How Newton deduced gravity obeys inverse square law | Hidden gems #2 скачать в хорошем качестве

How Newton deduced gravity obeys inverse square law | Hidden gems #2

Help provide internet access to underprivileged students: donate at https://giveinternet.org/mathemaniac Next video:    • All power-law force has a conformal dual   Second channel video:    • Newton’s powerful force-ratio formula   Both Newtonian gravity and Hooke's law admit elliptical orbits in 3D (or 2D, same thing since all solutions are planar), but is it a coincidence? Newton said no, but this connection was only discovered accidentally when he was trying to deduce why gravity obeys inverse square law from astronomical observations at the time. In fact, if you know the history between Newton and Hooke, you will find the close connection between these two forces ironic! This channel is meant to showcase interesting but underrated maths (and physics) topics and approaches, either with completely novel topics, or a well-known topic with a novel approach. If the novel approach resonates better with you, great! But the videos have never meant to be pedagogical - in fact, please please PLEASE do NOT use YouTube videos to learn a subject. Files for download: Go to https://www.mathemaniac.co.uk/download and enter the following password: newtonhookeduality Sources: Principia (Translated, first American edition): https://web.math.princeton.edu/~epryw... Tristan Needham’s account (I used a bit of the geometry parts here): https://www.jstor.org/stable/2323768 I also used a bit of this to clarify what is going on with the geometry in the initial bits: https://journals.sagepub.com/doi/abs/... Newton’s portrait: https://commons.wikimedia.org/wiki/Fi... Principia title page: https://commons.wikimedia.org/wiki/Fi... Principia’s false claim to have proved the converse: https://www.sciencedirect.com/science... 2/3 school children don’t have access to internet: https://www.unicef.org/press-releases... Internet access and academic results: https://ieeexplore.ieee.org/document/... Video chapters: 00:00 Introduction 02:05 Gist of Newton's argument 03:42 Three preliminary results 07:09 Acceleration formula purely from geometry 09:49 Acceleration ratio formula 14:21 Ellipse Hooke's law 17:57 Applying acceleration ratio formula 22:06 Parabolic / hyperbolic orbits? Other than commenting on the video, you are very welcome to fill in a Google form linked below, which helps me make better videos by catering for your math levels: https://forms.gle/QJ29hocF9uQAyZyH6 If you want to know more interesting Mathematics, stay tuned for the next video! SUBSCRIBE and see you in the next video! If you are wondering how I made all these videos, even though it is stylistically similar to 3Blue1Brown, I don't use his animation engine Manim, but I use PowerPoint, GeoGebra, and (sometimes) Mathematica to produce the videos. Social media: Facebook:   / mathemaniacyt   Instagram:   / _mathemaniac_   Twitter:   / mathemaniacyt   Patreon:   / mathemaniac   (support if you want to and can afford to!) Merch: https://mathemaniac.myspreadshop.co.uk Ko-fi: https://ko-fi.com/mathemaniac [for one-time support] For my contact email, check my About page on a PC. See you next time!