This is the Code Page you need in order to open all these doors. Alternatively you can simply count the symbols around the door.

Go to this location on the Map. It is from Central Hall up the stair case that twists into two, then up one flight of the spiral staircase and over the wooden floor. Take the first turn to the right and you find a chest that has this code inside of it.

Here you see the symbols that appear on these doors.
The top triangle refers to the dice on the left, the lower one to the dice on the right side of the door.
The number in the middle of each triangle is the sum of the three circles surrounding it. The animals stand for the numbers according to the Code on the first picture. Alternatively you can follow the animals around the door frame starting at the bottom left and starting with 0.

So the first triangle contains the number 9. The circles contain the Number 2, a Hydra which according to the code represents the Number 3 and a ?.
Simple calculate 9 = 2+3+x
Or otherwise: 9 - 2 - 3 = 4
According to the Code 4 is the Owl.

Roll the left dice to Owl:

Now for the lower triangle and the right dice:
4 = 0 + 1 + x or
4 - 0 - 1 = 3

Three stands for the Hydra.

Roll the right dice to the Hydra.

When you look at the door now, it shall say F to open. Press F

Now you unlocked the Arithmancy classroom!

Inside the Arithmancy classroom are 2 more riddle doors, as well as all over Hogwarts!
I hope my Guide helped you understand how to open them!
Happy calculating :D