# High School Math

MISSION STATEMENT: To encourage and promote a greater use of the internet and computer technology in the math classroom. For educators, students, parents and homeschoolers.

## Friday, December 29, 2006

### Curious 56

Curious 56's:

(111+1)/(1+1) = 56
(222+2)/(2+2) = 56
(333+3)/(3+3) = 56
...
(999+9)/(9+9) = 56

More Numbers at www.TheMathWebSite.com.

### Value of Pi

A unique value of pi.
x = (pi + 3)/2
2x =pi + 3
2x(pi - 3) = (pi + 3)(pi - 3)
2(pi)x - 6x = pi^2 - 9
9 - 6x = pi^2 - 2(pi)x
9 - 6x + x^2 = pi^2 - 2(pi)x + x^2
(3 - x)^2 = (pi - x)^2
3 - x =pi - x
3 = pi
But pi does not equal 3!
What is wrong here?

More Numbers at www.TheMathWebSite.com.

### Curious Ones

Curious multiplications using 1's:
1 x 1 = 1
11 x 11 = 121
111 x 111 = 12321
1111 x 1111 = 1234321
11111 x 11111 = 123454321
etc...

More Numbers at www.TheMathWebSite.com.

### Benford's Law

Benford's law, also called the first-digit law, first digit phenomenon, or leading digit phenomenon, states that in lists of numbers from many real-life sources of data, the digit 1 occurs almost one-third of the time, much greater than the expected 11.1% (i.e., one digit out of 9). The increasingly larger numbers occur less frequency as they grow in magnitude, to the point that 9 is the first digit less than one time in twenty.
This counter-intuitive result applies to a wide variety of figures, including electricity bills, street addresses, stock prices, population numbers, death rates, lengths of rivers, physical and mathematical constants. It is named after physicist Frank Benford, who stated it in 1938. It had been previously stated by Simon Newcomb in 1881. The first rigorous formulation and proof was made by Theodore Hill in 1988.

More Stuff at www.TheMathWebSite.com.

## Thursday, December 28, 2006

### Curious Nines

Curious arrangements with 9's:
1 x 9 + 2 = 11
12 x 9 + 3 = 111
123 x 9 + 4 = 1 111
1234 x 9 + 5 = 11 111
12345 x 9 + 6 = 111 111
123456 x 9 + 7 = 1 111 111
1234567 x 9 + 8 = 11 111 111
12345678 x 9 + 9 = 111 111 111

More Puzzles at www.TheMathWebSite.com.