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Very well done, bayes is too often misunderstood. The intuitive vs calculator only method is great.

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Your clarity of presentation is a gift! I'm glad to have found your channel. Thank you!

Where did you go my neurodivergent brain needs you to explain more maths 😊

Hi. I came across your website and video. I love how you explain things and how gently you move forward. This video visually explains it really well: Bayes theorem, the geometry of changing beliefs : 3Blue1Brown

Wow, what a fantastic explanation. I haven't fully internalized this formula yet, but this was an excellent 10 minutes spent in helping me get there. Well done, and thank you so much!

Still one question I have is why we multiply? I am not able to visualize why multiply A cos-theta . B? A cos-theta vector times of B? What is visual representation of multiplication? Kindly clarify.

Wow, wow this explanation was mind-blowing! You made such a complex topic feel so intuitive. Your teaching style is truly genius and your passion for teaching and clarity in explanation are truly commendable

Great presentation! Props! but i'm confused. Pythagorus turned counting and measuring distances and angles to form geometry, algebra was developed which made it easier to work with equations as units change. Euler led to polar notation (radius of a circle, and angles) which is really useful when things spin or move in a circle. trigonometry develops to make this easier. calculus makes it possible to calculate rates of change. all of this derives from Euclid's 5 axioms.. albert learned all these, but as a physicist, using maths to try to understand some things about the real physical world, realized that Newtons methods didnt work. but working with the maths, discovered equations that energy and mass and time and the speed of light were cleary in a very distinct relationship. he put gravity into the equations, and he resisted believing the implications. but the maths worked! and I may very well be wrong, but my understanding is that every rigorous experiment that tested these implications has confirmed them, in the real physical world ( i should say the physical universe we observe). He came to realize that it was possible, so the maths said, to make a very powerful bomb, and practical useful production of energy. So his equations describe very well our physical universe. everyone of these maths, from Euclid on up, stood on the shoulders of those who came before. and each one of these maths may have been essential to getting from how to add to nuclear power plants.. Silly question prob, but can you get to trig without Euler's equations? or are they essential to a geometry of spinning and moving in circles, and developing calculus, and Einstein's discoveries? prob an ignorant example, but do his equations say anything practical, useful about our real world like, growth of bacteria in a petri dish, spread of a virus in a population, or to make and use an MRI. its a cute equation, but is it practical, or only theoretical. the math works, but where does it work in the real world? or is it just a party trick? Too long, sorry..

dude, you are a legend, your didactic is so good

12 years later… thanks for this!

Sir i am from bangladesh. I have been looking for the REAL meaning of what dot product actually is from a long time. You really dont know HOW MUCH your video just help me. THANKS A LOT SIR. REALLY REALLY THANKS A LOT .

What's so ironic is you talk so much about not just memorizing and then just feed a bunch of mnemonics and labels to "parts" without really explaining where they come from. That's the opposite of what you are claiming the video is about. Trig is best taught with visuals and the algebra together. I'm sick of this "visual learner" crap. We learn in all ways. Just learn the unit circle (particularly the wrapping function), basic triangle geometry, the definitions of each trig function, and now you can solve any trig problem. Understand how sec is just the reciprocal of cos and csc is just the reciprocal of sin: e.g., cos = adj/hyp; sec = 1/cos; therefore sec = hyp/adj. That's a much better way to understand those trig functions than this stupid ladder and wall with a TV BS.

Golden content right here! So happy I saw this early) Thanks for your outside-the-box explanations!

This is fantastic, thanks for the explanation. The only area I'd challenge is your starting position with Usain Bolt...I think he'd still win with a 50 ft handicap!

Good Job - I like to think sqrt 2 is also an underappreciaated irrational number built into every square just like Pi is in every circle and e in anything that grows

Thank you! I've got halfway through understanding the Fourier transform before, but I think you've carried me the rest of the way. The only thing I disliked was the smoothie metaphor at the start - ever since I was a kid I've found metaphors unhelpful in scientific explanations. I still remember how annoyed I was at high school physics trying to talk about electricity in terms of water going through pipes! Solid explanation though, and I now feel the urge to write some slow ugly code to make it happen in front of me.

nice xplaner! wondering what if the signal is not sampled at uniform interval?

Thank you for creating this video. CZcams is full of "smart sounding" people who explain fourier with mumbo jumbo language. After two weeks of constant searching, I have finally found you. You explain it the best. Simply Genius! I can finally now understand fourier with your parables. Please keep posting more of your down to earth explanations. I will go through all of your videos.

Very well done. Please keep up the good work!

A great way to explain the concept. The perspective became much clearer. Thank you.

love you !! thanks so much

Good video.

Can you do a similar video that covers casino odds in different games like slots, roulette, poker, and sports bets?

4:18

1. i love the analogy of “we’re the aliens” 1a. also the dome thing 2. if you’re doing the “sine” -> “sign” pun i immediately start thinking of “cosine” as “go sign” as in “how far do i have to go to get to the sign” 3. in general, the spatialization of this is so brilliant

Where did Mr. Azad go? I don't receive emails anymore, it's been years, there's no trace of him on his usual teaching websites. He is the best math teacher ever, he made math fun and easy to understand, I hope he is ok.

i dont get what he means by wall at 5:03

math flawed turtle head

ily where did u goooo

i watched this video 5 years ago and i still think about it almost everyday

Many thanks for the intuition!

Fantastic.

Even 10 years later, the most revealing video for me on imaginary numbers for sure!

How is it that 2^x is 100% but also e^x is 100% growth?

This gives me the best intuition! thank you

Wow! I’ve been trying so hard to actually understand these concepts and the intuition and this video finally made things click. Thank you so much, you’re awesome!

凄い👍

Finally understood what the dot product actually does and where its applied,indeed better explained thanks for this video

Wonderfully explained. Thank you!

This is great.. I learn g10 cbse and trig rn is just starting but I've found the memorisation of formulas and ratios useless without knowing their origin or their link w geometry I've found ur website today and I'm so glad I did

Dude I came here for a simple explanation and this is just not that and furthermore it's still unbelievable

That was an amazing explanation. The best I’ve seen.

But does this give us a scalar product and not a vector product

Lateral

Well the math is already off there isn't 365 days in a year

Idk how it's possible I check IDs all day and I might get 1 evey couple days after seeing more then 100 people a day

Wow, what a mind blowing intuition, respect. 🙏🫂

So easy to understand, ty