Irish dance (typically the top half of dancers graded after the first two rounds) of dancers are invited back to perform. The Céilí dances used in competitions are more precise versions of those danced in less formal settings. There is a list of 30 Céilí dances which have been standardised and published in An Coimisiún's "Ar Rinncidhe Foirne" as examples of typical Irish folk dances; these are called the "book" dances by competitive stepdancers. Most Irish dancing competitions only ask for a short piece of any given dance, in the interests of time. There are two types of shoes; soft shoes (also
Magic square magic squares, were invented and named by Lee Sallows in 2001. In the example shown the shapes appearing are two dimensional. It was Sallows' discovery that "all" magic squares are geometric, the numbers that appear in numerical magic squares can be interpreted as a shorthand notation which indicates the lengths of straight line segments that are the geometric 'shapes' occurring in the square. That is, numerical magic squares are that special case of a geometric magic square using one dimensional shapes. In 2017, following initial ideas of William Walkington and Inder Taneja, the first linear area magic square (L-AMS) was