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Rational Trigonometry?

  • 12-04-2013 9:38pm
    #1
    Boggot Globule
    Closed Accounts Posts: 19 ✭


    Some bloke in Australia has reformulated trigonometry using a new concept of "spread" to measure the angle between two vectors. He reckons it makes geometry much simpler but I don't really see what's so amazing about it. :confused:

    https://www.youtube.com/watch?v=dVk3CpjHR4Y


Comments

  • #2
    CJC86
    Registered Users, Registered Users 2 Posts: 360 ✭✭CJC86


    I decided to watch it all, just in case there was some insight I might be missing, but it's just restating trigonometry with linear algebra and covering up the fact by using his own weird notation.

    Simply, the "quadrance" is the square of the length of a vector, he admits this openly, and the "spread" is the square of the sine of the angle between two vectors (but he either doesn't know this or is actively hiding it). All the "theorems" are just recalculations of the well-known trig theorems (Pythagoras, sin rule, cos rule).

    It's just another crazy person trying to make himself famous by reformulating everything, even if it adds nothing to Mathematics. A good reason why this is not as useful as normal sines and cosines is because it cannot be used for Fourier series.


  • #3
    locum-motion
    Registered Users, Registered Users 2 Posts: 5,143 ✭✭✭locum-motion


    CJC86 wrote: »
    I decided to watch it all, just in case there was some insight I might be missing, but it's just restating trigonometry with linear algebra and covering up the fact by using his own weird notation.

    Simply, the "quadrance" is the square of the length of a vector, he admits this openly, and the "spread" is the square of the sine of the angle between two vectors (but he either doesn't know this or is actively hiding it). All the "theorems" are just recalculations of the well-known trig theorems (Pythagoras, sin rule, cos rule).

    It's just another crazy person trying to make himself famous by reformulating everything, even if it adds nothing to Mathematics. A good reason why this is not as useful as normal sines and cosines is because it cannot be used for Fourier series.

    Degrees work fine for me; I don't need to mess around with Quadrances and Spreads.
    If I get an email from NASA telling me that I can see the Space Station 42 deg above the horizon at a particular time*, then that works fine.
    If the email said that it would be visible "at a spread corresponding to a quadrance of 17,000,000,000,000.23 (or whatever) square kilometres", then I don't have a clue where to look!

    * if anyone's interested, according to today's email, it will be visible for 4 mins from 10:28pm tonight, appearing in the W and disappearing in the SE, and reaching a max of 57 deg above the horizon. (Data valid for Dundalk, might be a little different if you're locate elsewhere)


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