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# 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 color, diagrams, visualization
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 binomial coefficients, consecutive, difference, integers, powers
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 binomial coefficients, diagram, Hasse, Pascal, subset
4 Comments

## Post without words #2

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