News and Events of the Bering Strait School District
Sunday May 28th 2017



Connecting the Dots

By Keith Carroll

Apaay and Spencer's work connecting the dots.

Apaay and Spencer’s work connecting the dots.


Apaay Campbell and Spencer Fackler are Pre Calculus students in Mr. Keith Carroll’s Class at John Apangalook School in Gambell. They are discovering recursive and explicit formulas in sequences. They looked at the problem of how many handshakes it would take x people to shake hands with each other once. Apaay and Spenser made models with dots to represent each person, and then connected the dots to represent handshakes. After a few models {(I,0), (2,1), (3,3), (4,6),(5,10)}, they were able to discover the recursive formula Un = (Un – 1 + (n – 1). So three people shake hands = U3 = Un – 1 + (n-1) = U2 + ( 3 – 1) = 2 + 1 = 3. Then they discovered the explicit formula, which was more difficult to find.

Apaay and Spencer used the fact that a circle has 360 degrees to evenly space the dots around the circumference. The two models pictured represent 15 people (105 hand shakes) and 20 people (190 hand shakes).