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*

## About Edmark M. Law

My name Edmark M. Law. I work as a freelance writer, mainly writing about science and mathematics. I am an ardent hobbyist. I like to read, solve puzzles, play chess, make origami and play basketball. In addition, I dabble in magic, particularly card magic and other sleight-of-hand type magic. I live in Hong Kong.
I blog at learnfunfacts.com. You can find me on Twitter @EdmarkLaw and Facebook. My email is edmarklaw@learnfunfacts.com

Fascinating facts.

LikeLike

Pingback: A Curious Property Of The Square Root Of 2 | SEO

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. ๐

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

๐

LikeLike

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

LikeLiked by 1 person

๐

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 โ2 is equal to 1. I stated that you multiply โ2 by 1, 2, 3, etc. and drop the decimal. So in this case โ2 ร 1 = 1, instead of 1.414…

This is the floor function, i.e. โ โ2 ร 1 โ = 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+โ2)].

LikeLiked by 2 people

Fascinating.

LikeLiked by 2 people

Thanks!

LikeLiked by 2 people

Very cool!

LikeLiked by 2 people

๐

LikeLiked by 2 people

I don’t think you’d catch me doing any square roots… unless they are attached to a tree…. ๐

LikeLiked by 4 people

Have you found any cube root? ๐

LikeLiked by 3 people

Ha ha! I’m still trying to find X ๐

LikeLiked by 3 people