Print leap years between 1000 and 2000

Preface ： Part of this article is quoted from Global information network

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Catalog

1. The calculation rules of leap years

2. Code display

3. Draw a picture

4. Why leap years occur

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1. The calculation rules of leap years

After the precise calculation of astronomers , Summarize the following three calculation rules for leap years .

1、 Not a whole century ： Can be 4 Divide without being 100 Divided by leap year .（ Such as 2016 Year is leap year ,2100 Year is not a leap year ）

2、 A hundred years ： Can be 400 Divide without being 3200 Divided by leap years .( Such as 2000 Year is a leap year ,3200 Year is not a leap year )

3、 For years with large values ： If you can divide this year 3200, And divisible 172800 It's a leap year . Such as 172800 Year is a leap year ,86400 Year is not a leap year .

The above rules are complicated , The simple rule we usually need to remember is ： Can be 4 Divide without being 100 Divisible 、 Can be 400 All divisible years are leap years . After all , We can't live 3200 year . That is what we often call a leap every four years , A hundred years without Leap , Four hundred years later .

2. Code display

#include<stdio.h>
int main() 
{
	int i = 1000;
	for (i; i >= 1000 && i <= 2000; i++)
		if (i % 4 == 0 && i % 100 != 0 || i%400==0)
			printf("%d ", i);
	return 0;
}

  The following contents give a detailed introduction to leap years , You can have a look if you're interested ：

3. Draw a picture

The math teacher said ： The combination of number and shape is good . Let's use a picture to remember .

The above rule says 3 Number ： Can be 4 Divisible number （ Write it down as A）、 Can be 100 Divisible number （ Write it down as B）、 Can be 400 Divisible number （ Write it down as C）.

Can be 400 The number divisible must be 100 to be divisible by , Can be 100 The number divisible must be 4 to be divisible by . Can you figure this out ？ If you remember 4 The multiple of is 4m,100 The multiple of can be expressed as 100m=4m*25,400 The multiple of can be expressed as 400m=100m*4.

Then the inclusion relationship in the figure below appears ：

According to rules ： Can be 4 Divide without being 100 Divisible 、 Can be 400 All divisible years are leap years . Then the year represented by the white shadow in the above figure is leap year .

  Here, as long as we master the principle of leap year , Writing code is relatively simple

4. Why leap years occur

The time when the earth revolves around the sun is not accurate 365 God , Probably 3651/4 God , To be more precise

365.24219 God . We can't treat time that is not an integer as a year , Only approximate 365 Days as a year . such , polymeric 1/4 Day accumulation 4 One more day in the year , Leap year's 2 One more day in a month , To make up for the gap between astronomical years and calendar years .

The more troublesome thing is ： It's not accurate to say that there is an extra day every four years , because 4*0.24219 Is not the same as 1 ah . The extra time every four years is not enough for one day , It's a little less every time , every 100 Year is one leap year less . So the saying that leap years occur every four years is wrong .

Every year, this 1/4 It can't be ignored . If we keep ignoring this every year 1/4 God ,100 After year , our “ Calendar year ” and “ Real year ” There's a difference between 25 God ！ Every century we will be less than nearly 1 months ;700 After year , We have less 175 God . October becomes spring , December turns into summer . In this way, the solar terms are disordered .