Cryptic crossword

Cryptic crossword from Contours magazine 2014-15 Edition

 1 2 Maths 3 Cryptic No 1 4

Across

1. Rings from void one (6)

2. Round decrepit relic found at the end of a field (6)

3. Maclaurin has such views about the Royal Institution (6)

Down

1. Function for confused car companies (6)

2. Principles: they're not necessarily right! (6)

Solutions

Across

1. Rings from void one (6)   ANNULI

Quite simply, annuli are rings - they are the space you find between two concentric circles:

(the rest of the clue works because void=ANNUL and one=I in Roman numerals).

2. Round decrepit relic found at the end of a field (6)   CIRCLE

As you probably know, a circle is round! The rest of the clue works because CIRCLE is C followed by an anagram of “relic” - and in maths, $$\mathbb{C}$$ is the symbol used to represent the set of complex numbers. The complex numbers are an example of a “field”, which is a kind of object studied in abstract algebra, and they include all the imaginary numbers such as the famous $$i=\sqrt{-1}$$.

3. Maclaurin has such views about the Royal Institution (6)   SERIES

Maclaurin series are a special kind of infinite sum; they are named after the mathematician Colin Maclaurin (who was a professor at the University of Edinburgh). The rest of the clue comes from views=SEES surrounding (“about”) RI=Royal Institution.

Down

1. Function for confused car companies (6)   ARCCOS

This is an anagram of CAR COS (= car companies), while “arccos” in maths is an example of a trigonometric function. Here is a graph of the function:

2. Principles: they're not necessarily right! (6)   IDEALS

Ideals are objects which are studied in ring theory, a branch of abstract algebra. They come in two types - left and right.