Mechanics and curves | Math History | NJ Wildberger

[@ffggddss]

Thank you, Prof. Wildberger, for these little excursions through mathematical history! I'm finding them quite mentally stimulating and fun. And they are filling in some gaps in my rather sparse knowledge of that history. In my youth, I was very keen on learning the math, and couldn't give a fig about the history; with time, the history is becoming much more interesting to me. I'm sure this is a very commonplace pattern. And, still having interest in the math itself, there are plenty of things that have fallen out of favor over the ages, that don't deserve to have, and which you've brought back into the light here. So thanks again for all of this. And every one of these sessions brings to mind some remarks and questions, which follow: ≈ 19 - 20 min - so to summarize the "hanging curves": • when the load is evenly spaced by arc length, you get a catenoid • when it's evenly spaced horizontally, you get a parabola ≈ 32:00: "max-min problem par excellence, though ..." Yes, because rather than merely optimizing over some finite number of variables, you have to optimize over an infinite number of variables: y = f(x) values for every x along some segment, of which there are infinitely many! So this obviously can't be done in the usual way; it's kind of a fascinating type of problem, where the "solution" is a differential equation, which must *itself* be solved in order to arrive at the desired function. I'm hoping that the calculus of variations comes up again in some later lecture. It was important, e.g., in re-casting Newton's laws of motion (by Lagrange, then by Hamilton) in a way that was used by Schrödinger to write the fundamental equation of "motion" for a quantum-mechanical wave function in the early 20th century. ≈ 40 min "Their (elliptic integrals') origins come from the lemniscate." Really? Cause I thought the very name itself came from the attempt to find arc length of an ellipse, which also results in an elliptic integral. Or were you referring to *just* that particular form, with an inverse radical of a quartic?

[@rajapothi]

Thanks Prof NJ Wildberger for sharing pragmatic lecture........ these are helpful .

[@christophem6373]

The 2 final curves are Bezier's curves, see for animations: en.wikipedia.org/wiki/B%C3%A9zier_curve#Constructing_B.C3.A9zier_curves

[@njwildberger]

Thanks. Of course the History of Mathematics is a story that goes back to the Greeks and earlier; the videos in this series are probably best viewed in sequence. You might find what you are looking for in other videos.

[@ralphwalters906]

Thank you for sharing these lectures. I like the flow of your presentations. You're really good, your students are blessed.

[@EclecticSceptic]

Great to see these videos back again!

[@madier1000]

Dear Wildberger, Thank you for such lecture. You mentionned Euler "Elastica" problem . It appears it has been an inspiration to "string theorists" as suggested by Prof. Gabrielle Veneziano and Prof. Leonard Susskind.

[@madhavannarayanan2147]

Mind blown!

[@brendawilliams8062]

Thankyou. 💕

[@lefthand84]

Time for my nightly jaunt to the University of New South Wales

[@صفوانالزرقا]

ورحمه عربى تنرنزلات عربى translations to Arabic