Why does the atomic radii between periods 1,2,and 3 have similar rise and falls when charted on a graph?

The radius of an atom is determined by the number of electrons present and the effective nuclear charge. In these terms it is not much influenced by the size of the nucleus!

Effective nuclear charge is basically the net charge of the nucleus after having accounted for the electrons i.e. the effect of shielding.

Atoms of elements in the same period experience roughly the same shielding because their valence electrons occupy the same shell. Because of their similar shielding for each successive element across a period, the effective nuclear charge increases by +1 (protons increase). This means that with each successive element the electron cloud is pulled more strongly towards the nucleus and thus a generalization for all periods is formed.

"atomic radii decrease across a period"

But like any generalization there are always exceptions. To be more specific, elements with electrons that end with lone pairs usually have a larger radius than those with complete electron pairing ..... 2s^2 < 2p^1    .... Beryllium has a large radius than Boron. It usually happens where an orbital is completed and another is formed but no always i.e. p orbitals fill up singly then together !