Euler gave us this jewel which is regarded by many as the most beautiful equation in mathematics; it has both elegance and simplicity. It is comprised of five fundamental numbers and the operations of addition, [more…]
A binary operation is said to commute if the order of the operands does not alter the result. In the real numbers, , the following commutative laws hold : for all for all Although these [more…]
Or : Multiplying by . The beginning of complex numbers is often attributed to Cardano (1501 – 1576). Complex numbers provide a solution to the equation . They are an extension of the number system [more…]
One sometimes gets very interesting results when one turns divergent sums upside down. The Basel problem was asked by Pietro Mengoli in . He asked what is the exact summation of the reciprocals of the [more…]
Painted in about 1470/75, it is in the National Gallery. One of my favourite carols: Merry Christmas! OldTrout 2018
Ingredients : 8oz (225g) unsalted, shelled pistachio nuts 1 pint (570ml) double cream 1 pint (570ml) single cream 4oz (110g) golden caster sugar 8 large egg yolks 1 1/2 tablespoons of custard powder Method [more…]
The Möbius function is denoted by , where is the Greek letter mu. Depending on the factorisation of , the function takes the values . The last says that if is even, then and if [more…]
“Rise above oneself and grasp the world” These are awarded every four years for advancement in the field of mathematics. There is an age limit of 40 on the recipients. It is a recognition of [more…]
Euler’s totient function counts the number of positive integers up to that are relatively prime to , where is considered to be relatively prime to all . These numbers are called the totatives of . [more…]
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