recursion
Applying iterative processes from the past could prove to be lengthy and tedious. With the advent of computer science, new avenues opened. Writing recursive programs, calling themselves, makes it easier to prove that an algorithm works correctly. From a practical standpoint, recursion offers an elegant and often clear alternative to loops. The (short) writing of these recursive programs, combined with increasing computing power, opens horizons in solving varied problems that still occupy mathematicians, in combinatorics, geometry or operations research. The development of fractals, so dear to Benoît Mandelbrot, also allows everyone to experiment today with this powerful concept of a function calling itself.
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Proving a program | Tangente
Writing a computer program is one thing. Proving that it actually produces the expected result is another! One major advantage of recursion is that it produces programs whose correctness is easy to prove. There is a link between writing a program and proving it correct.
Fractals: the aesthetics of iteration
Repeating a geometric transformation at different scales produces fascinating figures whose aesthetic appeal is far from their only attraction. Let's (re)discover the most iconic fractals!
The remarkably rich Prouhet–Thue–Morse sequence
The Morse word, or Prouhet–Thue–Morse sequence, is an easy-to-construct mathematical object with plenty of surprises in store. Join us in exploring a combinatorial sequence that would certainly deserve to be every bit as famous as Fibonacci's!
Computational geometry: key challenges | Tangente
It is easy to overlook, but many geometric problems can be solved by iterative methods or, more broadly, algorithms. These questions are the subject of computational geometry! This is a vibrant, highly active field in which many seemingly elementary questions still await solutions.
Continued fractions,
Real numbers can be written without making an arbitrary choice of base. Euclid's algorithm provides a method that extends to all real numbers and leads to the notion of a continued fraction. In this notation, the golden ratio becomes the simplest irrational number to write!
Loops in programming | Tangente
The various types of loops are fundamental programming constructs. Although using them often comes naturally, they nevertheless raise a number of issues, such as whether the program will ever stop. Recursion offers useful solutions.