Math for everyone
Mathematical content accessible to everyone
Linear programming
Linear programming deals with problems that seem elementary in formulation: optimizing linear functions over a set defined by linear inequalities. Yet this theory has many highly practical applications.
The Monte Carlo method
In practice, finding an optimal value often involves computing demanding integrals. How can this be done? Physicists developed the Monte Carlo method, whose complexity does not increase with the dimension of the integrals involved.
Good divisions
Beautiful problems are like delicious dishes: we love to share them. Sometimes the question of how to share them out becomes interesting in its own right, especially when we are generous by nature and want to be able to let as many people as possible enjoy them.
Shortest paths: graph algorithms | Tangente
Is the shortest path from A to B always a straight line? Usually, yes. But when we must follow the network of roads and intersections in a city, we need a different perspective. That is where Dijkstra's algorithm comes to the rescue!
Using the derivative to hit bottom
Finding the lowest point on a given curve requires considering how the curve is approximated by a line near one of its points. This is where the tangent enters the picture
Coloring problems for all ages
Assigning colors—and their associated sets of constraints—to the vertices of a graph opens up the fascinating world of graph-coloring problems.
Triangles, and more triangles!
What is the maximum number of triangles that can be drawn with a given number of line segments?
On persistence
Apply the same algorithm to the digits of a number, then repeat the process with the digits of the result, and you encounter the notion of persistence… and the questions it raises.
Kissing numbers: kisses in geometry | Tangente
Kiss anyone you like...
Optimal packing of squares in a larger square | Tangente
You'll never arrange your boxes the same way again!
Plane coloring and the minimum chromatic number | Tangente
In 1950, American mathematician Edward Nelson (1932–2014) proposed an entertaining coloring problem.
The moving sofa problem
Moving house always brings a host of problems... including mathematical puzzles! One of them was formalized by Leo Moser in 1966.
Matrimonial mathematics
Sets of points can give rise to some delightful optimization problems.
Word histories: maximum, minimum and Latin | Tangente
"Optimum," "maximum," "minimum," "extremum": Latin vocabulary has certainly been plundered for terms denoting the extreme values of a function.
Brachistochrone:
Is the shortest path always the fastest? Mathematicians have known since the 17th century that it is not. Skateboarders, too, have learned this through experience, ever since the profiles of their half-pipes began to follow the shape of a "brachistochrone" curve.
The art of avoiding crossings
Artists using mathematics: nothing new there. But artists posing optimization problems that mathematicians still cannot solve: now that is surprising! One seemingly innocuous conjecture about drawing graphs has resisted all attempts at proof for fifty years.
Graph vertex degree constraints | Tangente
What is the smallest graph with a given set of degrees? Forty years ago, an article provided an elegant, constructive answer to this question.
Randomness to the rescue of satisfiability
The Boolean universe is a small mathematical world in which only two values exist: True and False. Yet achieving satisfaction is already complicated! Fortunately, randomness comes to our rescue: choosing by a coin toss can sometimes bring us surprisingly close to the maximum we seek.
Hills and valleys
A real-life situation or a physics experiment generally depends on several parameters, not just one. We therefore need a deeper understanding of variation in this multidimensional setting. Partial derivatives provide just that.
Expander graphs – Network theory | Tangente
The notion of a combinatorial graph is one of the most intuitive and universal in mathematics and computer science. Graphs crop up everywhere, modelling an extraordinarily wide range of relationships between all kinds of objects.