Visual Cauchy-Schwarz Inequality

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  • เผยแพร่เมื่อ 29 ต.ค. 2024

ความคิดเห็น • 62

  • @ruthvikas
    @ruthvikas ปีที่แล้ว +82

    I love the graphical representation of maths. It just feels different and more clear.

  • @buffalonels988
    @buffalonels988 ปีที่แล้ว +69

    this was real intense for me

    • @MathVisualProofs
      @MathVisualProofs  ปีที่แล้ว +15

      too much for the shorts format? Too fast?

    • @rayansuneer
      @rayansuneer ปีที่แล้ว +10

      Theres too much information going on that it's a bit hard to understand
      Maybe make this a video?

    • @MathVisualProofs
      @MathVisualProofs  ปีที่แล้ว +13

      @@rayansuneer Here it is without words: th-cam.com/video/mKg_gVagHy8/w-d-xo.html . Perhaps the "matrix" cyberpunk music might not be your style :)

    • @rayansuneer
      @rayansuneer ปีที่แล้ว +9

      @@MathVisualProofs it was perfect. Down to the smallest detail

  • @realcontentgamer
    @realcontentgamer ปีที่แล้ว +29

    This man is literally better than my school teachers

    • @MathVisualProofs
      @MathVisualProofs  ปีที่แล้ว +2

      👍

    • @ts.nathan7786
      @ts.nathan7786 ปีที่แล้ว

      First thing school teachers can not make graphical animations on blackboard.
      Secondly , they may not know the graphical representations.

  • @abdullahyasinyagmur4687
    @abdullahyasinyagmur4687 ปีที่แล้ว +1

    This is just amazing. It's always nice to see the intuition geometrically

  • @rafaelrezende7953
    @rafaelrezende7953 ปีที่แล้ว +3

    NEVER STOP THIS VIDEOS

  • @Zangoose_
    @Zangoose_ ปีที่แล้ว +5

    This is what I needed back in college. Thanks, man

  • @Tiago-
    @Tiago- ปีที่แล้ว +30

    I didn't get any of this, but the shapes were pretty

  • @oliverpackham6278
    @oliverpackham6278 ปีที่แล้ว +14

    I always loved dot and cross product equalities. Michael Penn has a linear algebra playlist will all sorts of cool ones. The vector dotted with itself = it's magnitude^2 is a fun and easy one you could do a short on.

  • @asparkdeity8717
    @asparkdeity8717 ปีที่แล้ว +2

    This is so beautiful! Every linear algebra proof of Cauchy-Schwarz that I have come across is so messy and always involves the determinant of some quadratic, but u couldn’t have explained this in any simpler way, using nothing more than simple trigonometry. Thank you so much

  • @imchillbro479
    @imchillbro479 ปีที่แล้ว +6

    That's wonderful

  • @matthewbell4273
    @matthewbell4273 ปีที่แล้ว +2

    My main takeaway was how shapes can be really pretty

  • @alvargd6771
    @alvargd6771 ปีที่แล้ว +3

    when I saw Cauchy in the title got scared 😅 but it wasnt nearly as bad as I expected

  • @flamurtarinegjakyt3745
    @flamurtarinegjakyt3745 ปีที่แล้ว

    I needed this for calculus II, thank you

  • @StratosFair
    @StratosFair ปีที่แล้ว +2

    Ok, I have to subscribe to your channel after this

  • @SeanSkyhawk
    @SeanSkyhawk ปีที่แล้ว +8

    When will you be posting the Pythagoreran Theorem proof as recently published by Jackson and Johnson?

    • @MathVisualProofs
      @MathVisualProofs  ปีที่แล้ว +4

      Is a good idea! I will see if I can get around to it. I saw a few other videos done about it, and I haven't looked into it carefully yet.

    • @SeanSkyhawk
      @SeanSkyhawk ปีที่แล้ว

      @@MathVisualProofs It's quite elaborate and deals with infinite sums but in the end it's surprisingly clear and independent. As far as is known, this was the first proof that completely bypasses the so-called Pythagorean identity, which come to think of it can itself be proven via infinite series.

    • @MathVisualProofs
      @MathVisualProofs  ปีที่แล้ว

      @@SeanSkyhawk yes I know the details. I also know there is at least one other trig proof of the Pythagorean theorem though (see cut the knot website for instance). But the new one is much nicer (uses law of sines only). It’s a great accomplishment by them for sure. I’ll see if I can figure out a way to do it justice :)

  • @wryanihad
    @wryanihad ปีที่แล้ว +1

    Wonderful proof

  • @viking148
    @viking148 ปีที่แล้ว +1

    Lovely just lovely I wish I had you in my school

  • @TheCyanKiller
    @TheCyanKiller ปีที่แล้ว +3

    The number of times the word absolute was said was more than the number of times a word that was not absolute was said

  • @mathematicsman7454
    @mathematicsman7454 ปีที่แล้ว +2

    You are doing great like mind your descision

  • @Joffrerap
    @Joffrerap ปีที่แล้ว +2

    prerequisite:
    - pythagorean theorem
    - area of a parallelogram
    - triangle inequality and absolute value property
    ok not as much as i thought.

  • @teaaa2525
    @teaaa2525 ปีที่แล้ว +1

    Very nice

  • @Rócherz
    @Rócherz ปีที่แล้ว +1

    Now animate the 3D inequality *with cubes.*
    (It’s the meme of “now draw her stealling the Chaos Emeralds”, I’m neither actually asking nor demanding it.)

    • @MathVisualProofs
      @MathVisualProofs  ปีที่แล้ว +1

      But it is a good suggestion regardless :)

  • @arvindsrinivasan424
    @arvindsrinivasan424 ปีที่แล้ว +1

    I feel like this is better visualized with the vectors and using projections defined using dot products

    • @AnglandAlamehnaSwedish
      @AnglandAlamehnaSwedish ปีที่แล้ว

      Woah really u musta had a protractor born in ur hands n attached to ur hip ur whole life jk

  • @jupjup9737
    @jupjup9737 2 หลายเดือนก่อน

    You can also prove this using the dot product formula:
    abs(a•b=|a||b|cosθ)
    Since |cosθ| is less than or equal to 1 this also proves the inequality. However the proof for the dot product formula is more complicated than the one on the video.

  • @srikrishnaghosh7660
    @srikrishnaghosh7660 ปีที่แล้ว

    I have become fan of yours. Assuming this particular equation will be dealt with only after having the idea of dot product , it is quite straight forward that,
    ||(a,b)•(x,y)||=||(a,b)||•||(x,y)|||cos(z)|

  • @robertogajim470
    @robertogajim470 ปีที่แล้ว +1

    Tanks bro😮😮😮😮

  • @marshelldoonan7798
    @marshelldoonan7798 ปีที่แล้ว

    My mind blue screened

  • @mikaeo23
    @mikaeo23 ปีที่แล้ว

    I'll watch this again when I'm sober, stoned me can't understand 😅

  • @yeeter2785
    @yeeter2785 ปีที่แล้ว

    damn bro explained common sense wowowowowowowowow

  • @Seekqee
    @Seekqee ปีที่แล้ว +3

    I love inequalities but didn't know any book please tell me friends inequality books😢

    • @MathVisualProofs
      @MathVisualProofs  ปีที่แล้ว +4

      A good one for visualization is "When Less is More: Visualizing Basic Inequalities" by Roger Nelsen.

    • @robertogajim470
      @robertogajim470 ปีที่แล้ว

      ¯⁠\⁠_⁠(⁠ ͡⁠°⁠ ͜⁠ʖ⁠ ͡⁠°⁠)⁠_⁠/⁠¯

    • @robertogajim470
      @robertogajim470 ปีที่แล้ว

      .⁠·⁠´⁠¯⁠`⁠(⁠>⁠▂⁠

  • @lolzhunter
    @lolzhunter ปีที่แล้ว

    Oh yeah of course

  • @aedes9902
    @aedes9902 ปีที่แล้ว +2

    а Буняковский..

    • @MathVisualProofs
      @MathVisualProofs  ปีที่แล้ว +1

      Yes. I should have included that. It is in the original video description (th-cam.com/video/mKg_gVagHy8/w-d-xo.html)

  • @DOLfirst
    @DOLfirst ปีที่แล้ว +1

    Alrighty then

  • @GentlemanlyOtter
    @GentlemanlyOtter ปีที่แล้ว +1

    Is that Mozart d minor fantasia in the background?

  • @aidenhastings6341
    @aidenhastings6341 ปีที่แล้ว

    Is there an error when changing the inequality as sin(z) is removed? If 0

    • @MathVisualProofs
      @MathVisualProofs  ปีที่แล้ว

      When you remove the sin(z) on the right it is removing a multiplication by a number less than 1. So the equality is gone and the right hand side got larger (or stayed the same).

  • @robquinnpc
    @robquinnpc ปีที่แล้ว

    But why? Why do any of those things? Make it applicable.

  • @siguy715
    @siguy715 ปีที่แล้ว

    I know some of these words

  • @수하긴
    @수하긴 ปีที่แล้ว +3

    Jesus Christ......

  • @AnglandAlamehnaSwedish
    @AnglandAlamehnaSwedish ปีที่แล้ว

    Dot product i didnt know i would see that. Cool as f if its the dot product from physics i didn't do it in my notebook n stop n pause n rewind a million times i got not enough notebooks gotta by some more n pens n find my dam markers for my marker white board

  • @regularperson5647
    @regularperson5647 ปีที่แล้ว

    I'm too high for maths

  • @alessandropozzi2214
    @alessandropozzi2214 4 หลายเดือนก่อน

    totally unintelligible explanation... awful, even knowing it this is absolutely unnecessarily complicated