**Our Objective**

To implement a program is a function called "recursive palindrome" that checks whether a given string is a palindrome.

**The Theory**

Recursive Palindrome Theory is not a recognized theory or concept in computer science or mathematics. It seems that you may be referring to the general idea of using recursion to determine whether a string is a palindrome.

A palindrome is a sequence of characters that reads the same forwards and backward. Recursive palindrome algorithms apply the concept of recursion to solve the problem by breaking it down into smaller subproblems.

The recursive approach to check if a string is a palindrome typically follows these steps:

**Base Case:**

The base case is a condition that defines the simplest form of a palindrome. In this case, it is usually when the string has a length of 0 or 1 since an empty string or a single character is considered a palindrome.

**Recursive Step:**

If the string has a length greater than 1, the recursive step involves checking if the first and last characters of the string are equal. If they are, then the substring excluding the first and last characters is recursively checked using the same approach.

The recursive palindrome algorithm continues breaking down the string until it reaches the base case or determines that the string is not a palindrome.

**Learning Outcomes**

- Understanding the concept of a palindrome: Students will grasp the definition of a palindrome, which is a word, phrase, number, or sequence of characters that reads the same forwards and backwards.
- Recognizing the recursive nature of palindromes: Students will comprehend that palindromes can be analyzed recursively by breaking them down into smaller palindromic units.
- Analyzing recursive algorithms: Students will develop the ability to break down the process of determining whether a word or phrase is a palindrome recursively, understanding how to identify the base case and recursive steps.
- Implementing recursive palindrome functions: Students will gain proficiency in writing code to implement recursive functions that check whether a given word or phrase is a palindrome.
- Analyzing time complexity: Students will evaluate the time complexity of recursive palindrome algorithms, understanding how the algorithm's efficiency is affected by the length of the input.