Examining periodic trends in the physical properties of elements and recurring patterns in the chemical characteristics of components is done using the periodic classification of elements. The periodic table is a systematic arrangement of the elements based on their atomic number, electron configuration, and recurring chemical properties. It allows scientists to identify and understand the trends and patterns that exist among the elements.

Physical Properties of Elements:
1. Atomic Size:
- The atomic size generally decreases from left to right across a period due to the increase in the number of protons and electrons, leading to stronger nuclear attraction.
- The atomic size increases from top to bottom within a group due to the addition of new energy levels.

2. Ionization Energy:
- Ionization energy is the energy required to remove an electron from an atom.
- Ionization energy generally increases from left to right across a period due to the increased nuclear charge and decreased atomic size.
- Ionization energy decreases from top to bottom within a group due to the increased atomic size and shielding effect.

3. Electronegativity:
- Electronegativity is a measure of an atom's attraction for shared electrons in a chemical bond.
- Electronegativity generally increases from left to right across a period due to the increased nuclear charge and decreased atomic size.
- Electronegativity decreases from top to bottom within a group due to the increased atomic size and shielding effect.

Recurring Patterns in Chemical Characteristics:
1. Valence Electrons:
- The number of valence electrons determines the chemical properties of an element.
- Elements within the same group have the same number of valence electrons, leading to similar chemical characteristics.

2. Reactivity:
- Elements on the left side of the periodic table (Group 1 and 2) are highly reactive as they have low ionization energies and easily lose electrons to form positive ions.
- Elements on the right side of the periodic table (Group 17 and 18) are less reactive as they have high ionization energies and tend to gain electrons or form stable compounds.

3. Oxidation States:
- Elements in the same group tend to have similar oxidation states because they have the same number of valence electrons.
- Transition metals can exhibit multiple oxidation states due to the availability of d orbitals.

In conclusion, the periodic classification of elements allows scientists to examine and understand the periodic trends in the physical properties of elements and recurring patterns in the chemical characteristics of components. It provides a systematic framework for organizing and analyzing the properties and behavior of the elements.