0
votes
0answers
58 views

Cube Euclidean Metric Triangle Inequality?

I'm trying to prove that $d((x_1,y_1),(x_2,y_2)) = \sqrt[3]{|x_2 - x_1|^3 + |y_2 - y_1|^3}$ defines a metric. The problem is that I only know how to prove the triangle inequality for the Euclidean ...
9
votes
1answer
112 views

Geometric inequality with a triangle

The positive real numbers $x,y,z$ are the side lengths of a triangle iff $$x^2 + y^2 + z^2 < 2\sqrt{x^2y^2 + y^2z^2 + z^2x^2}$$
1
vote
1answer
1k views

The formula for finding the steepest curve between a range of x/y coordinates

I know approx what point i want from below diagram by looking at it(red circle), and im pretty sure there is some smart formula that does what im looking for, but how does the formula look like? ...
14
votes
3answers
729 views

The Notorious Triangle Problem

I was told this question by a friend, who said that their friend had thought about it on and off for six months without any luck. I have then had it for a while without any luck either. It is in the ...