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The normal approach to prove Thale's theorem should be induced from the property of central angle being twice of an inscribed angle that subtends the same arc. Since a diameter has central angle of 180 degrees, its corresponding inscribed angle should be half of 180, that is 90 degrees.

No, because if you do it that way, you wouldn't have Thales's Theorem. It would be Thales's Trivial Corollary.

Thales's Theroem is a simpler, easier to prove (as in OP), less powerful statement than the inscribed angle theorem.

Your second sentence denies the first sentence. The proof of the Inscribed angle theorem does not need Thale's Theorem, and it is stronger than Thale's Theorem.

No, many features are not implemented yet. I cannot use it now.

Can this service expand to include coding/programming?

Which programming subject do you want in particular? If it's coding syntax heavy, then the blackboard format might not be suitable. But if it's algorithm-heavy, then blackboard visuals could be very helpful.

Feel free to email me eltonlin@alum.mit.edu or if you prefer calling https://cal.com/eltonlin1998/15min

(BTW the things I described like overcrowded Office Hours etc., restricted access to past problems, were all Comp. Sci classes - Intro to Algorithms, Design & Analysis of Algorithms.)

has been fixed seems.

Is there an counterpart tool for ffmpeg with those parameters in GUI? That would be an omnipower app...

The Handbrake suggestion is a good one if your only interest is transcoding ... which barely scratches the breadth of what ffmpeg as a tool can do.

Try: https://amiaopensource.github.io/ffmprovisr/

for a 'better' ffmpeg CLI documentation, your mileage may vary, it's task and example focused.

Try: https://github.com/topics/ffmpeg-gui

for 66 variations on a GUI for ffmpeg of which I have no comment, I'm an old school CLI user through and through.

There are gajillions of ffmpeg UIs like Handbrake. But for me, more oftan than not GPT is the fastest way.

Try Handbrake!

I think the main key is the teacher. I followed the teacher in the class and the course was using CLRS, and I did not feel anything hard in homework and exams as long as I fully understood what was taught during the class time.

I did not see any content related to number theory and combinatorics (or counting) in the list of courses.

We should have those courses ready within the next year. Multivariable Calculus should be available in another few weeks, then Probability & Statistics at the end of July, then Methods of Proof, followed by Discrete Math, and Abstract Algebra later this fall. But courses in Number Theory, Graph Theory, Combinatorics, Real Analysis, etc. are all planned.

Quick question: is avoid prompting Xi / disabling satire about Xi the sufficient condition that would make Midjourney accessible to the people in China?

The answer is: NO. That's the point.

Is satire on June 4th, 1989, the tiananmen square massacre allowed in China? No! Is satire on COVID and Wuhan allowed in China? No! ... This list is so long in China that, eventually, if any person wants satire on some forbidden topics using Midjourney, this tool will be blocked. And very likely it would happen. The demand is not smaller than the endless gallery of women with huge boobs. So this is a hard problem.

Love this video and the people in the movie! Thanks for recommendation. It's really beautiful and warm.

If you enjoyed that there is a lovely series about old crafts in Japan that I watch periodically. This first video is about a man who repairs old books for his clients.

https://www.youtube.com/watch?v=SnPiOIqHkdI