# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

Message:αβγ
Message:abc
 Add Images & Files Posting Code: Name: Email:
Prob 1/4 of being in a cocked hat
From: Bill Lionheart
Date: 2021 Feb 20, 22:14 +0000

```The long debate over the figure 0.25 probability of being in a Cocked
hat continues to spill out of the pub after navigation classes and
into the scholarly and mathematical literature of navigation.

I think we noticed this one in pre print form but it has now appeared

The cocked hat: formal statements and proofs of the theorems
Imre Bárány , William Steiger  and Sivan Toled

Abstract

Navigators have been taught for centuries to estimate the location of
their craft on a map from three lines of position, for redundancy. The
three lines typically form a triangle, called a cocked hat. How is the
location of the craft related to the triangle? For more than 80 years
navigators have also been taught that, if each line of position is
equally likely to pass to the right and to the left of the true
location, then the likelihood that the craft is in the triangle is
exactly 1/4. This is stated in numerous reputable sources, but was
never stated or proved in a mathematically formal and rigorous
fashion. In this paper we prove that the likelihood is indeed 1/4 if
we assume that the lines of position always intersect pairwise. We
also show that the result does not hold under weaker (and more
reasonable) assumptions, and we prove a generalisation to n lines.
```
Browse Files

Drop Files

### Join NavList

 Name: (please, no nicknames or handles) Email:
 Do you want to receive all group messages by email? Yes No
You can also join by posting. Your first on-topic post automatically makes you a member.

### Posting Code

Enter the email address associated with your NavList messages. Your posting code will be emailed to you immediately.
 Email:

### Email Settings

 Posting Code:

### Custom Index

 Subject: Author: Start date: (yyyymm dd) End date: (yyyymm dd)