I would like to know on which day did the 4 th January 1957 fall?

Well this one will take up a little math, but figure out how many days have occured between then and now (# of years times 365.25) and then the number of days from the 4th of january to todays date.
now that you have that number you should be able to do a mod 7 and grab the remainder and multply by 7 that should give you the day. (remember there are 7 days a week thus the mod 7) There's a famous mathematician who used to use it that I read about it, but can't for the life of me remember what their name is (for some reason thinking gauss or descartes....)

According to this site the day was a Friday.

Hope that helps, I'm not sure if you're trying to build a "calculator" or just simply don't know the answer.

I'm not sure if you're trying to build a "calculator"

If so, you are going to have issues. In some cases, computers dont like dates before 1975.