Euler’s Phi Function from Wells’ Curious and Interesting Numbers

In 1986, David Wells, a mathematician specializing in number theory, wrote a delicious little book, entitled The Penguin Dictionary of Curious and Interesting Numbers. If you enjoy dabbling in math, each numerical entry, although brief, is a gateway into all sorts of realms of an incredibly diverse field. Although it goes without saying that without... Continue Reading →

How Solving Cubic Equations Led to the Discovery of Imaginary Numbers

In math, a complex number has a real and an imaginary component combined in the form of a + bi. a and b are real numbers, which means that they can include whole numbers, repeating decimals, terminating decimals and those that go on forever without patterns-- the transcendental numbers. Examples of transcendental numbers include e,... Continue Reading →

The Sum of Sums

In the previous essay, we saw how 1 + 2 + 3 +... n = n(n+1)/2, which can also be expressed using the sum symbol as But what if we wanted a formula for the sum of sums, specifically , 1 + 3 + 6 + 10 + ... n(n+1)/2, Notice that 1 = 1;... Continue Reading →

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