pocket calculator for scientists and scholars for cen-
turies to come.
Oughtred was also an accomplished scholar in sev-
eral branches of mathematics. In 1631 he published an
influential text, Clavis mathematicae (The key to math-
ematics), in which he described the H
INDU
-A
RABIC
NUMERALS
and
DECIMAL REPRESENTATION
, and also
outlined concepts in algebra. (At that time, Roman
numerals were still in use.) He introduced the symbols
×for multiplication and :: for proportion. In 1657
Oughtred also wrote one of the first comprehensive
texts on
TRIGONOMETRY
, introducing concise notation
for the topic for the first time. He also studied
SPHERI
-
CAL GEOMETRY
and astronomy.
Surprisingly, Oughtred received very little formal
education in the topic of mathematics. He received a
master’s degree from King’s College, Cambridge, in
1600, and was ordained an Episcopal minister in 1603.
In 1604 he became the vicar of Shalford and, later, the
rector of Albury, Surrey.
Oughtred offered mathematics instruction to a
number of private students who came to his house and
would live there free of charge. The famous mathemati-
cian J
OHN
W
ALLIS
(1616–1703), for instance, was one
of his pupils. Oughtred died in Albury, England, on
June 30, 1660.
outlier An observation that is deemed unusual, and
possibly erroneous because it is widely separated from
the main cluster of points in the sample, is called an
outlier. For example, in the set {4, 8, 3, 6, 5, 6, 903},
the observation 903 is an outlier. Outliers may be cor-
rect observations reflecting some abnormality in the
system being studied, or they might be the result of an
error in measurement or recording. For example, 903
could be a mistyping of 9, 3.
See also
DATA
;
STATISTICS
:
DESCRIPTIVE
.
oval Derived from the Latin word ovus for “egg,”
the term oval is a generic name for any curved figure
that resembles an elongated circle. There is no precise
mathematical definition for this term.
An
ELLIPSE
is considered an oval. It is defined to be
the set of points Pwhose sum of distances from two
fixed points Aand Bin the plane is constant: |AP| +
|BP| = k. The set of all points Pthat have constant
product from two fixed points Aand B, |AP| ×|BP| = k,
also describe curves that can look like ovals. These
curves were first studied by 17th-century Italian
astronomer Giovanni Domenico Cassini (1625–1712)
and are today called the ovals of Cassini.
370 outlier
William Oughtred, a scholar of the 17th century, invented the
modern slide rule. (Photo courtesy of the Science Museum, Lon-
don/Topham-HIP/The Image Works)