How to show the triangle inequality for the following metric
15365
Proving that the triangle inequality holds for a metric on $\mathbb{C}$
140692
Existence of a complete metric on $(0,1)$
121359
Show that $d_b(x,y)=\frac{d(x,y)}{1+d(x,y)}$ is a metric.
77867
Existence of a Riemannian metric inducing a given distance.
30044
Inequality with triangle sides
1932
How to show this equality of $\rho(X,Y)$
70448
Inequality for harmonic means
134764
Triangle Inequality question with fractions
77134
Proving a three variables inequality
40596
Proving a relation between inradius ,circumradius and exradii in a triangle
68869
How to show that the triangle is equilateral triangle?
145783
How can I prove this inequality in a triangle: $\frac{1}{(b+c-a)} +\frac{1}{(c+a-b)} +\frac{1}{(a+b-c)} \gt \frac{1}{a} +\frac{1}{b} +\frac{1}{c}$?
1316
Reverse Triangle Inequality in vector space
26299
Minkowski Metric Signature
112329
Show that $d(z,a)=|\frac{z-a}{1-\overline{a}z}|$ is a metric on the unit disk
155423
lower triangle inequality for complex numbers
3537
Show the Euclidean metric and maximum metric are strongly equivalent.