# geomerty Definition and Topics - 3 Discussions

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1. ### Prove the Extended Law of Sines

I just want to know if this proof is okay, and I would like advise on how to improve it. Proof: i. Proving that ∠BAC ⩭∠BDC: Let gamma be the circumscribed circle of ABC. Let D be the point on gamma such that DB is a diameter of gamma. The sum of the angles within a triangle equal to 180°. Adding...
2. ### Foundations I would love to see this book translated to English (Klein's Encyclopedia of Mathematical Sciences)

https://en.wikipedia.org/wiki/Klein%27s_Encyclopedia_of_Mathematical_Sciences Originals are in German or French, the Japanese version cut all the historical content :( Do you think that some day we will see this published in English? Size is big, 20k pages, but it cannot be more interesting I...
3. ### What is the best shape for a soccer goal post?

disclaimer: this is a made up question, so I don't know if theres a valid solution possible here First lets talk about the square post, it is clear that the shot will go in only if the ball hits the side AB of the square shown below, so the probability of a shot going in is simply ##\frac 1 3##...