Beyond ½ a b sin(C)

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  • Опубліковано 19 гру 2024

КОМЕНТАРІ • 26

  • @ConManAU
    @ConManAU 14 днів тому +14

    I was wondering if you’d derive Heron’s formula, very glad you got there at the end!

  • @RandomBurfness
    @RandomBurfness 13 днів тому +5

    It was at exactly 16:07 I realised where the video was ultimately heading to, and lo and behold when I saw Heron's formula at the end it was very satisfying to know I saw it coming!

  • @benshapiro8506
    @benshapiro8506 14 днів тому +4

    a masterful derivation of Heron's formula. well done Dr. Barker!

  • @yaroslavdon
    @yaroslavdon 14 днів тому +15

    In the Heron formula calculation, ain't it simpler to go through:
    sin C = √sin² C = √(1 - cos² C) = √((1 + cos C)(1 - cos C)) = ...
    instead of the double-angle formulae?

    • @DrBarker
      @DrBarker  14 днів тому

      Yes, this is much quicker and simpler!
      Originally, I thought about first deriving the formulae for sin(C/2) and cos(C/2) in terms of the semi perimeter as interesting results on their own (see e.g. here www.cuemath.com/jee/semiperimeter-and-half-angle-formulae-trigonometry/ ), then Heron's formula would follow pretty much immediately. But yes, this approach is quite inefficient, and doesn't make much sense without the extra results!

  • @KoiMorris
    @KoiMorris 14 днів тому +2

    Excellent derivation of Heron's Formula!

  • @RGP_Maths
    @RGP_Maths 14 днів тому +2

    At 7:49 you give a formula for cos C, from the cosine rule, which is in fact the negative of cos C. Fortunately this didn't matter since you use it to find sin C as sqrt(1 - cos²C), thus squaring that negative out of harm's way. And of course sin C can only be the positive square root, since 0

    • @DrBarker
      @DrBarker  14 днів тому +1

      Well-spotted! I'm very used to the standard labelling cos(A) = (b^2 + c^2 - a^2)/2bc, so switching the letters around wasn't a good idea!

  • @renatomello2849
    @renatomello2849 12 днів тому

    It's nice to see that theres is always some basic math to be learned.

  • @holyshit922
    @holyshit922 14 днів тому +2

    This Heron's formula works also for degenerated triangles
    For segment length triplets which cannot form triangle this formula gives imaginary result

  • @danjwheatley
    @danjwheatley 14 днів тому

    10/10 no notes:)

  • @Fereydoon.Shekofte
    @Fereydoon.Shekofte 14 днів тому +2

    @Professor Barker
    Best wishes for you and your family in the near year 2025 🎉🎉🎉🎉🎉
    😊😊😊😊😊
    ❤❤❤❤❤

  • @MrConverse
    @MrConverse 14 днів тому

    👎🏽 for saying “coz” and “cot” instead of “cosine” and “cotangent”. Good video otherwise.

    • @danjwheatley
      @danjwheatley 14 днів тому +9

      the maths involved was spot on, no mistakes and clear on the board using recognised symbols, there was no ambiguity and presumably you understood what he meant? so no problem here apart from your own unnecessary criticism afaics

    • @ngc-fo5te
      @ngc-fo5te 14 днів тому +7

      Almost everyone after their first hour or two of trig uses these standard shortened forms.
      Next you'll be wanting hyperbolic cotangent said instead of coth.

    • @peterhall6656
      @peterhall6656 14 днів тому +4

      A frustrated linguist unleashing his intellect on high school trig. Hilarious.

    • @DBbbbbbbbbbbbb9248
      @DBbbbbbbbbbbbb9248 14 днів тому

      Was I the only one who noticed that he said SEC at one point...."in a sec"......short for 'second' apparently😅

    • @ngc-fo5te
      @ngc-fo5te 14 днів тому +2

      @@DBbbbbbbbbbbbb9248 Standard slang - certainly in the UK