2021年9月12日 · Proving the triangle inequality for Euclidean metric. Ask Question ... The steps of the proof are a bit ...

Euclidean distance proof. Ask Question Asked 13 years, 3 months ago. Modified 9 years, 3 months ago ...

Proof of Extended Euclidean Algorithm? Ask Question Asked 12 years, 10 months ago. Modified 9 years, 7 ...

My favorite proof of the Pythagorean Theorem is a special case of this picture-proof of the Law of Cosines: Drop three perpendiculars and let the definition of cosine give the lengths of the sub-divided segments. Then, observe that like-colored rectangles have the same area (computed in slightly different ways) and the result follows immediately.

2015年1月17日 · I am grateful for the answer to my question and the comments. However, as my title says, this is a question about Euclidean norm being a norm. So for completeness I will provide the proof for 3 (sub-additivity). My proof goes like this:

2025年1月12日 · Use the indirect method of proof to show that if two angles of a triangle are equal, then the opposite sides are equal. [Suggestion: Suppose that angle A (Fig. 6–6) equals angle C, but that BC is greater than BA. Lay off BC’ = BA and draw AC’.

2020年12月10日 · $\begingroup$ The most general version of the Euclidean algorithm is that it holds in all Euclidean domains. The proof is standard and in most textbooks. But you will learn nothing if you read it. Someone showed you how to prove the Euclidean algorithm in Z already.

$\begingroup$ There is a proof here: ... Prove that Euclidean distance in $\mathbb{R}^n$ is a distance. 1 ...

$\begingroup$ Ok, as I commented to Dietrich, your answer follows the same logic as the proposition he talked about, the idea of using the division of $\mathbb{Q}[i]$ to get the structure of the remainder and verify the conditions, I'll look into it carefully and try to understand the whole proof, thank you :D $\endgroup$ –

2019年11月24日 · Understanding the proof that $\mathbb{Z}[i]$ is a euclidean domain. 2. Prove that there exists unique ...