The full paper develops the necessary tools to analyse the interesting sequences in more detail and also summarises the motivating properties of Pascal's Triangle
, including its fractal-like structure: colouring the odds and evens black and white results in the famous Sierpinski Triangle, if zoomed out far enough.
We investigate infinite log-concavity of the columns and other lines of Pascal's triangle
in Section 4.
This definition included a binomial term, and the mathematics simplified to the point where the second number in the given row of Pascal's Triangle
turned out to play an important role (see Figure 3).
So, having reeled off all sorts of numbers after applying Pascal's Triangle
and Poisson's Distribution (whatever they are), what has he come up with?
If the resulting signal from each overflow is tracked through the chain of summers, delay (D) and inverter (I) circuits, the same Pascal's triangle
sequence as that disclosed in Wells is built up.
The numbers 22, 343, 4664, 58985, 613316, 7367637, and 85922958, for example, can be identified in the Vedic matrix and arranged in Pascal's triangle
A senior at the North Carolina School of Science and Mathematics in Durham, Reither won a $40,000 scholarship for finding the dimensions of fractals generated by Pascal's triangle
and its higher analogs.
While teachers can use multiples of eleven to introduce palindromes, activities using Pascal's triangle
offer another introductory context for this investigation (see Schiller & Charles, 2004; Lemon, 1997).
She noticed that outcomes were triangular numbers, so she reasoned that perhaps she could find a connection to Pascal's triangle
This problem lays a foundation for a revisit when considering Pascal's Triangle
in later years.
This triangular pattern is known as Pascal's triangle
, named after the French mathematician Blaise Pascal (1623-1662).
I then used a follow-up lesson on Pascal's triangle