In a notable episode focused on positioning objects for maximum visibility (Season 3, Episode 2), the "Mathematics of Positioning" was applied to . The Problem : Stack 124 cannonballs on an
The following graph illustrates how positioning works in a 2D plane. By knowing the distance from three "satellites" (A, B, and C), the unique intersection point defines the exact position. Summary Table: Positioning Methods Data Required Common Use Case Distances from fixed points GPS, Radar, Cell tower location Triangulation Angles from fixed points Land surveying, Navigation (Compass) Multilateration Time Difference of Arrival (TDOA) Locating emergency calls, Aviation The Mathematics of PositioningDara O Briain: Sc...
This method uses the angles between the observer and two or more fixed reference points. In a notable episode focused on positioning objects
Positioning problems in the show typically focus on how to find a point ( ) when given its relationship to other fixed points. : This is the primary method used by GPS satellites. If you know your distance ( ) from three different points ( Summary Table: Positioning Methods Data Required Common Use
tray to create the tallest, most stable tower for pirate ships to see.
), you can determine your exact position in 2D space where the three circles centered at these points intersect.
: While a square-based pyramid is the intuitive "positioning" for each ball, a triangular-based (tetrahedral) pyramid is mathematically superior. Square Base ( for 64 balls) : Results in a height of approximately