In recreational mathematics, a magic square of order n is an arrangement of n² numbers, usually distinct integers, in a square, such that the n numbers in all rows, all columns, and both diagonals sum to the same constant. A normal magic square contains the integers from 1 to n². The term "magic square" is also sometimes used to refer to any of various types of word square.

Normal magic squares exist for all orders n ≥ 1 except n = 2, although the case n = 1 is trivial, consisting of a single cell containing the number 1. The smallest nontrivial case, shown below, is of order 3.

The constant sum in every row, column and diagonal is called the magic constant or magic sum, M. The magic constant of a normal magic square depends only on n and has the value

For normal magic squares of order n = 3, 4, 5, ..., the magic constants are:

Magic squares were known to Chinese mathematicians, as early as 650 BCE and Arab mathematicians, possibly as early as the 7th century, when the Arabs conquered northwestern parts of the Indian subcontinent and learned Indian mathematics and astronomy, including other aspects of combinatorial mathematics.^{[citation needed]} The first magic squares of order 5 and 6 appear in an encyclopedia from Baghdad circa 983 CE, the Encyclopedia of the Brethren of Purity (Rasa'il Ihkwan al-Safa); simpler magic squares were known to several earlier Arab mathematicians. Some of these squares were later used in conjunction with magic letters as in (Shams Al-ma'arif) to assist Arab illusionists and magicians.

Srīnivāsa Rāmānujan FRS  pronunciation (help·info) (Tamil: ஸ்ரீநிவாச ராமானுஜன்) (22 December 1887 – 26 April 1920) was an Indian mathematician and autodidact who, with almost no formal training in pure mathematics, made extraordinary contributions to mathematical analysis, number theory, infinite series and continued fractions. Ramanujan was said to be a natural genius by the English mathematician G.H. Hardy, in the same league as mathematicians like Euler and Gauss.

Born in a poor Brahmin family, Ramanujan's introduction to formal mathematics began at age 10. He demonstrated a natural ability, and was given books on advanced trigonometry written by S. L. Loney that he mastered them by age 12, and even discovered theorems of his own, including independently re-discovering Euler's identity. He demonstrated unusual mathematical skills at school, winning accolades and awards. By 17, Ramanujan conducted his own mathematical research on Bernoulli numbers and the Euler–Mascheroni constant. Ramanujan received a scholarship to study at Government College in Kumbakonam, but lost it when he failed his non-mathematical coursework. He joined another college to pursue independent mathematical research, working as a clerk in the Accountant-General's office at the Madras Port Trust Office to support himself. In 1912–1913, he sent samples of his theorems to three academics at the University of Cambridge. G. H. Hardy, recognizing the brilliance of his work, invited Ramanujan to visit and work with him at Cambridge. He became a Fellow of the Royal Society and a Fellow of Trinity College, Cambridge, dying of illness, malnutrition and possibly liver infection in 1920 at the age of 32.

Penn & Teller (Penn Jillette and Teller) are American illusionists and entertainers who have performed together since the late 1970s, and are known for their numerous stage and television shows. Their current Las Vegas show is an amalgam of illusion and comedy. Penn Jillette is a raconteur; Teller generally does not speak while performing, although his voice can occasionally be heard during their performance. They specialize in gory tricks, exposing frauds, and performing clever pranks. More recently they have become associated with atheism, scientific skepticism, and libertarianism, particularly through their television show Penn & Teller: Bullshit!.

Penn Jillette and Teller were introduced to one another by Weir Chrisimer, and they performed their first show together at the Minnesota Renaissance Festival on 19 August 1975. From the late 1970s through 1981, Penn, Teller, and Chrisimer performed as a trio called "The Asparagus Valley Cultural Society" which played in San Francisco at the Phoenix Theater. This act was sillier and less "edgy" than today's Penn & Teller act.^{[citation needed]} Chrisimer helped to develop some bits that continued, most notably Teller's "Shadows" trick, which involves a single red rose.