Erik D
United States Pasadena California

Some people sing in the shower, I come up with math equations.
Today I wondered how you would determine how many bowling pins you would need given the number of rows of pins in that lane. (Ex: a standard lane would have 4 rows of pins giving you 10 pins.) I was toying around with the relationship of the number of pins and rows and got this equation, where x is for rows and y is pins:
.5(x^2)+.5x = y
So my question is this: is there a practical application to this for reasons other than planning the world record for largest frame of bowling?
And now I'm being tired and lazy. How would I turn it around to solve for x?

Phillip Nguyen
United States Houston Texas

These are sometimes called triangular numbers,
T_1 = 1 T_2 = 3 T_3 = 6 T_4 = 10 ... T_n = n(n+1)/2
The wikipedia page has some more info:
http://en.wikipedia.org/wiki/Triangular_number
To solve for n in terms of T_n, you would apply the quadratic formula to the equation
n^2 + n  2T_n = 0
which gives n = (1 + sqrt(1 + 8T_n))/2

Michael
United States Lincoln NE: NEBRASKA

Glad I'm not the only one. I found this equation myself a while back while walking (as opposed to showering). Turns out it's quite well known and old. I don't know how practical the equation, but I myself have used it quite a bit as a shortcut in math puzzles or game design. For instance
1+2+3+4...+99+100=? can fit neatly in the equation with 100 as x. Of course that's not the only short way to solve that problem, but it's my favorite.

David Molnar
United States Ridgewood New Jersey

erak wrote:
So my question is this: is there a practical application to this for reasons other than planning the world record for largest frame of bowling?
yeah, it almost seems as though you could use it for something useful, like board games.

Brian Bankler
United States San Antonio Texas
"Keep Summer Safe!"

Triangular numbers appear fairly often in games, but there are a host of such sequences. Last night I came home and found my daughter's scratch work on math, and they were studying the Pentagonal Pyramid numbers. (I had to check the online encyclopedia of integer sequences to confirm the name).
http://oeis.org/A002411
I'm just not sure why they were doing this. I suspect it was just an example for their algebra class.

Key Locks
United States Indianapolis Indiana

This formula is usually one of the first examples in any math textbook that teaches induction, because it can be verified by induction pretty easily. The funny thing is that it took me a minute to recognize your formula, because it is usually expressed as n(n+1)/2.
Here's another cool one: The sum of the first n perfect square numbers is n(n+1)(2n+1)/6. See if you can verify this!

David Molnar
United States Ridgewood New Jersey

Bankler wrote: Triangular numbers appear fairly often in games, but there are a host of such sequences. Last night I came home and found my daughter's scratch work on math, and they were studying the Pentagonal Pyramid numbers. (I had to check the online encyclopedia of integer sequences to confirm the name). http://oeis.org/A002411I'm just not sure why they were doing this. I suspect it was just an example for their algebra class.
If they were learning the finite differences method, that's pretty freaking cool. (and underexposed)

Josh Jennings
United States San Diego CA

There are many anecdotes about how Carl Friedrich Gauss figured this out in grade school.


