Category Archives: pascal’s triangle

Visualizing Pascal’s triangle remainders

Posted on October 20, 2012 by Brent

In a comment on my previous post, Juan Valera mentioned something about visualizing multiples of prime numbers in Pascal’s Triangle: In college, there was a poster with different Pascal Triangles, each of them highlighting the multiples of different prime numbers. … Continue reading →

Posted in fractals, modular arithmetic, pascal's triangle, pattern, pictures | Tagged color, diagrams, visualization | 15 Comments

Differences of powers of consecutive integers, part II

Posted on February 16, 2012 by Brent

If you spent some time playing around with the procedure from Differences of powers of consecutive integers (namely, raise consecutive integers to the th power, and repeatedly take pairwise differences until reaching a single number) you probably noticed the curious … Continue reading →

Posted in arithmetic, iteration, pascal's triangle | Tagged binomial coefficients, consecutive, difference, integers, powers | 3 Comments

Some words about Post without words #2

Posted on September 11, 2011 by Brent

My previous post displayed this picture: As Yuriy Kashnikov guessed, I made this picture using diagrams, a Haskell library I am developing for creating images like this. (You can see the source code for this picture here.) If you haven’t … Continue reading →

Posted in counting, pascal's triangle, pattern, pictures | Tagged binomial coefficients, diagram, Hasse, Pascal, subset | 4 Comments

Post without words #2

Posted on September 6, 2011 by Brent

Posted in counting, pascal's triangle, pattern, pictures, posts without words | 10 Comments

Carnival of Mathematics #23: Haiku Edition

Posted on December 28, 2007 by Brent

Welcome to the 23rd Carnival of Mathematics: Haiku Edition! First, I must apologize for the delay: I usually have very little trouble with my hosting provider, but of course it went down just when the CoM was supposed to be … Continue reading →

Posted in algebra, books, calculus, challenges, counting, fractals, geometry, infinity, links, meta, number theory, pascal's triangle, pattern, people, sequences, trig, video | 17 Comments

The Binomial Theorem

Posted on March 9, 2007 by Brent

The Binomial Theorem is an extremely important and general (and totally sweet) result in the field of combinatorics (which is the branch of mathematics about counting things). Without further ado, here it is: Wait! Don’t let all the fancy symbols … Continue reading →

Posted in counting, pascal's triangle, pattern | 2 Comments

Challenge #9 Solution

Posted on March 4, 2007 by Brent

In Which Our Hero (You) Discovers Several Methods of Proving a Combinatorial Identity Involving Pascal’s Triangle (Read Challenge #9 first if you haven’t already…)

Posted in counting, pascal's triangle, proof, solutions | 4 Comments

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