Blanche Descartes

Blanche Descartes is the pseudonym of a group of English mathematicians: William Thomas Tutte , R. Leonard Brooks (1916-1993), Arthur Harold Stone (1916-2000) and the statistician Cedric Smith (1917-2002). The name Blanche containing the initials of the names of four ( B ill, L eonard, A rthur, Cedric ), the name may be used as word game blanche Carte or Descartes be understood.

The four mathematicians met in the mid-1930s as students at Trinity College at Cambridge University , where they founded the Trinity Mathematical Society. All four are known as the authors of a joint work on the so-called " squaring the square ", the division of a square into smaller squares (although they did not use a pseudonym). Under Blanche Descartes, they published a division of a square into rectangles of equal area ( division of Blanche ).

They published around 30 works under the pseudonym, including on entertainment mathematics, combinatorics, but also joke poems and similar mathematical jokes. For example, they published a solution to the problem of counterfeit coins: given 12 pennies (makes one shilling), one of them is wrong (and weighs a little more), what is the minimum number of weighings with a beam balance required to detect the wrong coin? The answer is three; Blanche Descartes found a solution in the general case for n coins.

Tutte published various works on graph theory under Blanche Descartes, for example on the coloring of graphs. So he published an example of a snark (the name comes from Martin Gardner after Lewis Carroll , Hunting of the Snark), that is, a graph in which every node has three neighbors and whose edges cannot be colored with three colors without that at one of the nodes two edges have the same color. They have been known since Peter Guthrie Tait's studies on the four-color problem , which, according to Tait, is equivalent to the statement that there are no planar snarks. The first snark discovered was by Julius Peter Christian Petersen (1898), two more by Danilo Blanuša (1946), Blanche Descartes discovered the fourth, George Szekeres found the fifth in 1973 and Rufus Isaacs found two infinite families in 1975.

literature

• Cedric Smith, Steve Abbott The story of Blanche Descartes , The Mathematical Magazine, Volume 87, 2003, pp. 23-33

Web links

• Brooks, Smith, Stone, Tutte, Part 1, Squaring Net , Part 2

Individual evidence

1. ↑ Brooks, Smith, Stone, Tutte Squaring the square , Canadian J. Math., 2 (1950) 197-209
2. ↑ Eric Weisstein, Blanche's Dissection, Mathworld . Blanche Descartes Division of a Square into Rectangles , Eureka, No. 34, 1971, pp. 31-35
3. ↑ z. B. Why are series musical? , Eureka, No. 27, 1964, pp. 27–31, Online ( Memento of the original from April 1, 2010 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. 
4. ↑ Hymn to Hymen , The Mathematical Gazette, Volume 86, 2002, pp. 133–136, allegedly alluding to two other pseudonyms used by groups of mathematicians on the occasion of the fictitious marriage of the fictional Hector Pétard with the fictional Betty Bourbaki . Cedric Smith wrote the poem back in the 1930s for the wedding of Frank Smithies .
5. ↑ Eureka, No. 13, 1950, previously Cedric Smith The counterfeit coin problem , Mathematical Gazette, Volume 31, 1947, pp. 31-39. The problem arises in the Mathematical Snapshots by Hugo Steinhaus on.
6. ↑ Blanche Descartes Network-colors , The Mathematical Gazette, Volume 32, 1948, pp. 67-69