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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 Pascalâ€™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