Pascal's Triangle

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Related to Pascal's Triangle: Blaise Pascal, binomial theorem

Pascal's triangle

[pa′skalz ′trī‚aŋ·gəl]
A triangular array of the binomial coefficients, bordered by ones, where the sum of two adjacent entries from a row equals the entry in the next row directly below. Also known as binomial array.

Pascal’s Triangle


a triangular array of numbers used to obtain binomial coefficients. It was published by B. Pascal.

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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.