mathematical dialogues

23 September 2019
Yet another triangle
As we have seen in another post, identities involving inverse tangent look much less mysterious if analyzed from a purely geometrical perspective. Here you have the chance to...
Leggi di più - Read more
26 July 2019
Feeling grilled?
Get pen and paper and draw a cartesian plane. Then draw, on it, a set of points with integer coordinates, such as \(A(1,1)\), \(B(1,0)\), \(C(2,0)\), \(D(3,2)\), and so forth......
Leggi di più - Read more
10 July 2019
The bare necessities
This is the first of a series of posts in which a problem is presented to the reader, who in invited to solve it by following a proposed path. The background knowledge required...
Leggi di più - Read more
9 July 2019
Rock and rolle
Continuing were we left on a previous post about non differentiable functions that however have a well defined right derivative, we want now to show that...
Leggi di più - Read more
6 July 2019
Ups and downs
We are given a function \(f(x)\), for which the right derivative \[f'_+(x) = \lim_{h\rightarrow 0^+}\frac{f(x+h)-f(x)}{h}\] is defined in \(\Bbb R\). We also know...
Leggi di più - Read more
9 June 2019
Monotonically speaking
The concepts of monotonicity and continuity are very different. However, if we consider a monotonic function whose domain is an interval, we can deduce that right and left limits...
Leggi di più - Read more