in turn, led to a better approximation of pi (π). Through his iterations, he determined
that 223/71 < π< 22/7; the average of his two numbers equals 3.141851 (and so on).
(For more about Archimedes, see “History of Mathematics” and “Geometry and Trig-
onometry.”)How was the value of pi determined arithmetically?
One of the earliest mathematical formulas for pi was determined by English mathe-
matician John Wallis (1616–1703), who wrote the notation as:
2/π(1.3.3.5.5.7. ...) / (2.2.4.4.6.6. ...)
Another more commonly recognized notation for pi is often attributed to German
philosopher and mathematician Baron Gottfried Wilhelm Leibniz (1646–1716), but it
is more likely the work of Scottish mathematician James Gregory (1638–1675):π/4 1 1/3 1/5 1/7 ...
Both are amazing examples of something that was not only figured out using geo-
metric methods but also arithmetic methods.What are the measurementsof a circle using pi?
There are many measurements of a circle. The perimeter of a circle is called the cir-
cumference;to calculate it, multiply pi (π) times the diameter, or c(πd), or pi (π)
times twice the radius, (c 2 πr). The area (a) of a circle is calculated by multiplying
40 pi (π) times the radius squared, or aπr^2.
Who first suggested the symbol for pi?
T
he symbol for pi (π) was used by English mathematician William Oughtred
(1575–1660) in 1647, to describe “periphery,” or the then-common term for
circumference. But the symbol also meant a number of other things, including a
point, a positive number, and various other representations. The symbol was
again used in 1697 by Scottish mathematician James Gregory (1638–1675), who
used it as π/r for the ratio of the circumference of a circle to its radius; but he
never truly wrote down his formulas containing pi. The modern use of πdidn’t
occur until 1706, when Welsh mathematician William Jones (1675–1749)
described it as “3.12159 andc. [sic] π.” Even then, not everyone used it as a
standard symbol for pi. By 1737, Swiss mathematician Leonhard Euler (1707–
1783), one of the most prolific mathematicians who ever lived, adopted the sym-
bol in his work, making πa standard notation since that time.