302.II.3B: Constructible Numbers & Fields

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  • Опубликовано: 23 дек 2024

Комментарии • 22

  • @ryanhayes5475
    @ryanhayes5475 3 года назад +3

    The geometric mean! I teach it to my sophomores but never realized that it has implications in constructible numbers. Brilliant explanation!

    • @stapleman007
      @stapleman007 2 года назад +2

      The more one studies disparate math subjects, the more one realizes it is just the same bowl of pudding.

    • @PunmasterSTP
      @PunmasterSTP 4 месяца назад

      How have your classes been going since COVID?

  • @davidkwon1872
    @davidkwon1872 5 лет назад

    One of the greatest curiosities in my life has solved and I am very happy now.

  • @MatthewSalomone
    @MatthewSalomone  10 лет назад +6

    I think you're right, Cori. (Since the constant term should be the product of the roots 4 ± sqrt(5), which is 11.) I'll add a note.

  • @davidkwon1872
    @davidkwon1872 5 лет назад

    Thank you. I really appreciate you for transforming the mythology into a logos.

  • @Mrpallekuling
    @Mrpallekuling Год назад

    13:27 This example involves the square root of 7.
    But the minimum polynomial will be the same if 7 is replaced by 3 or 10, or *anything*. Is that OK, professor?

  • @PunmasterSTP
    @PunmasterSTP 4 месяца назад

    9:18 It's cool to know there's more algebra beyond this, and I'm sure it's irrationally great!

  • @dcterr1
    @dcterr1 4 года назад +3

    Another very good video! However, I caught another mistake. (4 + √5)(4 - √5) = 11, not 9.

  • @duckymomo7935
    @duckymomo7935 5 лет назад +1

    how are you able to draw unit segment (since you can't measure it)?

    • @MatthewSalomone
      @MatthewSalomone  5 лет назад +2

      Step 1: draw a fixed segment of arbitrary length. Step 2: there is no step 2. 😉

    • @duckymomo7935
      @duckymomo7935 5 лет назад +1

      Matthew Salomone
      Lol you clown

  • @Akroker1
    @Akroker1 9 лет назад +1

    Can you explain why *all* constructible numbers must lie in K0,K1,K2,...? I understand why all of the numbers that belong to this list must be constructible, but I do not understand why all constructible numbers *must* belong K0,K1,K2,... . In other words, in the constructible numebr theorem, I understand the "if" but i do not understand why it must be an "if and only if"

  • @duckymomo7935
    @duckymomo7935 6 лет назад

    Do you talk about integral domains anywhere?

  • @shawnpheneghan
    @shawnpheneghan 8 лет назад

    I concur with Akroker - You certainly did explain how to construct square roots - and how they generate throughout the Ki, but you never even stated (no less proved) that square roots were the only root constructions that could be accomplished.

  • @AnthonyCasadonte
    @AnthonyCasadonte 10 лет назад

    Ahh I miss these videos! And great one by the way :) I do think now that I've experienced how some math professors teach at usc that you spoil your students with how well explained and easily accessible the content of your lectures are (especially since you use these videos). I have had to get use to fumbling and a lack of interaction especially with this one math professor. But anyways I was wondering..what is a definition for a direct limit and what in another example of one?

  • @p0gr
    @p0gr 2 года назад

    you seem to arbitrarily take Q (certainly constructible) and iteratively add square roots. this gives you your set K. so your set K is certainly constructible. by why not more? why not start instead of Q start with a set that also includes some cube roots? or why only add square roots to Q, why not cube roots?

  • @hyperduality2838
    @hyperduality2838 3 месяца назад

    The power of two is duality -- constructable numbers are dual!
    Real is dual to imaginary -- complex numbers are dual.
    The master is dual to the apprentice -- the rule of two, Darth Bane, Sith Lord.
    "Always two there are" -- Yoda.

  • @duckymomo7935
    @duckymomo7935 6 лет назад

    Ah geometric means theorem

  • @dct7b
    @dct7b 5 лет назад

    Where's the note?? I rediscovered the error too, please add the note so I can discover something useful. But thanks for the video, it is very well done otherwise!!. . ..