The BSD conjecture states that if your name is long enough, it will always count as two letters on a famous conjecture.
Maybe also insert a joke about BSD Operating Systems if you're into that kind of stuff.
The conjecture states that Equation 1. "BSD conjecture" holds for every elliptic curve over the rational numbers (which is defined by its constants and )
Equation 1. . Where the following numbers are defined for the elliptic curve we are currently considering, defined by its constants and :
- : number of elements of the elliptic curve over the finite field, where the finite field comes from the reduction of an elliptic curve from to . can be calculated algorithmically with Schoof's algorithm in polynomial time
- : rank of the elliptic curve over the rational numbers. We don't really have a good general way to calculate this besides this conjecture (?).
- : a constant
The conjecture, if true, provides a (possibly inefficient) way to calculate the rank of an elliptic curve over the rational numbers, since we can calculate the number of elements of an elliptic curve over a finite field by Schoof's algorithm in polynomial time. So it is just a matter of calculating like that up to some point at which we are quite certain about .
The Wikipedia page of the this conecture is the perfect example of why it is not possible to teach natural sciences on Wikipedia. A million dollar problem, and the page is thoroughly incomprehensible unless you already know everything!
Birch and Swinnerton-Dyer conjecture by Kinertia (2020)
Source. The $1,000,000 Birch and Swinnerton-Dyer conjecture by Absolutely Uniformly Confused (2022)
Source. A respectable 1 minute attempt. But will be too fast for most people. The sweet spot is likely 2 minutes.When Ciro Santilli was studying electronics at the University of São Paulo, the courses, which were heavily inspired from the USA 50's were obsessed by this one! Thinking about it, it is kind of a cool thing though.
That Wikipedia page is the epitome of Wikipedia failure to explain things in a way that is of any interest to any learner. Video 1. "Tutorial on LC resonant circuits by w2aew (2012)" is the opposite.
Tutorial on LC resonant circuits by w2aew (2012)
Source. - youtu.be/hqhV50852jA?t=239 series LC circuit on a breadboard driven by an AC source. Shows behaviour on oscilloscope as source frequency is modified. We clearly see voltage going to zero at resonance. This is why thie circuit can be seen as a filter.
- youtu.be/hqhV50852jA?t=489 shows the parallel LC circuit. We clearly see current reaching a maximum on resonance.
LC circuit dampened oscillations on an oscilloscope by Queuerious Guy (2014)
Source. Finally a video that shows the oscillations without a driving AC source. The dude just move wires around on his breadboard manually, first charging the capacitor and then closing the LC circuit, and is able to see damped oscillations on the oscilloscope.Introduction to LC Oscillators by USAF (1974)
Source. - youtu.be/W31CCN_ZF34?t=740 mentions that LC circuit formation is the root cause for Audio feedback with a quick demo. Not very scientific, but cool.
LC circuit by Eugene Khutoryansky (2016)
Source. Exactly what you would expect from an Eugene Khutoryansky video. The key insight is that the inductor resists to changes in current. So when current is zero, it slows down the current. And when current is high, it tries to keep it going, which recharges the other side of the capacitor.