July 29, 2009

High School Musical and Formulas for Pi

Toward the end of the first paper that he published in England, famed Indian mathematician Srinivasa Ramanujan (1887–1920) offers three series representations of the inverse of the constant pi (1/π).

Amazingly, two of these formulas appear on a blackboard in a scene in the insanely popular Disney movie High School Musical, except that one of the formulas isn't quite right. In the movie, young star Vanessa Anne Hudgens plays brainy Gabriella Montez, who asks her teacher, "Shouldn't the second equation read sixteen over pi." The expression on the board reads 8/π.

"Sixteen over pi," the teacher replies. "That's impossible." She then whips out a calculator and somehow figures out that Gabriella is right. "I stand corrected," she concedes.

The correct version of Ramanujan's series for 1/pi that appears in High School Musical.

That bit of dialog near the beginning of the movie helps establish where Gabriella stands as a student at her high school. This movie moment also now figures in a paper published in the August-September issue of the American Mathematical Monthly. Nayandeep Deka Baruah, Bruce C. Berndt, and Heng Huat Chan provide a survey of Ramanujan’s series for 1/π and start off with the formulas that play a part in High School Musical.

An acknowledgement from the authors notes, "We are pleased to thank Si Min Chan and Si Ya Chan for watching High School Musical, thereby making their father aware of Walt Disney Productions' interest in Ramanujan's formulas for 1/π."

The paper originally appeared in a special issue of the Indian journal The Mathematics Student, published in 2007 by the Indian Mathematical Society in its centennial year.


Baruah, N.D., B.C. Berndt, and H.H. Chan. 2009. Ramanujan's series for 1/π: A survey. American Mathematical Monthly 116(August-September):567-587.


Gerry said...

There seems to be something wrong with the formula. What is the meaning of (1/2) with a superscript 3 and a subscript n? The formula as given in Arndt and Haenel, Pi Unleashed, page 226, is
16 / pi =
sum on n from zero to infinity
(2 n choose n) cubed
(42 n + 5)
over 2-to-the-(12 n).

Anonymous said...

What is the meaning of the term (1/2)^2_n??

Math Tourist said...

The formula appears in the given form in the Monthly paper by Baruah, Berndt, and Chan, and among the formulas at http://mathworld.wolfram.com/PiFormulas.html.

I believe the notation (x)_n is the Pochhammer symbol for a rising or falling factorial. See http://mathworld.wolfram.com/PochhammerSymbol.html.

Manjil P. Saikia said...

I think the formula is correct, as I have seen DR.Baruah,Prof. Berndt and Porf.Chan's preprint, and have verified it with the movie too.

Its interesting that the Disney folks came up with Ramanujan's formula in one of their movies.

Kacey M said...

hello, im using this formula for my math in the movies project at school. I have never learned about summations or infinite series. For y project do I try to solve this problem or state it? I have no idea how to solve or use this formula? thanks, Kacey