[extropy-chat] hole in the triangle

[scerir]

> Fascinating!
> Can someone explain? 
> Pietro Ferri

How to pinpoint the location of an artillery 
gun, by means of a triangle, and make a hole 
exactly there?

That was a major problem for our Alpini corps,
during WWI, in Alps and northern Italy, you
know, Pietro. 

Well a triangle was extremely useful.
Actually by listening to the sound
of the shot from three different points !  

The three observation points synchronize their 
clocks to the second and then note the exact 
second that they hear the gun's sound.  

Then on a map of the battle field the three 
points were plotted. Around the two points
where the sound arrived latest (the two 
furthest from the gun) draw a circle whose 
radius is the distance that sound travels 
during the number of seconds since the sound 
reached the first observation spot.  

The location of the gun is at the center 
of the circle that is tangent (on the outside)
to the two constructed circles and passes 
through the first observation point.

Instead of drawing the first two circles 
around the points where the sound arrived 
latest one draws those circles around the 
two points where the sound arrived earliest, 
and the circle passing through the remaining
point is drawn as tangent on the inside 
(instead than on the outside) to the first two 
circles, one obtains as well the correct solution.

That's why we were so strong, in war, Pietro,
some decades ago :-)