Pascal's triangle - Wikipedia
WEBIn mathematics, Pascal's triangle is an infinite triangular array of the binomial coefficients which play a crucial role in probability theory, combinatorics, and algebra.
The Sierpinski Triangle - Math is Fun
WEBThe Sierpinski Triangle. An ever repeating pattern of triangles. Here is how you can create one: 1. Start with a triangle. 2. Shrink the triangle to half height, and put a copy in each of the three corners. 3. Repeat step 2 for the smaller triangles, again and again, for ever!
Sierpinski Triangle - zeuscat.com
WEBRecall Pascal's Triangle, in which the outer edges are filled with ones and each inner element is the sum of its upper adjecent elements. This is a fascinating creature; Pascal's Triangle has always seemed to pop up in the strangest places: number theory, probability theory, even polynomial expansion.
Sierpinski Gasket and Tower of Hanoi - Alexander Bogomolny
WEBAs was discovered by Ian Stewart, puz (Tower of Hanoi) has a surprising relationship to the Sierpinski gasket (also known as the Sierpinski triangle) and, therefore, to Pascal's triangle. In the Tower of Hanoi puzzle, disks stacked on one peg are to be moved to another with, perhaps an intermediate stop at a third, auxiliary peg.
WEBAbstract. ety XY , where instead of multiplication, we take the Nim-product. Its geometry turns out to be the Sierpi ́nski sieve, whi. h is well known to be connected to Pascal’s triangle modulo two. We generalize Nim-sums and -products to what we call q-sums and …
Sierpiński Sieve -- from Wolfram MathWorld
WEBAug 22, 2024 · The Sierpiński sieve is a fractal described by Sierpiński in 1915 and appearing in Italian art from the 13th century (Wolfram 2002, p. 43). It is also called the Sierpiński gasket or Sierpiński triangle.
Top 10 Secrets of Pascal’s Triangle | by Brett Berry - Medium
WEBJun 19, 2017 · Secret #6: The Sierpinski Triangle Using the original orientation of Pascal’s Triangle, shade in all the odd numbers and you’ll get a picture that looks similar to the famous fractal ...
Pascal's Triangle - What It Is and How to Use It - Science Notes …
WEBOct 1, 2022 · The graphic you get from coloring in the odd numbers of Pascal’s triangle resembles the Sierpinski triangle, which is a fractal with an overall appearance of an equilateral triangle subdivided into smaller equilateral triangles.
combinatorics - Pascal Triangle Vs Sierpinski Triangle
WEBMar 26, 2017 · If one takes Pascal's triangle with $2n$ rows and colors the even numbers white, and the odd numbers black, the result is an approximation to the Sierpinski triangle. More precisely, the limit as $n$ approaches infinity of this parity-colored $2n$ -row Pascal triangle is the Sierpinski triangle.
WEBIn this paper we consider a quantum version of Pascal’s triangle. Pascal’s triangle is a well-known triangular array of numbers and when these numbers are plotted modulo 2, a fractal known as the Sierpinski triangle appears. We rst prove the appearance of more general fractals when Pascal’s triangle is considered modulo prime powers.
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