Leonardo of Pisa's fame as a gifted problem solver caused the Holy Roman Emperor Frederick II to come to Pisa joined by a team of mathematicians to publicly test his reputation.

One of the challenges was:

Find a square number from which, when five is added or subtracted, always arises a square number.

(Clearly, the quest was for a rational number, since no integer solution exists.)

After pondering for a while the genial Leonardo delivered a correct solution (strictly pen and paper - in 1225 there were neither laptops nor Google) and nowadays there is no exact knowledge how he accomplished the task.

Try to tackle it, using only the simple tools available in the XIII century, and only then allow yourself the indulgence of having a small toolbox of Google and/or software.

Above all – enjoy!

Rather than right triangles, Leonardo's thinking was driven by consideration of the sums of consecutive odd numbers.

Posted by xdog on 2017-12-18 09:23:34