Monthly Archives: February 2007

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

Posted on February 27, 2007 by Brent

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

Posted on February 24, 2007 by Brent

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 →

Posted in links | Comments Off on Carnival of Mathematics

Tetrahedral numbers, exposed!

Posted on February 20, 2007 by Brent

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

Posted on February 17, 2007 by Brent

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

Posted on February 16, 2007 by Brent

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

Posted in famous numbers, solutions | 6 Comments

Binomial coefficients

Posted on February 14, 2007 by Brent

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)

Posted on February 12, 2007 by Brent

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