Post by mccjeff on Oct 19, 2016 9:00:22 GMT -5
Among his accomplishments as a mathematician is
deriving two approximations of pi, (3.1415926538932...) which held as the most accurate approximation for π for over nine hundred years. His best approximation was between 3.1415926 and 3.1415927, with 355/113 (密率, milü, close proportion) and 22/7 (約率, yuelü, approximate proportion) being the other notable approximations. He obtained the result by approximating a circle with a 24,576 (= 213 × 3) sided polygon. This was an impressive feat for the time, especially considering that the device Counting rods he used for recording intermediate results were merely a pile of wooden sticks laid out in certain patterns. Japanese mathematician Yoshio Mikami pointed out, "22/7 was nothing more than the π value obtained several hundred years earlier by the Greek mathematician Archimedes, however milü π = 355/113 could not be found in any Greek, Indian or Arabian manuscripts, not until 1585 Dutch mathematician Adriaan Anthoniszoon obtained this fraction; the Chinese possessed this most extraordinary fraction over a whole millennium earlier than Europe". Hence Mikami strongly urged that the fraction 355/113 be named after Zu Chongzhi as Zu's fraction.[1] In Chinese literature, this fraction is known as "Zu's ratio". Zu's ratio is a best rational approximation to π, and is the closest rational approximation to π from all fractions with denominator less than 16600.
deriving two approximations of pi, (3.1415926538932...) which held as the most accurate approximation for π for over nine hundred years. His best approximation was between 3.1415926 and 3.1415927, with 355/113 (密率, milü, close proportion) and 22/7 (約率, yuelü, approximate proportion) being the other notable approximations. He obtained the result by approximating a circle with a 24,576 (= 213 × 3) sided polygon. This was an impressive feat for the time, especially considering that the device Counting rods he used for recording intermediate results were merely a pile of wooden sticks laid out in certain patterns. Japanese mathematician Yoshio Mikami pointed out, "22/7 was nothing more than the π value obtained several hundred years earlier by the Greek mathematician Archimedes, however milü π = 355/113 could not be found in any Greek, Indian or Arabian manuscripts, not until 1585 Dutch mathematician Adriaan Anthoniszoon obtained this fraction; the Chinese possessed this most extraordinary fraction over a whole millennium earlier than Europe". Hence Mikami strongly urged that the fraction 355/113 be named after Zu Chongzhi as Zu's fraction.[1] In Chinese literature, this fraction is known as "Zu's ratio". Zu's ratio is a best rational approximation to π, and is the closest rational approximation to π from all fractions with denominator less than 16600.
