Recent content by shybishie

Ah, there is indeed a big typo on my part. The inequality is actually. ||\vec{BC}|| -|| \vec{AD}|| \leq ||\vec{BA} - \vec{CD}|| . And as the user Office_Shredder pointed out, this turns out to be fairly obvious. ||\vec{BA} - \vec{CD}|| = ||[\vec{b}-\vec{a}] - [\vec{c}-\vec{d)]|| = ||...

Thank you Eynstone, that was very helpful :).

Thank you, markly. In retrospect, I should have framed this question to be less trivial sounding than it came out.

This is a (fairly basic) lemma without proof I saw in a research paper. Wasn't sure how to classify it exactly, but decided it's closest to vector (and linear) algebra. It goes like this, consider a quadrilateral in the plane with vertices A, B, C, D in clockwise order. It is given that...

Suppose I have three vectors a,b and c in R^d , And, I have that a.b < c.b(assume Euclidean inner product). What are the ways to visualize relation between a,b and c geometrically? I realize this is slightly open-ended, but am looking for insight here. Thanks in advance. PS: I have a thought...

Place 6 points in the plane, such that ratio of maximum distance / minimum distance (over these points) is as small as possible. The question is - what is the smallest ratio possible, and can we prove this is a tight bound? The following is my attempt for 6 (and fewer points): 1) For three...