# Did ninjas use Pythagoras' theorem to determine the depth of moats?

Ninjas are alleged to have determined the depth of moats by taking a reed that's attached to the bottom of the moat, and measuring the height of the reed above water, and how far forward they had to push the reed until it was submerged, and using Pythagoras' theorem. Is this the case?

Some characters in the Japanese drama series "Nihonjin No Shiranai Nihongo" debate this claim, starting from around here in this YouTube clip. As background, while most of the students in the class are fairly silly, the character who speaks at 2:48 saying that Pythagoras' theorem was mentioned in Edo period documents is a very serious and studious individual, and therefore unlikely to support bogus claims.

The claim is also mentioned in this CIA document posted in 2007. Apart from the paragraph about ninjas turning into a stone, most of the content in the document is at least plausible.

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Reading the CIA document, it says "calculate by a sort of empirical Pythagorean geometry". I interpret that (in context) to mean performing a mental triangulation from two footpoints (where the reed hits the water) and bearings (angle of the reed), rather than finding the root of the difference between the squares. I don't think that counts. – Oddthinking Jan 22 '12 at 9:34
I read it a calculating the depth of the moat, assuming a constant slope: i.e. `depth = distance x slope`. Not the length of the hypotenuse. – ChrisW Mar 18 '13 at 23:45
That CIA document also says ninjas carried "hydrogen pellets a half inch in diameter made of carrot extract" - what on earth does that mean? – Ken Y-N Oct 22 '14 at 1:18
@KenY-N From what I gather they were nutrient pills or something like solid astronaut food. – SBoss Oct 22 '14 at 12:26