Pascal's Triangle


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

Pascal's triangle

[pa′skalz ′trī‚aŋ·gəl]
(mathematics)
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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WASHINGTON, May 10, 2013 /PRNewswire/ -- Today 325 participants of the 2013 Raytheon MATHCOUNTS National Competition successfully set a new GUINNESS WORLD RECORDS title: Fastest Time to Construct the First 25 Rows of Pascal's Triangle (Human Formation).
The 244 Mathletes were joined by 61 coaches and 20 advisors to arrange themselves in order of the first 25 rows of Pascal's Triangle in a record-setting 6 minutes, 16 seconds, 57 tenths of a second.
We investigate infinite log-concavity of the columns and other lines of Pascal's triangle in Section 4.
Now to prove that any row of Pascal's triangle is infinitely log-concave, one merely lets a computer find [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] for i up to some bound I.
This triangular pattern is known as Pascal's triangle, named after the French mathematician Blaise Pascal (1623-1662).
Pascal's triangle can also be seen in a square grid such as the 5 x 5 array shown in Figure 2 , or one even longer.
Pascal's triangle is an arrangement of the binomial coefficients in a triangle.
The array of numbers below is called Pascal's triangle.
In this way students can not only see, and perhaps produce, say Pascal's triangle, they can hear it.
One of my students then commented that topics like Pascal's Triangle, the Fibonacci Sequence, Golden Ratio, etc.
While related to the content of the chapter, they also serve to provide exposition on many of the things that mathematicians normally take for granted, like knowing the names of the letters of the Greek alphabet and other idiosyncrasies of mathematical notation, the different ways to approach a proof, the golden ratio, and the always handy Pascal's triangle.
The activities on the pyramids, cairns, apex card trick and Pascal's triangle all come under the large umbrella of what is called Additional Content in the new syllabus.