Rational reconstruction is like taking apart a puzzle, understanding every piece, and then putting them back together in a different way to find a hidden code.
In mathematics, it means discovering a particular way that numbers can be put together to form a larger number. These larger numbers are called rational numbers. When you find a code like this, you can reconstruct the original equation that created it.
For example, if you know that the code is based on the sequence 1, 3, 7, and 13, you can put them together in many different ways to make larger numbers.
One way is:
1 + 1/3 + 1/7 + 1/13 = 521/273
In this equation, the four numbers are added together, and they form the fraction 521/273. This is an example of a rational number.
The process of finding this equation is called rational reconstruction. It involves digging deep into the patterns and relationships between the numbers to uncover the hidden code.
Overall, rational reconstruction is a method of discovering hidden mathematical patterns by breaking them down into simpler pieces and putting them back together in a new way.