Task
Create a spreadsheet that finds and organises Pythagorean Triads.
Description
Pythagoras' Theorem is one of the best known mathematical formulas in the world: ${a}^{2} + {b}^{2} = {c}^{2}$. It is used to find the hypotenuse of a right-angled triangle, given its two "short" sides.
If you are to find $c$ for most whole-number values of $a$ and $b$, you will end up with an irrational number:
Let $a = 2$
Let $b = 3$
Then ${c}^{2} = {a}^{2} + {b}^{2} = {2}^{2} + {3}^{2} = 4 + 9 = 13$
And $c = \sqrt{13} = 3.605551275...$
Sometimes, whole-number values of a and b will give you a whole-number value for c:
Let $a = 3$
Let $b = 4$
Then ${c}^{2} = {a}^{2} + {b}^{2} = {3}^{2} + {4}^{2} = 9 + 16 = 25$
And $c = \sqrt{25} = 5$
The three whole numbers 3 - 4 - 5, because they satisfy Pythagoras' Theorem, are known as a Pythagorean Triad.
Instructions
(a) Create a new spreadsheet, called "Triad.xlsx".
(b) Try to systematically search through all pairs of numbers from 1 to 40, looking for Pythagorean Triads. When you find one, write the triad down on a second sheet in your Excel workbook.
(c) Find a way to organise the triads you have found into some sort of order. Does this order help you predict other triads?
