18} | 10^{30} |

Sextillion | 10^{21} | 10^{36} |

Septillion | 10^{24} | 10^{42} |

Octillion | 10^{27} | 10^{48} |

Nonillion | 10^{30} | 10^{54} |

Decillion | 10^{33} | 10^{60} |

Undecillion | 10^{36} | 10^{66} |

Duodecillion | 10^{39} | 10^{72} |

Tredecillion | 10^{42} | 10^{78} |

Quattuordecillion | 10^{45} | 10^{84} |

Quindecillion | 10^{48} | 10^{90} |

Sexdecillion | 10^{51} | 10^{96} |

Septendecillion | 10^{54} | 10^{102} |

Octodecillion | 10^{57} | 10^{108} |

Novemdecillion | 10^{60} | 10^{114} |

Vigintillion | 10^{63} | 10^{120} |

Centillion | 10^{303} | 10^{600} |

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, Nicolas 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). (source)

A *googol* is the name for the number 10^{100}, 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 10^{100}. This number would be written as 1 followed by 10^{100} 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. (source)

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. (source)

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. (source)

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. (source)

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. (source)

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 ⅔ 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.

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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. (source)

The foot as a unit of length is defined today as 0.3048 metres, but during the reign of Edward VI (1547–1553), the foot was defined as follows, according to a book published at that time: "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." (source)

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. (source)

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. (source)

The word "mile" comes from the Roman *milia*, "thousands". The Romans measured distances in paces (from left foot to left foot; we would regard these as double paces), which were about five feet. So, *milia passuum*, 1,000 paces or about 5,000 feet, was the length of a mile. (source)

The length of a mile was once 5,000 feet exactly. 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. (source)

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 the ounce. (source)

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. (source)

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. (source)

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. (source)

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. (source)

A portion of the Rhind Mathematical Papyrus containing the work's title.

One of the oldest surviving works 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". (source)

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. (source)

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. (source)

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. (source)

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 in Europe 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.

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