Welcome to the NavList Message Boards.


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

Compose Your Message

Add Images & Files
    Re: Emergency Navigation
    From: Alexandre Eremenko
    Date: 2012 Jul 14, 04:32 -0400

    Computing the sines of few angles is easy.
    The only thing which I recommend to memorize is pi.
    To memorize pi, I recommend this:
    (for English, French or Russian speakers:-)
    Then you proceed as follows: if x is your angle in degrees,
    then y=2.pi.x/360 is your angle in radians.
    sin(y)=y-y^3/6+y^5/120-y^7/( etc.
    This is better to use for small angles. If your angle is not small
    use the doubling formulas like sin(2t)=2sin(t)cos(t),
    cos(t)=1-t^2/2+t^4/24-t^6/ etc.
    Dividing a 1-foot ruler into 1/10 of an inch divisions,
    without any instruments, is a much
    harder task:-)
    P.S. This is a late XVII century math. Ptolemy had to use a different
    method, much more sophisticated, starting from few angles (30, 45, 60, 90)
    for which sine and cosine can be found precisely,
    and then using division and addition formulas. To be more precise, he
    did not use our modern functions, sine and cos, but used the chord instead,
    chd(x)=2sin(x/2). His book contains the first table of chords that
    survived to out time. He also had to compute without having our decimal
    positional system, poor guy:-)

    Browse Files

    Drop Files


    What is NavList?

    Join NavList

    (please, no nicknames or handles)
    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 Settings

    Posting Code:

    Custom Index

    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