7 Math Oddities

Today, I'm taking a look at math oddities such as the Fibonacci sequence resembles a snail shell the way it spirals around because most students see only the standard math we teach but we don't always look at math oddities as much.

1. Automorphic numbers are numbers whose square number has the same ending digits as the original number.  For instance 25^2 give 625 or 76^2 is 5776.  It turns out that 25 and 76 are the only two automorphic numbers found in the first 100 numbers.  One other interesting thing is that 625^2  gives 390,625 so you have a number squared and then squared again.

2. Strobogrammatic numbers are numbers that can be rotated 180 degrees and still appear the same.  The only three strobogrammatic numbers are 0, 1 and 8.  They look the same up right or upside down.  The digits 6  when rotated 180 degrees becomes 9 so 69 when rotated turns into 96 but 101 can be rotated 180 degrees and still remain the same.

3. Paladromic numbers are numbers that read the same both front ways and backwards.  These numbers include all the single digits 0 to 9, 11, 22, 33, 44, 55, 66,  77, 88, 99, 101, 111, 121, 131, 141, 151, 161, 171, 181, 191, 202, 212, 222, 232, etc.  There are also the ones like 1, 11, 111, 1111, 11111, etc.

4.  Jeff Tucker created this formula - 1/2 [mod([y/17]2^(-17[x]-mod([y],17)),2)] which produces the same formula in graphed form.  Its called a self referential formula.

5.  If you multiply 12345679 by 8 you get 98765432 but if you multiply 12345679 by 9 your result is 111111111.

6. Perfect numbers are numbers whose factors add up to the original number or largest factor.  For instance, the factors of 6 are 1,2,3,6 and 6 = 1 + 2 + 3 = 6 or 28 = 1 + 2 + 4 + 7 + 14.

7. Figurate numbers are numbers that look like the shape they are named after.  There are three types.
Perfect squares are numbers that can be made into squares like 4, 9, 16.  The second is triangular numbers such as 3, 6, 10, 15, 27 which when built into shapes look like triangles.  Then there are Center Hexagonal numbers are numbers that when arranged around a center make a hexagonal shape such 1, 7, 19 and 37.

There you are, seven mathematical oddities which are fun and entertaining.  Let me know what you think, I'd love to hear.