Mathematics in the street

Mathematics in the street in Valladolid, Spain

Mathematics in the street is a popular mathematics outreach initiative that involves taking mathematics in public spaces.

It is a protest act to raise awareness about the importance of mathematics, and it is a method of teaching and promoting mathematics.

It is particularly popular in Spain, where this activity is often carried out, though not exclusively.

History

Professor Sixto Romero Sánchez stated in an article in 1999 that 'mathematics must be taken to the streets.

In the year 2000, coinciding with the World Mathematical Year, the first Salon de la culture et des jeux mathématiques (Exhibition of Culture and Mathematical Games) was organized in France.

The National Math Festival is the country's first national festival dedicated to discovering the delight and power of mathematics in everyday life. Since 2015, it is organized every year.

In Spain it is organized every year in the different autonomous communities, with the help of the Spanish Federation of Societies of Mathematics Teachers. Mathematics popularizer Nicolás Atanes has used this method since too.

Every year, around International Day of Mathematics, many mathematical societies around the world organize Mathematics in the street simultaneously in different places.

Examples

Animation of an iterative algorithm solving 6-disk problem

Before and after the spin

A Superflip pattern

12 sectors: Green area equals orange area

During a Mathematics in the street initiative, several desks are put in a town square, or broad streets locating mathematics like in a street market.

Many of these games are usually exposed in a mathematics museum, specially Mathematica: A World of Numbers… and Beyond.

In this desks, usually mathematics experts sit to explain what they present. Mathematics games or puzzles are usually shown, like:

1. Towers of Hanoi, a mathematical game or puzzle consisting of three rods and a number of disks of various diameters, which can slide onto any rod. The puzzle begins with the disks stacked on one rod in order of decreasing size, the smallest at the top, thus approximating a conical shape. The objective of the puzzle is to move the entire stack to the last rod, obeying 3 following rules: only one disk may be moved at a time, each move consists of taking the upper disk from one of the stacks and placing it on top of another stack or on an empty rod, no disk may be placed on top of a disk that is smaller than it. The minimal number of moves required to solve a Tower of Hanoi puzzle is 2ⁿ − 1, where n is the number of disks.
2. Buffon's needle problem, is a question first posed in the 18th century. We have a floor made of parallel strips of wood, plane ruled with parallel lines t units apart, each the same width, and we drop a needle onto the floor. What is the probability that the needle will lie across a line between two strips? This can be used to design a Monte Carlo method for approximating the number π. Suppose we drop n needles, where the needle length l, and find that h of those needles are crossing lines, so π is approximated by the fraction $\pi \approx {\frac {2l\cdot n}{th}}.$
3. Galton board, is a device invented by Sir Francis Galton to demonstrate the central limit theorem, in particular that with sufficient sample size the binomial distribution approximates a normal distribution. The Galton board consists of a vertical board with interleaved rows of pegs. Beads are dropped from the top and, when the device is level, bounce either left or right as they hit the pegs. Eventually they are collected into bins at the bottom, where the height of bead columns accumulated in the bins approximate a bell curve.
4. Prime distribution, another interesting activity can be the use of prime number properties to distribute a prime number of objects, such as coins or any other items. Additionally, packages of a and b elements, where a and b are coprime numbers, can be utilized to determine how many packages of a and how many packages of b are needed to achieve various sums. Mathematics says that the smallest positive integer number from which all numbers can be obtained through integer combinations of a and b is a·b − a − b.
5. Rubik's Cube, is a combinatorics puzzle. 43,252,003,274,489,856,000 possible states can be obtained by applying sequences of moves to the solved state. Despite this complexity, it was shown in 2010 that Rubik's Cube can always be solved in 20 moves or fewer, regardless of the initial state. Also, you can explain Rubik's Cube group, Each element of the set G corresponds to a cube move, and the operations are the different moves. Moving right face clockwise three times, is the same as once turn the right face counter-clockwise. The cardinality of G is the number of possible states. The superflip or 12-flip is a Rubik's Cube configuration in which all 20 of the movable pieces are in the correct permutation, and the eight corners are correctly oriented, but all twelve of the edges are oriented incorrectly ("flipped"). It is one of the configurations which shortest path between a solved cube and the Superflip position requires at least 20 moves.
6. Pizza theorem, states the equality of two areas that arise when one partitions a disk in a certain way. Chosen a point inside a circle, and let n be a multiple of 4 that is greater than or equal to 8. Form n sectors of the disk with equal angles by choosing an arbitrary line through p. The sum of the areas of the odd-numbered sectors equals the sum of the areas of the even-numbered sectors.
7. Dividing a circle into areas, is a recreational mathematics problem, sometimes called Moser's circle problem, has a solution by an inductive method. Using a circle, someone can ask the number of areas created by chords of the circle with no three internally concurrent. When taking 1, 2, 3, 4… chords, the solution is 2, 4, 8, 16… But when 5 chords are added, there are 31 areas, not 32. Mathematics failed the logic and intuition, and there is no induction solution for the problem. The solution in terms of the number of chords in the circle is $f(n)={\frac {n}{24}}(n^{3}-6n^{2}+23n-18)+1$.
8. Tangram, is a dissection puzzle consisting of seven flat polygons, called tans, which are put together to form shapes.
9. Topological games, using chords and hands, one can try to solve String Handcuffs puzzles. There are also rope topological games that involves also thinking but no knots in hands.
10. Missing square puzzle, is an optical illusion used in mathematics classes to help students reason about geometrical figures.
11. Knot theory, using a cork board, thumbtacks, and a closed string or chain, you can demonstrate the Jordan Curve Theorem. By placing thumbtacks either outside or inside (but not mixed), you can pull one end and remove the chain or string without taking out the thumbtacks. Similar to this problem, there is a mathematical puzzle that can be illustrated with a heavy rectangle attached to a rope by two points, closing the loop. The puzzle states that there is a way to position the rope around n thumbtacks or nails, with n = 2 being the simplest case, such that removing any nail will cause the rectangle to fall.

Usually mathematical jokes are also commented, and some mathematical riddles too, like Missing dollar riddle or Unexpected hanging paradox.