Category Archives: pascal’s triangle

Visualizing Pascal’s triangle remainders

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 , , | 15 Comments

Differences of powers of consecutive integers, part II

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 , , , , | 3 Comments

Some words about Post without words #2

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 , , , , | 4 Comments

Post without words #2

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

Carnival of Mathematics #23: Haiku Edition

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

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

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)

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