recursion.erl

-module(recursion).
-export([fib/1,fibTail/1,pieces/2]).
-export([fibTest/0,fibTailTest/0,piecesTest/0]).

% Fibonaaci
fib(0) -> 0;
fib(1) -> 1;
fib(N) when N>1 ->
  fib(N-2) + fib(N-1).

fibTest() ->
  0 = fib(0),
  1 = fib(1),
  1 = fib(2),
  2 = fib(3),
  3 = fib(4),
  5 = fib(5),
  8 = fib(6),
  13 = fib(7),
  55 = fib(10),
  passed.

% Tail recursive fibonacci
fibTail(N) -> fibTail(N, 0, 1).
fibTail(0, A, _) -> A;
fibTail(N, A, B) -> fibTail(N-1, A+B, A).

fibTailTest() ->
  0 = fibTail(0),
  1 = fibTail(1),
  1 = fibTail(2),
  2 = fibTail(3),
  3 = fibTail(4),
  5 = fibTail(5),
  8 = fibTail(6),
  13 = fibTail(7),
  55 = fibTail(10),
  passed.

% N cuts
% Reference: http://www.jlmartin.faculty.ku.edu/MiniCollege2012/handout.pdf
pieces(_,0) -> 1;
pieces(0,_) -> 1;
pieces(N, D) when N>=0, D>=1 ->
  pieces(N-1,D-1) + pieces(N-1, D).

piecesTest() ->
  % Dimension 0
  1 = pieces(0,0), % 0 cuts in dimension 0
  1 = pieces(1,0), % 1 cuts in dimension 0 ¯\_(ツ)_/¯
  % Dimension 1
  1 = pieces(0,1),
  2 = pieces(1,1),
  3 = pieces(2,1),
  % Dimension 2
  1 = pieces(0,2),
  2 = pieces(1,2),
  4 = pieces(2,2),
  7 = pieces(3,2),
  11 = pieces(4,2),
  % Dimension 3
  1 = pieces(0,3),
  2 = pieces(1,3),
  4 = pieces(2,3),
  8 = pieces(3,3),
  15 = pieces(4,3),
  % Dimension 4
  1 = pieces(0,4),
  2 = pieces(1,4),
  4 = pieces(2,4),
  8 = pieces(3,4),
  16 = pieces(4,4),
  31 = pieces(5,4),
  passed.

thank you for mentioning the link to the reference.

Nice job!
Sytlistic tip: Erlang community (and tools, like eunit) tend to prefer using snake_case (i.e. pieces_test/0) over camelCase for function names, module names, and atoms in general.