Differential Geometry | Math History | NJ Wildberger

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  • เผยแพร่เมื่อ 24 ธ.ค. 2024

ความคิดเห็น • 63

  • @the_informative_edge
    @the_informative_edge ปีที่แล้ว +1

    Best visual explainations of involute, evolute, osculating circle etc. I have ever heard. No book can explain like this. Only such explaination are available at the stage of best teacher like Prof. Wildberger. Thank you so much respectable sir..

  • @njwildberger
    @njwildberger  11 ปีที่แล้ว +8

    But I will be starting a course on Differential Geometry shortly, which will be videoed.

  • @njwildberger
    @njwildberger  12 ปีที่แล้ว +1

    We will be mentioning Riemann in our next lecture on Topology.

  • @njwildberger
    @njwildberger  12 ปีที่แล้ว +9

    Sounds good, you could also use the Extended Spread law (Thm 82 of my book) to get the formula of the circumquadrance of a triangle (Exer.12.2 on the following page). How about some examples ---can you calculate the curvature of a parabola y=x^2 or some other curve, or perhaps recover the Huygens/Newton formula for curvature?

  • @njwildberger
    @njwildberger  12 ปีที่แล้ว +1

    Even simpler! If these formulas are indeed correct, they are a very worthwhile addition to the literature. I strongly encourage you to write them both up---especially with some interesting examples.

  • @njwildberger
    @njwildberger  11 ปีที่แล้ว

    Sorry, I have never had a series on Diff Geom. However there is one on Algebraic Topology.

  • @TheAlison1456
    @TheAlison1456 ปีที่แล้ว +1

    oh, thanks, history is awesome, and it has chapters too!!!
    11:22 very interesting. Definition of the center of curvature. I always wondered how they found this out!!
    20:38 he just wrote down a function there! Except it doesn't look all fancy in single letters.
    35:00-37:40 my god, it feels like this can totally be used to map 2D planar images onto curves.
    46:05 so this is what a Gaussian curvature is!!!

  • @kenroyadams2762
    @kenroyadams2762 9 ปีที่แล้ว +84

    This lecture was awe inspiring to say the least. Thanks for taking the time and effort to upload this. As a math major I truly appreciated this.

    • @njwildberger
      @njwildberger  9 ปีที่แล้ว +31

      +Kenroy Adams Thanks. As an undergrad you can gain a lot from watching all the of MathHistory lectures. I will also be posting some more next year.

    • @sundaranarasimhan58
      @sundaranarasimhan58 6 ปีที่แล้ว +4

      @@njwildberger certainly sir
      Thank you very much for your efforts

    • @pinklady7184
      @pinklady7184 3 ปีที่แล้ว +1

      Insights into Mathematics I am just now checking out your Math History playlist. Thank you for making that playlist.
      th-cam.com/play/PL55C7C83781CF4316.html

  • @QuantumBunk
    @QuantumBunk 12 ปีที่แล้ว +2

    This guy does a great job describing conceptually. Thanks!

  • @hunterbaywolf577
    @hunterbaywolf577 2 ปีที่แล้ว +1

    You Pendulum Clock is Properly Refered to as a Grand Father or Grand Mother Clock Depending on the Size. Which are Either Chain Set or Key. Depending on age.

  • @njwildberger
    @njwildberger  12 ปีที่แล้ว

    Have a think about what happens if the arc happens to be part of a circle. This is the important example to consider.

  • @elamvaluthis7268
    @elamvaluthis7268 2 ปีที่แล้ว +1

    Very useful lectures thank you sir.

  • @njwildberger
    @njwildberger  12 ปีที่แล้ว +1

    Thanks for that. This is, I believe, well worth writing up, again with a proof and some illustrative examples! Could you post a pdf somewhere?

  • @Gabriel-lc7bc
    @Gabriel-lc7bc 2 ปีที่แล้ว +1

    Great lecture!

  • @njwildberger
    @njwildberger  12 ปีที่แล้ว

    Very interesting. This is worthwhile writing up, with an explanation, ie proof, and perhaps a few examples. Can I suggest you do so and post it somewhere, and then provide a link. Also, are you sure about the minus sign?

  • @njwildberger
    @njwildberger  12 ปีที่แล้ว +5

    Sounds good! Look forward to it.

  • @stealthmonkey3G
    @stealthmonkey3G 4 ปีที่แล้ว +4

    This is the most beautiful and surprising math I have learned yet. Thank you. Incredible job of explaining an incredibly difficult concept

  • @rodolforesende2048
    @rodolforesende2048 ปีที่แล้ว +3

    12:34 professor norman lost the opportunity to explain that "osculating" means "kissing"... It would be one of the rare moments where a poetic image is revealed to the mathematician to be.He did not insist on the technique that proves the unicity of the kissing circle. A monogamous relationship😂

  • @marcellkalman
    @marcellkalman 11 ปีที่แล้ว +1

    Hello, I greatly appreciate your work! You used to have a series of videos on this topic (differential geometry), they're no longer available. Would you be so kind to upload them again? Thank you in advance!

  • @njwildberger
    @njwildberger  12 ปีที่แล้ว

    That's true, the sphere is exceptional in that the two extreme values agree.

  • @requerioayala5108
    @requerioayala5108 9 ปีที่แล้ว +17

    Very informative and helpful for understanding some basic motivations behind differential geometry, thank you.

    • @njwildberger
      @njwildberger  9 ปีที่แล้ว +7

      +Requerio Ayala You're welcome.

  • @sijojosephdr
    @sijojosephdr 12 ปีที่แล้ว +2

    Thankyou professor !! I am a physicist ..hence I hope that you will give a lecture on Riemann's work.

  • @adamfrank5678
    @adamfrank5678 3 ปีที่แล้ว +2

    This is incredible. Great lecture and great content.

  • @zeeshan008x52
    @zeeshan008x52 9 ปีที่แล้ว +2

    Excellent lecture. I was just glued. it was like a story. The lecture unfolded differential geometry beautifully. looking for more. can I get such more lecture on differential geometry.

  • @davidpitkanen4237
    @davidpitkanen4237 9 ปีที่แล้ว +1

    I love how he introduces Gauss in the video.at 39:00 as the GREAT mathematician. Nice.

  • @fadesingh
    @fadesingh 3 ปีที่แล้ว +2

    Brilliant presentation, extremely lucid as always. Thank you, Prof. Wildberger.

  • @phononify
    @phononify 6 ปีที่แล้ว +4

    i like your way of teaching - great videos, all of them. My father was prof. for experimental physics and very interested always in history ... i somehow inherited his interest ... your videos find their tangling bonds in my world picture therefore. Thanks a lot!

  • @lukedavis6711
    @lukedavis6711 3 ปีที่แล้ว

    I learned the radius of curvature formula from Calculus Early Transcendentals by Stewart. Doesn't explain it well but it's in there.

  • @jamesbra4410
    @jamesbra4410 5 ปีที่แล้ว +2

    Yes very good geometric introduction. Thank you professor.

  • @BarriosGroupie
    @BarriosGroupie 11 ปีที่แล้ว +1

    This history of mathematics! I love it! Mr (Dr ?) njwilderger I bow before your scholarship

  • @AICodingAdventures
    @AICodingAdventures 9 ปีที่แล้ว +2

    Very good video! Thank you for the whole course.

  • @Pygmygerbil88
    @Pygmygerbil88 3 ปีที่แล้ว +1

    Dear professor.
    Thank a milion for the lecture.
    Coud you please do a lecture on knot theory .

  • @박용석-n8y
    @박용석-n8y 4 ปีที่แล้ว

    Thank you so much !
    37:00 44:00

  • @jpdemont
    @jpdemont 7 ปีที่แล้ว +2

    Another awesome video, Professor Wildberger. Thank you for sharing it.

  • @huyle3597
    @huyle3597 3 ปีที่แล้ว

    mind-blowingly beautiful

  • @njwildberger
    @njwildberger  12 ปีที่แล้ว

    Do the physicists know these formulas?? They look interesting.

  • @satyajandhyala3912
    @satyajandhyala3912 4 ปีที่แล้ว

    Thank you so much for providing the education.

  • @gamigonyt4228
    @gamigonyt4228 7 ปีที่แล้ว +2

    great lecture, thanks for taking the time to uploading this video. really helped!

  • @samshane5896
    @samshane5896 8 ปีที่แล้ว

    Nice trip sir..! thank you

  • @edkaekania
    @edkaekania 5 ปีที่แล้ว

    Great video

  • @njwildberger
    @njwildberger  11 ปีที่แล้ว

    In fact the Playlist is now up: DiffGeom at this channel.

  • @ronakchavda2295
    @ronakchavda2295 3 ปีที่แล้ว

    Thank you 😃 for the lecture I had great time and have good Idea about the differential geometry ..

  • @hassanchhaiba154
    @hassanchhaiba154 8 ปีที่แล้ว

    Thank you very much. I have a serious problem to understand what the meaning of Fiber in the differential geometry.

  • @UntEyEHero
    @UntEyEHero 11 ปีที่แล้ว +1

    Sir, thank you so much for your good work. Please keep it up :)

  • @NoActuallyGo-KCUF-Yourself
    @NoActuallyGo-KCUF-Yourself 6 ปีที่แล้ว +1

    This one is so good; I love it!

  • @pjayasinghe
    @pjayasinghe 12 ปีที่แล้ว

    Thanks for the lecture

  • @Avose243
    @Avose243 7 ปีที่แล้ว +1

    Thanks so much for uploading this, great content

  • @79wx9z
    @79wx9z 4 ปีที่แล้ว

    Still quite enjoyable after 8 years!

    • @cielant
      @cielant 3 ปีที่แล้ว

      That's the thing about mathematics: won't get older really and if so: always ages comparably well.

  • @cr7madrid695
    @cr7madrid695 9 ปีที่แล้ว +1

    thanks professor ,I hope really to be your student,Am in Belgium,I study (géométrie différentielle) :) I appreciated your lesson,it's great,thanks from heart :)

  • @hx11hx1
    @hx11hx1 11 ปีที่แล้ว

    So great.

  • @therealjordiano
    @therealjordiano 12 ปีที่แล้ว

    thanks for this

  • @cowboys4ever348
    @cowboys4ever348 6 ปีที่แล้ว +6

    I freaking love math. It was my favorite subject all the way through college. Hope I become a teacher someday.

    • @raymondfrye5017
      @raymondfrye5017 4 ปีที่แล้ว +1

      Better than to become a teacher, become an applied mathematician.

    • @dansaunders6957
      @dansaunders6957 4 ปีที่แล้ว

      @@raymondfrye5017 We need more time, ie less pressure from bills to focus on whats important instead of what rich people want us to do.

  • @rionbreffeny4498
    @rionbreffeny4498 11 ปีที่แล้ว +2

    I would say that this is one of the (and not just in maths) best lectures that I've ever heard. Oddly enough (other than several art lectures) i had an Australian chap for Thermodynamics who was one of the other excellent lecture-ers.
    One of the worst (who happened to be one of my advisors) simply read to the class directly out of the textbook (which, naturally, we all had a copy of).
    Again, well done sir. -r. (onward to Topology - or is it typography, topography, or teleology ;? -- ah jargon).

  • @plower221
    @plower221 9 ปีที่แล้ว

    Terrific! thanks for the lucid introduction!

  • @comment8767
    @comment8767 2 หลายเดือนก่อน

    Almost no Australian accent!