What? No Pythagoras?

A common solution to finding MH370’s endpoint on the final ping makes use of the Pythagorean Theorem, as discussed in earlier posts. But for those who may wonder if the Ancient Greeks are the only ones who would have found the plane in a timely manner, the answer is “Yes, but there were lots of Greeks”. And another Greek of some geometric repute was known as Euclid. It was the esteemed Euclid who assembled much of the then-current geometry in 13 books or chapters around 300 BC.

Euclid’s books are collectively known as “Euclid’s Elements”, and tucked away in Proposition 35 of Book 3 is Euclid’s description of an important relationship between the intersecting chords of a circle. It is known as the Intersecting Chords Theorem and it is a valuable tool. Here is an example:

We can use the Intersecting Chord Theorem to locate MH370 on its 7th and final ping. We can use it because we know the diameter of the final ping (9,758 km), and we know where the plane departed on its final flight. That is all the information we need. We simply draw two chords that intersect one another at Gate C-1 of the Kuala Lumpur Airport. While we do not yet know the distance from the airport to either the China or Batavia location, we know Chord AB is the perpendicular bisector of Chord CD. It follows then that segment C and segment D are each equal to the square root of A * B. And that is perhaps the simplest of all solutions to a six-year mystery.