Math Wall Clock (Medium)

If you prefer interesting mathematical theorems and concepts over mindless number crunching (as can be seen in most other designs), then this might be the right product for you. If any of the items are unclear, please consult the list below for a brief explanation and consider it as a starting point for further investigation. 0 [sic!] - General Mathematics: By an amazing identity of Leonhard Euler, this expression is equal to 0. It is by many considered as one of the most beautiful equations in mathematics. 1 - Axiomatic Set Theory: The set that contains only the empty set. This is how 1 is defined in von Neumann's construction of the ordinals. 2 - Linear Algebra: The dimension of the set of complex numbers, when seen as a real vector space, is equal to 2. The most natural basis consists of the two elements 1 and i. 3 - Graph Theory: The chromatic number of the Petersen graph is equal to 3, which means that its vertices can be colored with three colors so that no two adjacent vertices get the same color. Incidentally, the Petersen graph is famous for being a notorious counterexample to many optimistic propositions about graphs. 4 - Combinatorics: The rate of exponential growth of the Catalan numbers is equal to 4. These numbers are remarkable because they occur as the counting sequence of literally hundreds of different combinatorial structures. 5 - Geometry: There are exactly 5 platonic solids, that is, regular and convex polyhedra. They are named after the number of faces: tetrahedron (4), hexahedron (6), octahedron (8), dodecahedron (12) and icosahedron (20). 6 - Number Theory: For any natural number n, Euler's totient function tells us how many numbers there are in 1,...,n which are relatively prime to n. Since n = 7 is itself prime, there are 6 such numbers, namely 1,2,3,4,5,6. Any efficient algorithm for computing this function would immediately break the widely used RSA encryption scheme. 7 - Probability Theory: In expectation, rolling two customary dice results in a 7. Incidentally, the mathematical theory of probability has its roots in trying to understand games of chance such as rolling dice and flipping coins. 8 - Coding Theory: The number 8 has the representation 1100 in binary Gray code. Compared to conventional binary encodings, Gray codes have the sometimes desirable property that the encodings of two consecutive numbers differ in exactly one bit. 9 - Real Analysis: This is a convergent infinite series. Its limit is seen to be equal to 9 by using the formula for infinite geometric series. 10 - Complex Analysis: Cauchy's coefficient formula allows to extract coefficients of the Taylor expansion of an analytic function. Note that (1+z)^5 is the generating function for the binomial coefficients (5 choose 0), (5 choose 1), ..., (5 choose 5). 11 - Formal Languages: The depicted string belongs to the regular language of hexadecimal number literals. The semantic value of this string is 11.