Greek letter: π
Capital letter: π
Lowercase letter π
Pi, generally expressed by π, is a common mathematical constant in mathematics and physics. It is defined as the ratio of the circumference to the diameter of a circle. It is also equal to the ratio of the area of a circle to the square of its radius. Accurate calculation of geometric shapes such as circle perimeter, circle area and sphere volume is the key value. In the analysis, π can be strictly defined as the smallest positive real number x satisfying sin(x) = 0.
Second, radian.
π= 180 degrees
Third, use.
Capital letter π:
Product operator in mathematics
Find the total product, see π.
Lowercase letter π
π refers to pi in geometry. The ratio of circumference to diameter of any circle is a fixed value π, which is an infinite acyclic decimal, usually 3. 14.
Fourth, mathematics.
Constant pi ≈3. 14 Preliminary calculation of Zu Chongzhi (China) 3. 14 15926
∏ In mathematics, it is multiplication.
Verb (abbreviation for verb) function
(mathematics) π(n) is the number of prime numbers not greater than n.
π in particle physics
The intransitive verb profit
Inflation rate in economics.
Seven. Ethnicity
1, experimental period
An ancient Babylonian stone tablet (about BC 1900 to BC 1600) clearly recorded that pi = 25/8 = 3. 125. Rhind papyrus, an ancient Egyptian cultural relic of the same period, also shows that pi is equal to the square of score 16/9, which is about 3. 1605. [5] The Egyptians seem to have known pi at an earlier time. British writer john tyler (1781–1864) wrote in his masterpiece The Great Pyramid: Why was it built and who built it? ) It is pointed out that the pyramid of khufu built around 2500 BC is related to pi. For example, the ratio of the circumference to the height of a pyramid is equal to twice the pi, which is exactly equal to the ratio of the circumference to the radius of a circle. The Brahman of Sa tabata, an ancient Indian religious masterpiece written from 800 to 600 BC, shows that pi is equal to 339/ 108, which is about 3. 139.
2. Geometric method cycle
As an ancient geometric kingdom, ancient Greece made great contributions to pi. Archimedes (287–2 BC12), a great mathematician in ancient Greece, initiated the theoretical calculation of the approximate value of pi in human history. Starting from the unit circle, Archimedes first found that the lower bound of pi was 3 by inscribed regular hexagon, and then found that the upper bound of pi was less than 4 by pythagorean theorem. Then, he doubled the number of sides of inscribed regular hexagon and circumscribed regular hexagon to inscribed regular hexagon 12 and circumscribed regular hexagon 12 respectively, and then improved the upper and lower bounds of pi with the help of Pythagorean theorem. He gradually doubled the number of sides inscribed with regular polygons and circumscribed with regular polygons until inscribed with regular polygons and circumscribed with regular polygons. Finally, he found that the upper and lower bounds of pi were 223/7 1 and 22/7, respectively, and took their average value of 3. 14 185 1 as the approximate value of pi. Archimedes used the concepts of iterative algorithm and bilateral numerical approximation, which is the originator of computational mathematics.