# mathematical dialogues

14 November 2019
###### Non sequitur
In this post the behavior of sequences obtained by convolving two sequences is analyzed. In particular, we will give sufficient conditions for the convolution to be a null...
26 October 2019
###### Menelaus and infinitesimals
We show another application of Menalaus's Theorem, that, together with some infinitesimal calculus, will yield an unexpectedly simple result. Consider a square of side...
22 October 2019
###### The revenge of Menelaus
This post is devoted to Menelaus's Theorem, named for the astronomer Menelaus of Alexandria. It is a very imporant theorem in geometry, relating the ratios of the segments...
10 October 2019
###### My slant on asymptotes
In this post we will investigate the connection between slant asymptotes and the behavior of the derivative at $$\infty$$ for differentiable real functions. We say that a...
2 October 2019
###### Repetita iuvant
We present another excersise of Euclidean geometry. It is a "classical" problem on the "$$80-80-20$$" isosceles...
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...
22 August 2019
###### Losing it on a tangent
Osserviamo Osserviamo alcune identità...
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......
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...
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...
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...
4 July 2019
###### Should you be hesitant, value the discriminant
The problem, presented in a previous post, of determining the point on a circumference that is closest to a given interior point $$P$$, changes radically if we consider an...
3 July 2019
###### If you fear your lack of ability, use triangular inequality
Consider a circle and a point $$P$$ inside it. We know that the minimum distance between $$P$$ and the points on the circumference is $$2$$ cm, while the maximum distance is...
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...
Milano - Milan
###### Matteo Albanese
chi sono e come lavoro
who I am & what I do
###### Contacts
se hai bisogno di lezioni di matematica non esitare!
If you need help with maths, don’t hesitate!