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.

Fig. 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.

Fig. 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

etc.

### Like this:

Like Loading...

*Related*

Interesting! I might use this knowledge in my GMAT exam for graduate school.

LikeLike

Fascinating facts.

LikeLike

Very interesting

I also have some things I discovered myself about square roots

LikeLike

Nice to see someone smart and humble about Math. Thaniks mate. :)

LikeLike

Interesting post! I’m a starting blogger who wishes to write on interesting math stuff too, and these are the kinds of post I see myself writing.

LikeLike

Very fascinating!

LikeLiked by 1 person

Thanks.

LikeLike

:-D

LikeLike

Thanks for the like on my site. Peace be the Botendaddy.

LikeLiked by 1 person

:)

LikeLike

Sqrt(2)*1 does not equal 1 it equals sqrt(2)!

LikeLiked by 1 person

Please reread the instruction. I have never said that √2 is equal to 1. I stated that you multiply √2 by 1, 2, 3, etc. and drop the decimal. So in this case √2 × 1 = 1, instead of 1.414…

This is the floor function, i.e. ⌊ √2 × 1 ⌋ = 1

LikeLiked by 2 people

Interesting. I wonder if this can be shown to be generally true. Can we define a function which would easily give us the sequence of “missing” numbers from the list?

LikeLiked by 2 people

It can be proven through induction.

As for the function for the sequence of missing numbers:

a(n) = floor[n(2+√2)].

LikeLiked by 2 people

Fascinating.

LikeLiked by 2 people

Thanks!

LikeLiked by 2 people

Very cool!

LikeLiked by 2 people

:)

LikeLiked by 2 people

I don’t think you’d catch me doing any square roots… unless they are attached to a tree…. 😉

LikeLiked by 4 people

Have you found any cube root? :)

LikeLiked by 3 people

Ha ha! I’m still trying to find X 😉

LikeLiked by 3 people