cab1729:

From Pascal’s Triangle to the Bell-shaped Curve

Blaise Pascal (1623-1662) did not invent his triangle. It was at least 500 years old when he wrote it down, in 1654 or just after, in his Traité du triangle arithmétique. Its entries C(n, k) appear in the expansion of (a + b)n when like powers are grouped together giving C(n, 0)an + C(n, 1)an-1b + C(n, 2)an-2b2 + … + C(n, n)bn; hence binomial coefficients. The triangle now bears his name mainly because he was the first to systematically investigate its properties. For example, I believe that he discovered the formula for calculating C(n, k) directly from n and k, without working recursively through the table. Pascal also pioneered the use of the binomial coefficients in the analysis of games of chance, giving the start to modern probability theory. In this column we will explore this interpretation of the coefficients, and how they are related to the normal distribution represented by the ubiquitous “bell-shaped curve.”
read more: http://www.ams.org/samplings/feature-column/fcarc-normal

cab1729:

From Pascal’s Triangle to the Bell-shaped Curve

Blaise Pascal (1623-1662) did not invent his triangle. It was at least 500 years old when he wrote it down, in 1654 or just after, in his Traité du triangle arithmétique. Its entries C(nk) appear in the expansion of (a + b)n when like powers are grouped together giving C(n, 0)an + C(n, 1)an-1b + C(n, 2)an-2b2 + … + C(nn)bn; hence binomial coefficients. The triangle now bears his name mainly because he was the first to systematically investigate its properties. For example, I believe that he discovered the formula for calculating C(nk) directly from n and k, without working recursively through the table. Pascal also pioneered the use of the binomial coefficients in the analysis of games of chance, giving the start to modern probability theory. In this column we will explore this interpretation of the coefficients, and how they are related to the normal distribution represented by the ubiquitous “bell-shaped curve.”

read more: http://www.ams.org/samplings/feature-column/fcarc-normal

(via mathematica)

mathematica:

Yesterday, two of my friends and I finally went to the National Museum of Mathematics — MoMATH — downtown in Manhattan, New York. MoMATH is located across 26th Street from Madison Square Park, and after yesterday, I’d definitely recommend it to anyone, regardless of age or experience with math. I had a lot of fun, and I absolutely think my knowledge of mathematics enhanced, not diminished, my appreciation for museum content.

In my mind, there are a number of reasons why MoMATH is important, and why it should be a cornerstone of any trip to New York:

  1. I’m a huge fan of museums of science, but I think it’s a good thing to have a museum just for mathematics. There is something unique to mathematics, a certain drive towards understanding beyond the world, that an appreciation for science, in all its glory, cannot muster.
  2. MoMATH in particular is engineered in a way that’s accessible to people of all ages. The activities and exhibits themselves are clearly designed for children — with the exception of the art exhibit Composite, which is clearly designed for a more critical audience, and the “puzzle cafe,” for which adult patience and/or guidance is essential — but each has a nearby computer display with an easy-to-understand explanation including more advanced mathematics.
  3. People, especially young children, deserve the chance to experience math in the right way — by exploring patterns and structure in the world for themselves, not by learning arithmetic by rote. And if that experience can’t be effected in the classroom just yet, what better place than a museum dedicated to generating it?

[CJH]

Have any of you guys been to MoMATH? What’d you think? How about anyone who hasn’t been yet — what are your thoughts? Do you think mathematics is something you can capture, at least in part, in a museum?