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Show a stochastic process is a martingale using Ito's lemma
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Prove that the square root of 3 is irrational
Almost sure identity $F^{-1}(F(X))=X$ where $F$ is the CDF of $X$
Hyperbolic geometry and the Triangle Inequality

I am a postgraduate student of mathematics from Slovenia (central Europe) with quite some experience in mathematics. While answering questions on this site, I often encounter the function $\sec(x)$ which is, as I understand, defined as $\sec(x) = \frac1{\cos x}$. During my studies, I never encountered this function.

I am wondering two things:

- How widespread is the notation $\sec x$? As I see it, it is completely standard notation in US schools, but not as common in Europe. Is there a historic reason behind this dichotomy?
- Is there a reason for calling the function $\sec$? Is there some geometric interpretation behind the name?

- Errors of Euler interpretation?
- Tips on writing a History of Mathematics Essay
- Who first discovered that some R.E. sets are not recursive?
- Why are the Trig functions defined by the counterclockwise path of a circle?
- What is the smallest unknown natural number?
- history of the contraction mapping technique

- Elementary geometry from a higher perspective
- How did Hermite calculate $e^{\pi\sqrt{163}}$ in 1859?
- history of the contraction mapping technique
- Blow up of a solution
- What are some examples of mathematics that had unintended useful applications much later?
- What is more elementary than: Introduction to Stochastic Processes by Lawler
- Research Experience for Undergraduates: Summer Programs (that accept non-American applicants)
- Surprising identities / equations
- Learning differential calculus through infinitesimals
- Did Leonardo of Pisa prove $n=4$ case of FLT?

First of all, the use of $\sec$ is standard in the United Kingdom which is part of Europe. The fact might be that $\sec$ is used in English-speaking countries, of which Slovenia is not.

The word Secant comes from a Latin word meaning “to cut”. This picture shows the definition of sine, tangent and secant. It justifies the naming of both the tangent and secant functions. This picture shows the co-functions, e.g. co-sine, co-tangent and co-secant.

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