Monte Carlo method
1 and Monte Carlo method are also called statistical simulation method and statistical test method. It is a numerical simulation method with probability phenomenon as the research object. It is a calculation method to estimate unknown feature quantity by obtaining statistical value according to sampling survey method. Monte Carlo is a famous casino in Monaco. The law is named to show the essence of its random sampling. Therefore, it is suitable for the calculation and simulation test of discrete systems.
2. In calculation and simulation, we can simulate the random characteristics of the system by constructing a probability model similar to the system performance and conducting random tests on a digital computer. ?
Secant iteration method
1, tangent circle iteration method uses the inner tangent polygon of the circle as the outer tangent polygon. By increasing the number of tangents of polygons to a certain value, the perimeters of two polygons (circle and regular polygon) are approximately equal, thus π and n are obtained, and then calculated.
2. The principle of secant circle method is to make the length of vertical line segment close to the diameter of circle by gradually reducing the side length of square, so as to calculate the approximate value of pi. After each round cutting, the vertical line and tangent point of the circle can be used as the sides of the new square, and the round cutting operation can be repeated to continuously approach the shape of the circle. The advantage of secant circle method is simple and easy to understand, and it can be calculated only with some basic geometric knowledge.
It does not depend on complicated mathematical theory and is suitable for beginners. The accuracy of determining pi depends on the number of times the circle is cut. Every time the circle is tangent, it will approach the circumference of the circle, so the more times the circle is tangent, the closer the calculation result is to the real pi. Secant circle method is an ancient and simple method to find pi.
It obtains the approximate value of pi by cutting the circle step by step and using the geometric relationship. Although the result is not accurate, the tangent circle method intuitively explains the calculation process of pi, which is suitable for beginners to understand. Using this method, the true value of pi can be approached continuously in the process of repeated calculation.
Mechin formula
The form of McKin formula is: where sum is a positive integer, and it is a non-zero integer and a positive integer. The application of Machin formula can be combined with Taylor series expansion of arc tangent function. Pi is a mathematical constant of the ratio of the circumference to the diameter of a circle.