Welcome to the NavList Message Boards.

NavList:

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

Compose Your Message

Message:αβγ
Message:abc
Add Images & Files
    or...
       
    Reply
    Re: That darned old cocked hat
    From: Gary LaPook
    Date: 2010 Dec 9, 21:20 -0800
    I see why the 2/3rds length works from this excerpt from Wilipedia (http://en.wikipedia.org/wiki/Centroid) since it locates the centroid:

    [edit] Of triangle and tetrahedron

    Triangle centroid 1.svg Triangle centroid 2.svg

    The centroid of a triangle is the point of intersection of its medians (the lines joining each vertex with the midpoint of the opposite side). The centroid divides each of the medians in the ratio 2:1, which is to say it is located ⅓ of the perpendicular distance between each side and the opposing point (see figures at right). Its Cartesian coordinates are the means of the coordinates of the three vertices. That is, if the three vertices are a = (xa,ya), b = (xb,yb), and c = (xc,yc), then the centroid is

      C = \frac13(a+b+c) = \left(\frac13 (x_a+x_b+x_c),\;\;
  \frac13(y_a+y_b+y_c)\right).

    The centroid is therefore at \left(\frac13,\frac13,\frac13\right) in barycentric coordinates.

    The centroid is also the physical center of mass if the triangle is made from a uniform sheet of material; or if all the mass is concentrated at the three vertices, and evenly divided among them. On the other hand, if the mass is distributed along the triangle's perimeter, with uniform linear density, the center of mass may not coincide with the geometric centroid.


    --- On Thu, 12/9/10, Gary LaPook <glapook@pacbell.net> wrote:

    From: Gary LaPook <glapook@pacbell.net>
    Subject: [NavList] Re: That darned old cocked hat
    To: NavList@fer3.com
    Date: Thursday, December 9, 2010, 3:33 PM

    BTW, my "2/3 of the length of the line connecting the midpoint to the opposite angle as another way to determine the fix using the midpoint method" works for triangles of other shapes, not just right triangles.

    gl
    ----------------------------------------------------------------
    NavList message boards and member settings: www.fer3.com/NavList
    Members may optionally receive posts by email.
    To cancel email delivery, send a message to NoMail[at]fer3.com
    ----------------------------------------------------------------

       
    Reply
    Browse Files

    Drop Files

    NavList

    What is NavList?

    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)

    Visit this site
    Visit this site
    Visit this site
    Visit this site
    Visit this site
    Visit this site