Beyond ½ a b sin(C)

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  • Опубликовано: 14 дек 2024

Комментарии • 26

  • @ConManAU
    @ConManAU 8 дней назад +14

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

  • @RandomBurfness
    @RandomBurfness 7 дней назад +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 8 дней назад +4

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

  • @KoiMorris
    @KoiMorris 8 дней назад +2

    Excellent derivation of Heron's Formula!

  • @yaroslavdon
    @yaroslavdon 8 дней назад +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  8 дней назад

      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!

  • @RGP_Maths
    @RGP_Maths 8 дней назад +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  8 дней назад +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 7 дней назад

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

  • @holyshit922
    @holyshit922 8 дней назад +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 8 дней назад

    10/10 no notes:)

  • @Fereydoon.Shekofte
    @Fereydoon.Shekofte 8 дней назад +2

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

  • @MrConverse
    @MrConverse 8 дней назад

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

    • @danjwheatley
      @danjwheatley 8 дней назад +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 8 дней назад +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 8 дней назад +4

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

    • @DBbbbbbbbbbbbb9248
      @DBbbbbbbbbbbbb9248 8 дней назад

      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 8 дней назад +2

      @@DBbbbbbbbbbbbb9248 Standard slang - certainly in the UK