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...
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...
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Matteo Albanese
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se hai bisogno di lezioni di matematica non esitare!
If you need help with maths, don’t hesitate!