I get the following compiler errors/warnings:

In file included from main.c:38:
algorithms.h:9: error: two or more data types in declaration specifiers
make: * [main.o] Error 1

Then, after I fixed that and retried the compile I got:

cc -g -pedantic -Wall -O2  -c -o main.o main.c
cc -g -pedantic -Wall -O2  -c -o mymath.o mymath.c
cc -g -pedantic -Wall -O2  -c -o algorithms.o algorithms.c
algorithms.c: In function ‘john_wallis’:
algorithms.c:142: error: ‘i’ undeclared (first use in this function)
algorithms.c:142: error: (Each undeclared identifier is reported only once
algorithms.c:142: error: for each function it appears in.)
make: * [algorithms.o] Error 1

Finally, after I fixed that I got a successful build!

I have one question about it also. Why are you using a long double for i when i is storing whole numbers?