# Monthly Archives: February 2007

## More fun with Pascal's triangle (Challenge #9)

Remember Pascal’s triangle? 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1 1 7 21 35 35 21 7 1 1 … Continue reading

Posted in challenges, pascal's triangle, pattern, proof | 25 Comments

## Carnival of Mathematics

My most recent post about tetrahedral numbers is included in this week’s issue of the Carnival of Mathematics, which can be found here, in Mark Chu-Carroll’s blog, Good Math, Bad Math. (Just so you aren’t misled into thinking this is … Continue reading

## Tetrahedral numbers, exposed!

And now, the triumphant termination to the tantalizing tale of tetrahedral totals! To sum up so far: we began by observing that the number of gifts in the popular song The Twelve Days of Christmas can be described by tetrahedral … Continue reading

Posted in counting, famous numbers | 8 Comments

## Binomial coefficients and Pascal's triangle

In a previous post, I introduced binomial coefficients, and we saw that they can be given by the formula Let’s make a table of binomial coefficient values — that is, we’ll make a table where you can look up a … Continue reading

Posted in counting, famous numbers | 8 Comments

## Challenge #8 solution

…in which you were asked to find a formula for , the nth triangular number.

Posted in famous numbers, solutions | 6 Comments

## Binomial coefficients

Today I’m going to talk about something pretty nifty called binomial coefficients. It may not be immediately apparent to you why they’re so nifty, but take my word for it: they show up all over the place in mathematics! [And … Continue reading

Posted in computation, counting, famous numbers | 6 Comments

## Triangular number formula (Challenge #8)

More hosting issues recently… sigh. I’m seriously considering moving TMLT to a different hosting provider… the only problem being that right now, my hosting is free, and it might be hard to find another host which provides all the tools … Continue reading

Posted in challenges, computation, famous numbers, sequences | 12 Comments