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In Europe it derived from the Greek mathematike. Mathematic was a singular noun until the late 14th Century, when mathematics started to replace it. By the 17th Century it was mathematics across the English speaking world. This was abbreviated to maths in most of the English speaking world but for some strange reason the US chose to go for math in the late 19th Century. The guilty individual has still to be identified!
Paper routes, mail routes, door to door sales, street cleaning, painting the lines on a street, garbage trucks. If you can find a way to only go down each street you need to go down only once and end up at your starting point (Euler Circuit) you will probably save time, money or both.
Caen University
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Consider following figure with n = 4. Clearly, number of vertices (v) = 14, number of edges (e) = 24 and number of faces (f) = 12. According to Euler's formula, v + f = e + 2 i.e. v + f = 14 + 12 = 26 = e + 2. In general we have, v = 2n + nC2 and e = 2n + n2. Hence, using Euler's formula, f = e + 2 - v = 2n + n2 + 2 - 2n + nC2 After simiplication we have,