TOPICS
Search

Christmas Stocking Theorem


ChristmasStockingTheorem

The Christmas stocking theorem, also known as the hockey stick theorem, states that the sum of a diagonal string of numbers in Pascal's triangle starting at the nth entry from the top (where the apex has n=0) on left edge and continuing down k rows is equal to the number to the left and below (the "toe") bottom of the diagonal (the "heel"; Butterworth 2002). This follows from the identity

 sum_(i=0)^(k-1)(n+i; i)=(k+n; k-1),

where (n; k) is a binomial coefficient.


See also

Binomial Coefficient, Binomial Sums, Pascal's Triangle, Star of David Theorem

Explore with Wolfram|Alpha

References

Butterworth, B. "The Twelve Days of Christmas: Music Meets Math in a Popular Christmas Song." Inside Science News Service, Dec. 17, 2002. http://www.aip.org/isns/reports/2002/058.html.

Referenced on Wolfram|Alpha

Christmas Stocking Theorem

Cite this as:

Weisstein, Eric W. "Christmas Stocking Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ChristmasStockingTheorem.html

Subject classifications