Visual Calculus - Tangentially Related

[@foreveryx]

Yes! Tom M. Apostol and Mamikon's works are always fascinating!...💕

[@manswind3417]

Incredible work mate, please keep these coming! Such a nice little trick, can be quite potent in evaluating areas when finding the locus goes awry.

[@mostly_mental]

Thanks for watching! I'm glad you liked it.

[@diribigal]

KZbin recommended this to me because I had just seen Physics for the Birds' video on exactly these topics. I prefer the pedagogy of your approach, though I can't deny the other video is flashier. Both videos are great

[@mostly_mental]

I'm glad you like it. Thanks for watching!

[@KaliFissure]

Beautifully clear and useful. 👍🤘🖖

[@ARBB1]

Great work. Always been curious to what visual calculus was.

[@pingnick]

🥂

[@petercrossley1069]

Excellent video. Instantly subscribed for more.

[@mostly_mental]

Thanks! I'm glad you liked it.

[@astlast8796]

This is very cool! Thank you

[@mostly_mental]

Glad you like it!

[@johnchristian5027]

Nice video!

[@mostly_mental]

Glad you liked it. Thanks for watching!

[@russchadwell]

Newton's Fluxion method anything at all like this? His method is never taught anymore, and basically seems lost, sadly. I, for one, would really like to see the geometric calculus called the Flexion Method...

[@mostly_mental]

I'm not too familiar with it, but from a quick search, the Fluxion Method seems to be essentially the modern derivative interpreted a little differently (and without the rigor). If you know some clever insight I missed, I'm happy to look into it.

[@russchadwell]

@@mostly_mental that's what I get too, upon searching. But, the book, "Never at Rest" heavily implies that after say 1750, much of what Newton actually had stated and was having taught in schools was basically replaced with the Leibniz method. So, we see Leibniz today when discussing Newton, but with slightly different notations for Newton (dot over derivative or tick mark for Newton instead of the dy/dx style of Leibniz). But, much of what is in Never at Rest and in the old archives at the Royal Society, detail diagrams and geometric discussion for it.

[@mostly_mental]

I'll take another look. Thanks for the suggestion!

[@russchadwell]

@@mostly_mental you'd apparently be bringing back the now dead art of Newton himself. A feat not yet managed by academia! I truly, truly hope that you do it and publish it again in order to bring it back to life!! And, not knowing how Fluxions really looked halted my personal ambitions to write a screenplay on the three: Hooke, Newton, and Leibniz. So, a neat video would go a long way! Thank you, sincerely!

[@ss_avsmt]

Why did you find the area swept by the string dragging the toy? What's the use of that? Isn't the locus of the curve much useful?

[@mostly_mental]

We wanted to find the area to show off the technique. It's just a toy example (if you'll pardon the pun). Sure, the curve is usually more useful (if you can find an equation). But there's insight to be gained by solving the problem another way. And in this case, the visual calculus answer generalizes to a whole family of curves, most of which can't be nicely described as a locus.

[@suhasisroy7240]

Wow

[@pingnick]

⭕

[@pingnick]

@@at7388 emojilicious