One day, while doing some calculations involving the square root of 2, of which you’d most likely find boring, I discovered a little curiosity involving the square root of 2 by chance.
Multiply by 1, 2, 3 and so on but drop the decimals from the products. For instance, is equal to 8.485… but you don’t have a need for the decimal part. Thus, in this case is 8.
This has nothing to do with rounding up or down. You just have to drop the decimal part. In technical term, this is called the floor function , though you don’t have to worry about that.
The following shows the products of the square root of 2 multiplied by 1 through 25 without their decimal parts.
Write down each answer in a horizontal in a horizontal line as shown in Figure 1.
Now, you will notice that some numbers are missing from the sequence. Write these missing numbers under the numbers in Figure 1. This is shown in Figure 2.
Subtract the upper number from the lower number.
Note that the difference in these pairs is 2, 4, 6, 8, 10 and so on.
3 – 1 = 2
6 – 2 = 4
10 – 4 = 6
13 – 5 = 8
17 – 7 = 10