More Beauty In Math

It has been a while since we shared some fun with math in Science Club.  WIth nothing up our sleeves we proceed with some mathemagics.  As in three earlier sessions (#1 and #2 and #3) we use the operations of multiplication and addition to build a fascinating sequence.

1 x 9 + 2 = 11

12 x 9 + 3 = 111

123 x 9 + 4 = 1111

1234 x 9 + 5 = 11111

12345 x 9 + 6 = 111111

123456 x 9 + 7 = 1111111

1234567 x 9 + 8 = 11111111

12345678 x 9 + 9 = 111111111

123456789 x 9 +10 = 1111111111

On occasion one might be a lonely number but we have demonstrated methods to form phalanxes of ones which are hardly lonely.

One is the Loneliest Number

Mathtoid:

ELEVEN PLUS TWO = TWELVE PLUS ONE = 13

But did you realize that ELEVEN PLUS TWO is an anagram of TWELVE PLUS ONE

More Beauty In Math

We are going to do a little math in Science Club today – actually some mathemagics.  In two previous sessions (#1 and #2) we used the operations of multiplication and addition to build some remarkable sequences.  Today we shall do another.

Try this:

9 x 9 + 7 = 88
98 x 9 + 6 = 888
987 x 9 + 5 = 8888
9876 x 9 + 4 = 88888
98765 x 9 + 3 = 888888
987654 x 9 + 2 = 8888888
9876543 x 9 + 1 = 88888888
98765432 x 9 + 0 = 888888888

There we are,  You can say what you like about us but you have to admit that, at least in numbers, we are very well rounded at the School Of Hard Rocks.

More Beauty In Math

The last time we toyed with numbers, we admired the symmetric array produced by massively multiplying bunches of ones (see post 20120409).  Today we operate on an ascending sequence to develope a descending pattern.  Everything is really going the right way – multiplying and adding do indeed give us larger numbers each time but the digits roll off in a delightful way.  Maybe the government could use this technique to make our collective debt seem less frightening.

1 x 8 + 1 = 9
12 x 8 + 2 = 98
123 x 8 + 3 = 987
1234 x 8 + 4 = 9876
12345 x 8 + 5 = 98765
123456 x 8 + 6 = 987654
1234567 x 8 + 7 = 9876543
12345678 x 8 + 8 = 98765432
123456789 x 8 + 9 = 987654321

Beauty In Math – Kaprekar’s Constant

6174

6174 is a special number now known as Kaprekar’s constant – after the great Indian mathematician D.R. Kaprekar who discovered this constant in 1949.  Kaprekar showed that 6174 is the limit attained as one repeatedly subtracts the highest and lowest numbers that can be constructed from a set of four digits that are not all identical.

Let’s try two examples.

First we’ll select the number 5379.  Composing the largest possible number from its four digits and then the smallest and subtracting gets us to 6174 in one step.

9753 – 3579  =  6174

Next we’ll try 4563.  It takes a couple of turns of the crank but we get to Kaprekar’s constant.  Pretty neat for a guy working in the days before electronic calculators.

6543 – 3456 = 3087

8730 – 0378 = 8352

8532 – 2358 = 6174

Kaprikar’s Constant

Beauty In Math

Tax day is approaching.  That means lots of us are crunching numbers – which is usually a pretty fun thing to do.  Sometimes the numbers can evolve in unexpected but very satisfying patterns.  Here is one example.

1 x 1 = 1
11 x 11 = 121
111 x 111 = 12321
1111 x 1111 = 1234321
11111 x 11111 = 123454321
111111 x 111111 = 12345654321
1111111 x 1111111 = 1234567654321
11111111 x 11111111 = 123456787654321
111111111 x 111111111 = 12345678987654321

One may be the loneliest number but not for long if you multiply.