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**Representing integers as a sum of two squares**

Almost 400 years ago, Pierre de Fermat stated that every odd prime of the form `4k+1` can be expressed as the sum of two squares: `p = x^2 + y^2` with integers `x` and `y`, if and only if `p ≡ 1 mod 4` Later on, around the year 1747, Leonhard Euler was ab...

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**Representing integers as a difference of two squares**

Most integers can be represented as the difference of two squares, where each square is a non-negative integer. Algebraically speaking: `n = x^2 - y^2` for some non-negative integers `x` and `y`. In this blog post we're going to look at a simple and elegant...

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**Various representations for famous mathematical constants**

In this unusual post, much like in the older post, The beauty of Infinity , we're listing the most famous mathematical constants as representations of infinite series , infinite products and limits . The list of constants considered in this post, are: A...

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**Umbrele dorințelor**

Universul vesel, roșu. Sângeriu. Cu-n cer purpuriu ce ceartă. E în flăcări iarna noastră, Și mă-mbrac în verde veșted, Monoton. Brațe calde. Vreau să fiu! Tremur tot. Tu să-mi cânți dorința-n versuri! Cam tăcut, cutreierând nevinovat aceleași sensuri. Fugin...

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**Singur pe barcă**

Dulce trist. Nu mă iubi! Sunt plin de praf. Culoare caldă. Tu să-mi pui sare pe rană! Idealu-i cam pretext; să pice! Dorința-i vagă; dama-n râs de pică, Omidă-n carne. Carnaval. Matinalu-i alb. Nu mai pot să fug desculț. Am barcă. Tăcerea mea-i pe stradă. D...

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**Thoughts on programming language notations**

Some posts ago, we looked at what it's required in creating a new programming language . In this post we're going a little bit more into it, trying to find ways to effectively express meanings in natural ways, similar to what we can express in a natural lan...

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**Bacovia: a new symbolic math library**

Named after the great symbolist poet, George Bacovia , I created this new library to symbolically manipulate mathematical relations in a very simple and elegant way. Before writing a symbolic math library, this was a pretty mysterious subject to me, but in ...

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Frog jumping solutions for each value of n in the range [14, 40].

Numberphile video: https://www.youtube.com/watch?v=X3HDnrehyDM

Numberphile video: https://www.youtube.com/watch?v=X3HDnrehyDM

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**Mandelbrot set**

The Mandelbrot set and its complex beauty. Credit: Wolfgang Beyer # Formula At its simplest, the Mandelbrot set is defined iteratively by the following formula: `z_(n+1) = (z_n)^2 + c` # Generation The rules for generating the Mandelbrot set are surprisingl...

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**RSA algorithm**

RSA is a practical public-key cryptosystem , which is widely used on modern computers to communicate securely over large distances. The acronym of the algorithm stands for Ron Rivest , Adi Shamir and Leonard Adleman , which first published the algorithm 1978...

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