Application of simple equation in grade five The simplest

Application of simple equation in grade five The simplest

There are two groups of students to pick flowers, group a picked 123, group B picked 57, ask how many flowers from group A to group B will make group B four times as much as group A? Use a 50 cm long, 40 cm wide rectangular iron sheet to make a 10 cm deep uncovered rectangular iron sheet box (regardless of the thickness of the welding iron sheet)

The formula of PI in grade six of primary school

Here's an all inclusive one
1² π=3.14 2² π=12.56 3² π=28.26 4² π=50.24 5² π=78.5 6² π=113.04 7² π=153.86 8² π=200.96 9² π=254.34 10² π=314 11² π=379.94 12² π=452.16 13² π=530.66 14² π=615.44 15² π=706.5 16² π=803.84 17² π=907.46 18² π=1017.36 19² π=1133.54 20² π=1256 21² π=1384.74
22² π=1519.76 23² π=1661.06 24² π=1808.64 25² π=1962.5 26² π=2122.64 27² π=2289.06 28² π=2416.76 29² π=2640.74 30² π=2826 31² π=3017.54 32² π=3215.36 33² π=3419.46 34² π=3629.84 35² π=3846.5 36² π=4069.44 37² π=4298.66 38² π=4534.16 39² π=4775.94 40² π=5024 41² π=5278.34 42² π=5538.96
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43² π=5805.86 44² π=6079.04 45² π=6358.5 46² π=6644.24 47² π=6936.26 48² π=7234.56 49² π=7593.14 50² π=7850 51² π=8167.14 52² π=8490.56 53² π=8820.26 54² π=9456.24 55² π=9498.5 56² π=9847.04 57² π=10201.86 58² π=10562.96 59² π=10930.34 60² π=11304 61² π=11683.94 62² π=12070.16 63² π=12462.66 64² π=12861.44
65² π=13266.5 66² π=13677.84 67² π=14095.46 68² π=14519.36 69² π=14949.54 70² π=15386 71² π=15828.74 72² π=16277.76 73² π=16733.06 74² π=17194.64 75² π=17662.5 76² π=18136.64 77² π=18617.06 78² π=19103.76 79² π=19596.74 80² π=200.96 81² π=20601.54 82² π=21113.36 83² π=21631.46 84² π=22155.84 85² π=22686.5 86² π=23223.44
87² π=23766.66 88² π=24316.16 89² π=24871.94 90² π=25434 91² π=26002.34 92² π=26576.96 93² π=27157.86 94² π=27745.04
95² π=28338.5 96² π=28938.24 97² π

PI formula
Clean up
An iron can with a bottom and a lid. It is 16 meters in diameter and 1.5 cm in thickness. What is the weight of the can?

The ancients generally used the method of cutting circle to calculate the circumference of a circle. Archimedes used the regular 96 polygon to get the accuracy of 3 decimal places of the circumference. Liu Hui used the regular 3072 polygon to get the accuracy of 5 decimal places. Rudolph used the regular 262 polygon to get the accuracy of 35 decimal places. This geometry based algorithm has a large amount of calculation and slow speed, With the development of mathematics, mathematicians have found many formulas for calculating pi intentionally or unintentionally. Here are some classic formulas to introduce. In addition to these classical formulas, there are many other formulas and the formulas derived from these classical formulas
1. Ma Qing formula
π=16arctan1/5-4arctan1/239
This formula was discovered by British astronomy Professor John Maqing in 1706. He used this formula to calculate the 100 digit PI. Maqing formula can get 1.4 decimal precision for each calculation item. Because the multiplier and divisor in the calculation process are not greater than long integers, it can be easily programmed on the computer
There are also many arctangent formulas similar to Ma Qing's formula. Among all these formulas, Ma Qing's formula seems to be the fastest. Nevertheless, if you want to calculate more digits, such as tens of millions of digits, Ma Qing's formula is not enough
2. Ramanugin formula
In 1914, ramanukin, a talented Indian mathematician, published a series of 14 formulas for the calculation of PI in his paper. Each term of this formula can get 8 decimal precision. In 1985, Gosper used this formula to calculate 17.5 million digits of PI
In 1989, David chudnovsky and Gregory chudnovsky improved ramanukin's formula, which is called chudnovsky's formula. Each term can get 15 decimal precision. In 1994, chudnovsky brothers used this formula to calculate 4044000, Another more convenient form of chudnovsky formula for computer programming is:
3. AGM (arithmetic geometric mean) algorithm
Gauss Legendre formula:
In September 1999, Takahashi and kanada of Japan used this algorithm to calculate 206158430000 bits of PI, setting a new world record
4. Bolvin's four times iteration formula:
This formula was published by Jonathan bolvin and Peter bolvin in 1985
5. Bailey borwein Plouffe algorithm
This formula is called BBP formula for short, which was jointly published by David Bailey, Peter borwein and Simon Plouffe in 1995. It breaks the traditional algorithm of PI, and can calculate any n-th bit of PI instead of the previous n-1 bit. This provides feasibility for distributed calculation of PI
6. Chudnovsky formula
It was discovered by the chudnovsky brothers. It is very suitable for computer programming. It is a formula that computers use faster at present