Concept
13 (thirteen) is the natural number following 12 and preceding 14. Strikingly folkloric aspects of the number 13 have been noted in various cultures around the world: one theory is that this is due to the cultures employing lunar-solar calendars (there are approximately 12.41 lunations per solar year, and hence 12 "true months" plus a smaller, and often portentous, thirteenth month). This can be witnessed, for example, in the "Twelve Days of Christmas" of Western European tradition. The number 13 is the sixth prime number. It is a twin prime with 11, as well as a cousin prime with 17. It is the second Wilson prime, of three known (the others being 5 and 563), and the smallest emirp in decimal. 13 is: The second star number: The third centered square number: A happy number and a lucky number. A Fibonacci number, preceded by 5 and 8. The smallest number whose fourth power can be written as a sum of two consecutive square numbers (1192 + 1202). The sum and the difference of 2 consecutive squares: 13 = (22 + 32) = (72 - 62). Also, There are 13 ways for the three fastest horses in a horse race to finish, allowing for ties, a fact that can be expressed mathematically by 13 being the third ordered Bell number. Since 52 + 122 = 132, (5, 12, 13) forms a Pythagorean triple, and as such represent the sides of a right triangle. A 13-sided regular polygon is called a tridecagon. There are 13 hexagonal isohedral tilings. There are 13 distinct cubic distance-regular graphs, of which the Platonic Tetrahedral graph and Dodecahedral graph are part. There are 13 Archimedean solids without counting enantiomorphic forms. Some also include the Elongated square gyrobicupola as another Archimedean solid. There are 13 architectonic honeycombs: 8 originate from the cubic group and 5 originate from the alternated cubic group and cyclic group. The 13 dual honeycombs to these are the 13 catoptric honeycombs, which are made of 13 types of stereohedra. A standard torus can be sliced into 13 pieces with just 3 plane cuts.