COMING SOON! Version 1.1 with pascal's music! 1. Pick the mod. *See what's special about prime mod. *See the relations between a triangle mod n and mod n*k. *See the relations between a triangle mod n and mod n^2. 2. Pick the zoom. The bigger the size- the lower the zoom. *Watch the same triangle in different zooms. 3. Watch your beautiful and colorful Pascal's triangle. *What's special about the rows n, n^2, n^3? 4. Click on "another one" for, well, another one. Some superficial informal mathematical explanations may be found under "Notes and Credits".
PASCAL'S TRIANGLE On Pascal's triangle, every number is the sum of the two numbers above it. In this project you may see how wonderful the numbers look when you change them to themselves in mod n, and use colors instead of numbers. BUT WHAT IS "MOD"?! Modulus of a natural number, or for shortness, "mod n", is the reminder when you try to divide this number by n. A clock, for example, works in mod 12. More examples: 1. 71 is 1 mod 70 2. 38 is 3 mod 7 3. 35 is 0 mod 5 BINOMIAL COEFFICIENTS What's the coefficient of a^k*b^(n-k) in (a+b)^n? It is, of course, C(n,k)=n!/(k*!(n-k)!) . this number is also the number that appears in row n, place k, in Pascal's triangle! If you read this far and learned something new, let me know. Maybe I'll add some more facts...
