Glossary

Contents

A

affix: Let z = a + ib in its geometric representation. Affix is the point in the complex plane corresponding to this number, i.e., the point with Cartesian coordinates (a,b), or by a vector with the origin (0,0). The affix is sometimes identified with the complex number itself.

Argand (or Gauss) plane: The complex plane is sometimes called the Argand plane because it is used in Argand diagrams. These are named after Jean-Robert Argand (1768–1822), who was an amateur mathematician and a keeper of a bookstore in Paris, although they were first described by Danish land surveyor and mathematician Caspar Wessel (1745–1818). The complex plane is basically a modified Cartesian plane where the x-axis and the y-axis have been dubbed the “real axis” and the “imaginary axis,” respectively.

biquadratic: A biquadratic polynomial is a type of quartic polynomial which only has terms of powers 4, 2, and 0. It is therefore of the form:

ax⁴ + bx² + d

The fourth root is called biquadratic as we use the word quadratic for the power of “2”.

Blackboard bold: Blackboard bold is a typeface style that is often used for certain symbols in mathematical texts, in which certain lines of the symbol (usually vertical or near-vertical lines) are doubled. The symbols usually denote number sets. One way of producing blackboard bold is to double-strike a character with a small offset on a typewriter. Thus, they are also referred to as double struck.

Blackboard bold

coffin problems: “Coffin problems” are extremely difficult math problems which, nevertheless, have elementary solutions. They were devised for and used by admission committees at Soviet universities in the 70’s and 80’s to keep Jewish candidates (and other “undesirables”) out of the most prestigious universities, such as Moscow State. Only undesirable candidates were asked these questions in the oral entrance exams.

Cossic art, the: The English called the study [of algebra with symbols] “the Cossic Art” which means “the Art of Things”. Algebraists were called cossists, and algebra the cossic art, for many years. Three stages of Algebra: 1. Rhetorical Stage, 2. Syncopated Stage, and 3. Symbolic Stage

Double factorial: Double factorial of a non-negative integer n, is the product of all the integers from 1 to n that have the same parity (odd or even) as n. It is also called as semifactorial of a number and is denoted by !!. For example, double factorial of 9 is 9*7*5*3*1 which is 945, and the double factorial of 6 is 6*4*2 which is 48. Note that a consequence of this definition is 0!! = 1.

porism: A porism is a mathematical proposition or corollary. It has been used to refer to a direct consequence of a proof, analogous to how a corollary refers to a direct consequence of a theorem. In modern usage, it is a relationship that holds for an infinite range of values but only if a certain condition is assumed, such as Steiner’s porism. The term originates from three books of Euclid that have been lost. A proposition may not have been proven, so a porism may not be a theorem or true.

quartic: A quartic polynomial is a polynomial with a degree of 4. It is of the form:

ax⁴ + bx³ + cx² + dx + e

where a ≠ 0

semi-straight line (ray): A semi-straight line is a line which has a boundary or a defined point on one side and is infinite on the other side. The below semi-straight line is expressed as follows [X Y).

surds: The Latin meaning of the word “Surd” is deaf or mute. In earlier days, Arabian mathematicians called rational numbers and irrational numbers as audible and inaudible. Since surds form are made of irrational numbers, they were referred to as asamm (deaf, dumb) in Arabic language, and were later translated in Latin as surds.

Surds are expressions that contain a square root, cube root or other roots. They are roots of numbers that produce an irrational number as a result, with infinite decimals. Therefore, they are left in their root form to represent them more exactly. For example, √2, √3, √5, √6, √7.

A “surd” is an irrational number such as √3 but they are not just restricted to square roots.

If we use indices instead of the root signs, it becomes clearer to answer your question.

FUN FACT: When I first used to teach surds to students, they would never have heard of irrational numbers before and the idea of “never ending” decimal numbers sounds to be quite ridiculous or absurd and I used to say that this is probably where the word SURD came from! (rightly or wrongly but it is a fun idea!)

Lloyd, Philip. “How Do We Find The Square Root Of A Surd?”. 2023. Quora. https://qr.ae/pymaYj.

surreal number: The surreal numbers are a generalization of the reals. Each surreal number consists of two parts (called the left and right), each of which is a set of surreal numbers. For any surreal number N, these parts can be called N_L and N_R. (This could be viewed as an ordered pair of sets, however the surreal numbers were intended to be a basis for mathematics, not something to be embedded in set theory.) A surreal number is written N = { N_L | N_R }. Not every number of this form is a surreal number. The surreal numbers satisfy two additional properties. First, if x ∈ N_R and y ∈ N_L then x &nle; y. Secondly, they must be well founded.

vinculum: A vinculum (from Latin vinculum ‘fetter, chain, tie’) is a horizontal line used in mathematical notation for various purposes. It may be placed as an overline (or underline) over (or under) a mathematical expression to indicate that the expression is to be considered grouped together. Historically, vincula were extensively used to group items together, especially in written mathematics, but in modern mathematics this function has almost entirely been replaced by the use of parentheses. It was also used to mark Roman numerals whose values are multiplied by 1,000. Today, however, the common usage of a vinculum to indicate the repetend of a repeating decimal is a significant exception and reflects the original usage.

ZFC, or Zermelo-Fraenkel set theory: Zermelo–Fraenkel set theory (abbreviated ZF) is a system of axioms used to describe set theory. When the axiom of choice is added to ZF, the system is called ZFC. It is the system of axioms used in set theory by most mathematicians today. After Russell’s paradox was found in the 1901, mathematicians wanted to find a way to describe set theory that did not have contradictions. Ernst Zermelo proposed a theory of set theory in 1908. In 1922, Abraham Fraenkel proposed a new version based on Zermelo’s work.

The featured image on this page is from the BKA Content website.