Question

What do the following have in common? MOM; POP; NOON; MADAM, I'M ADAM; A MAN, A PLAN, A CANAL: PANAMA.

Short answer

All the words and phrases are palindromes.

Step-by-step solution

- Identify Each Phrase

First, list out each of the phrases and words given in the question: MOM, POP, NOON, MADAM, I'M ADAM, A MAN, A PLAN, A CANAL: PANAMA.

- Remove Non-alphanumeric Characters

For phrases that include punctuation and spaces, remove them to work only with the letters. For example, 'MADAM, I'M ADAM' becomes 'MADAMIMADAM' and 'A MAN, A PLAN, A CANAL: PANAMA' becomes 'AMANAPLANACANALPANAMA'.

- Check for Palindromes

Check if each word or phrase reads the same forward and backward. If the spelling remains unchanged when reversed, then it is a palindrome.

- Confirm the Property

Upon reversing each word or phrase: 'MOM' remains 'MOM', 'POP' remains 'POP', 'NOON' remains 'NOON', 'MADAMIMADAM' remains 'MADAMIMADAM', 'AMANAPLANACANALPANAMA' remains 'AMANAPLANACANALPANAMA'. Since all these are unchanged, they are palindromes.

Key concepts

Symmetry in Words

Symmetry in words is a fascinating concept. When discussing symmetry in language, we often refer to palindromes. A palindrome is a word, phrase, number, or other sequence of characters that reads the same forward and backward.
For example, in the words 'MOM' and 'POP', if you reverse the letters, they spell the same word. Hence, both words exhibit symmetry.
Palindromes can also be found in longer phrases. Take 'A MAN, A PLAN, A CANAL: PANAMA' for instance. Despite the spaces and punctuation, when read backward after removing non-alphanumeric characters, it remains the same.
Such symmetrical features can be fun and challenging to identify, providing both educational and recreational value.

Reversibility

Reversibility is the heart of understanding palindromes. A word or phrase shows reversibility if you can flip it around and still get the exact same sequence.
In the provided examples, 'NOON', 'MOM', and 'POP' remain unchanged when reversed. This property makes them palindromes.
Longer examples like 'MADAM, I'M ADAM' and 'A MAN, A PLAN, A CANAL: PANAMA' also maintain their structure and letters when reversed. However, all non-alphanumeric characters need to be removed first.
Practicing reversibility helps in identifying palindromes effectively and even in creating new ones, enhancing your literary creativity and understanding.

Alphanumeric Characters

Alphanumeric characters include both letters and numbers. When dealing with palindromes, it's important to focus on alphanumeric characters, as punctuation and spaces are usually ignored.
For instance, in the phrase 'MADAM, I'M ADAM', removing the comma, apostrophe, and space gives 'MADAMIMADAM', which reads the same backward, revealing its palindrome nature.
Similarly, 'A MAN, A PLAN, A CANAL: PANAMA' becomes 'AMANAPLANACANALPANAMA' once non-alphanumeric elements are removed.
This practice of focusing on alphanumeric characters simplifies the identification and confirmation of palindromes, making it easier to see the symmetry and reversibility in words and phrases.