Have you ever come across a word, phrase or sequence that, when reflected, is exactly the same? Have you ever wondered what the term for this is? Well you are in luck because I can answer that. The name for this particular form is known as a palindrome. An example;

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The phrase race car is a palindrome.

Can you guess this palindrome?

The phrase is taco cat.

I was both surprised and intrigued to find out that palindromes are not restricted to words, but as Rob Eastaway suggests in his book ‘How Many Socks Make A Pair?’ they can also be found in mathematics.

Take the multiplication sum:

3 x 7 x 11 x 13 x 37

The answer:

111,111

A perfect palindrome.

Eastaway (2010), identifies that the number 11 is not only featured in this pattern but also as the root number for numerous other aesthetically pleasing patterns. For example;

1 x 1 =                              1

11 x 11 =                       1 2 1

111 x 111 =                1 2 3 2 1

1111 x 1111 =         1 2 3 4 3 2 1

11111 x 11111 =  1 2 3 4 5 4 3 2 1

This palindrome has the ability to continue up until the number 111,111,111, however, this would require the solution to be acquired by hand as a standard calculator cannot display numbers over 12 digits long. Eastaway (2010) also suggests that there are many other forms of palindromes and pretty patterns that can be formed using numbers. Therefore, proving once again how mathematics can be linked to a variety of situations. Palindromes are traditionally looked within literacy however the links within mathematics prove to be very interesting as well.

References

Eastaway, R. (2010) How Many Socks Make A Pair? London: JR Books